Identifier
-
Mp00012:
Binary trees
—to Dyck path: up step, left tree, down step, right tree⟶
Dyck paths
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
St000935: Integer partitions ⟶ ℤ
Values
[.,.] => [1,0] => [1] => [1] => 1
[.,[.,.]] => [1,0,1,0] => [1,2] => [1,1] => 1
[[.,.],.] => [1,1,0,0] => [2,1] => [2] => 2
[.,[.,[.,.]]] => [1,0,1,0,1,0] => [1,2,3] => [1,1,1] => 1
[.,[[.,.],.]] => [1,0,1,1,0,0] => [1,3,2] => [2,1] => 2
[[.,.],[.,.]] => [1,1,0,0,1,0] => [2,1,3] => [2,1] => 2
[[.,[.,.]],.] => [1,1,0,1,0,0] => [2,3,1] => [2,1] => 2
[[[.,.],.],.] => [1,1,1,0,0,0] => [3,1,2] => [2,1] => 2
[.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,1,1,1] => 1
[.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => [2,1,1] => 2
[.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,1,1] => 2
[.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,1,1] => 2
[.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => [2,1,1] => 2
[[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,1] => 2
[[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,2] => 3
[[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,1,1] => 2
[[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => [3,1,2,4] => [2,1,1] => 2
[[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,1,1] => 2
[[.,[[.,.],.]],.] => [1,1,0,1,1,0,0,0] => [2,4,1,3] => [2,1,1] => 2
[[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => [2,2] => 3
[[[.,[.,.]],.],.] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => [2,1,1] => 2
[[[[.,.],.],.],.] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => [2,1,1] => 2
[.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,1,1,1,1] => 1
[.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [2,1,1,1] => 2
[.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,1,1,1] => 2
[.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [2,1,1,1] => 2
[.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [2,1,1,1] => 2
[.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,1,1,1] => 2
[.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,2,1] => 3
[.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [2,1,1,1] => 2
[.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [2,1,1,1] => 2
[.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,1,1,1] => 2
[.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [2,1,1,1] => 2
[.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [2,2,1] => 3
[.,[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [2,1,1,1] => 2
[.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [2,1,1,1] => 2
[[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,1,1] => 2
[[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,2,1] => 3
[[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,2,1] => 3
[[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,2,1] => 3
[[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [2,2,1] => 3
[[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,1,1,1] => 2
[[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,2,1] => 3
[[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [2,1,1,1] => 2
[[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [2,2,1] => 3
[[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,1,1,1] => 2
[[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [2,1,1,1] => 2
[[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [2,2,1] => 3
[[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [2,1,1,1] => 2
[[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [2,1,1,1] => 2
[[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,1,1,1] => 2
[[.,[.,[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [2,1,1,1] => 2
[[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [2,2,1] => 3
[[.,[[.,[.,.]],.]],.] => [1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [2,1,1,1] => 2
[[.,[[[.,.],.],.]],.] => [1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [2,1,1,1] => 2
[[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [2,2,1] => 3
[[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [2,2,1] => 3
[[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [2,2,1] => 3
[[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [2,2,1] => 3
[[[.,[.,[.,.]]],.],.] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [2,1,1,1] => 2
[[[.,[[.,.],.]],.],.] => [1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [2,1,1,1] => 2
[[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [2,2,1] => 3
[[[[.,[.,.]],.],.],.] => [1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [2,1,1,1] => 2
[[[[[.,.],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [2,1,1,1] => 2
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [2,1,1,1,1] => 2
[.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,1,1,1,1] => 2
[.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [2,1,1,1,1] => 2
[.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [2,1,1,1,1] => 2
[.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,1,1,1,1] => 2
[.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [2,2,1,1] => 3
[.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [2,1,1,1,1] => 2
[.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [2,1,1,1,1] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [2,1,1,1,1] => 2
[.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [2,1,1,1,1] => 2
[.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [2,2,1,1] => 3
[.,[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [2,1,1,1,1] => 2
[.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [2,1,1,1,1] => 2
[.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,1,1,1,1] => 2
[.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,2,1,1] => 3
[.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,2,1,1] => 3
[.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [2,2,1,1] => 3
[.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [2,2,1,1] => 3
[.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [2,1,1,1,1] => 2
[.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [2,2,1,1] => 3
[.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [2,1,1,1,1] => 2
[.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [2,2,1,1] => 3
[.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [2,1,1,1,1] => 2
[.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [2,1,1,1,1] => 2
[.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [2,2,1,1] => 3
[.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [2,1,1,1,1] => 2
[.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [2,1,1,1,1] => 2
[.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,1,1,1,1] => 2
[.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [2,1,1,1,1] => 2
[.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [2,2,1,1] => 3
[.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [2,1,1,1,1] => 2
[.,[[.,[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [2,1,1,1,1] => 2
[.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [2,2,1,1] => 3
[.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [2,2,1,1] => 3
[.,[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [2,2,1,1] => 3
[.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [2,2,1,1] => 3
>>> Load all 1985 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [2,1,1,1,1] => 2
[.,[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [2,1,1,1,1] => 2
[.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [2,2,1,1] => 3
[.,[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [2,1,1,1,1] => 2
[.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [2,1,1,1,1] => 2
[[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,1,1,1] => 2
[[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,2,1,1] => 3
[[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,2,1,1] => 3
[[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,2,1,1] => 3
[[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [2,2,1,1] => 3
[[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,2,1,1] => 3
[[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,2,2] => 4
[[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,2,1,1] => 3
[[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [2,2,1,1] => 3
[[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,2,1,1] => 3
[[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [2,2,1,1] => 3
[[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [2,2,2] => 4
[[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [2,2,1,1] => 3
[[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [2,2,1,1] => 3
[[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,1,1,1,1] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,2,1,1] => 3
[[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,2,1,1] => 3
[[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,2,1,1] => 3
[[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [2,2,1,1] => 3
[[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [2,1,1,1,1] => 2
[[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [2,2,1,1] => 3
[[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [2,2,1,1] => 3
[[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [2,2,1,1] => 3
[[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [2,2,1,1] => 3
[[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,1,1,1,1] => 2
[[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [2,2,1,1] => 3
[[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [2,1,1,1,1] => 2
[[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [2,2,1,1] => 3
[[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [2,2,1,1] => 3
[[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [2,2,2] => 4
[[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [2,1,1,1,1] => 2
[[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [2,2,1,1] => 3
[[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [2,1,1,1,1] => 2
[[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [2,2,1,1] => 3
[[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,1,1,1,1] => 2
[[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [2,1,1,1,1] => 2
[[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [2,2,1,1] => 3
[[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [2,1,1,1,1] => 2
[[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [2,1,1,1,1] => 2
[[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [2,2,1,1] => 3
[[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [2,2,1,1] => 3
[[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [2,2,1,1] => 3
[[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [2,2,1,1] => 3
[[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [2,1,1,1,1] => 2
[[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [2,1,1,1,1] => 2
[[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [2,2,1,1] => 3
[[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [2,1,1,1,1] => 2
[[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [2,1,1,1,1] => 2
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,1,1,1,1] => 2
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [2,1,1,1,1] => 2
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [2,2,1,1] => 3
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [2,1,1,1,1] => 2
[[.,[.,[[[.,.],.],.]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [2,1,1,1,1] => 2
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [2,2,1,1] => 3
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [2,2,1,1] => 3
[[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [2,2,1,1] => 3
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [2,2,1,1] => 3
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [2,1,1,1,1] => 2
[[.,[[.,[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [2,1,1,1,1] => 2
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [2,2,1,1] => 3
[[.,[[[.,[.,.]],.],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [2,1,1,1,1] => 2
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [2,1,1,1,1] => 2
[[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [2,2,1,1] => 3
[[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [2,2,1,1] => 3
[[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [2,2,2] => 4
[[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [2,2,1,1] => 3
[[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [2,2,1,1] => 3
[[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [2,2,1,1] => 3
[[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [2,2,1,1] => 3
[[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [2,2,1,1] => 3
[[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [2,2,1,1] => 3
[[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [2,2,1,1] => 3
[[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [2,2,1,1] => 3
[[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [2,2,2] => 4
[[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [2,2,1,1] => 3
[[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [2,2,1,1] => 3
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [2,1,1,1,1] => 2
[[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [2,1,1,1,1] => 2
[[[.,[[.,.],[.,.]]],.],.] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [2,2,1,1] => 3
[[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [2,1,1,1,1] => 2
[[[.,[[[.,.],.],.]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [2,1,1,1,1] => 2
[[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [2,2,1,1] => 3
[[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [2,2,1,1] => 3
[[[[.,[.,.]],[.,.]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [2,2,1,1] => 3
[[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [2,2,1,1] => 3
[[[[.,[.,[.,.]]],.],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [2,1,1,1,1] => 2
[[[[.,[[.,.],.]],.],.],.] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [2,1,1,1,1] => 2
[[[[[.,.],[.,.]],.],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [2,2,1,1] => 3
[[[[[.,[.,.]],.],.],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [2,1,1,1,1] => 2
[[[[[[.,.],.],.],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [2,1,1,1,1] => 2
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 1
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 2
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 2
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => 2
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 2
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 2
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [2,2,1,1,1] => 3
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [2,1,1,1,1,1] => 2
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [2,1,1,1,1,1] => 2
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [2,1,1,1,1,1] => 2
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [2,1,1,1,1,1] => 2
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [2,2,1,1,1] => 3
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [2,1,1,1,1,1] => 2
[.,[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 2
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 2
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [2,2,1,1,1] => 3
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [2,2,1,1,1] => 3
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [2,2,1,1,1] => 3
[.,[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [2,2,1,1,1] => 3
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [2,1,1,1,1,1] => 2
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [2,2,1,1,1] => 3
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [2,1,1,1,1,1] => 2
[.,[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [2,2,1,1,1] => 3
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [2,1,1,1,1,1] => 2
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [2,1,1,1,1,1] => 2
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [2,2,1,1,1] => 3
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [2,1,1,1,1,1] => 2
[.,[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [2,1,1,1,1,1] => 2
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [2,1,1,1,1,1] => 2
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [2,1,1,1,1,1] => 2
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [2,2,1,1,1] => 3
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [2,1,1,1,1,1] => 2
[.,[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [2,1,1,1,1,1] => 2
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [2,2,1,1,1] => 3
[.,[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => [2,2,1,1,1] => 3
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [2,2,1,1,1] => 3
[.,[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [2,2,1,1,1] => 3
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [2,1,1,1,1,1] => 2
[.,[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [2,1,1,1,1,1] => 2
[.,[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [2,2,1,1,1] => 3
[.,[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => [2,1,1,1,1,1] => 2
[.,[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 2
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 2
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [2,2,1,1,1] => 3
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [2,2,1,1,1] => 3
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [2,2,1,1,1] => 3
[.,[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [2,2,1,1,1] => 3
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [2,2,1,1,1] => 3
[.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [2,2,2,1] => 4
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [2,2,1,1,1] => 3
[.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [2,2,1,1,1] => 3
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [2,2,1,1,1] => 3
[.,[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => [2,2,1,1,1] => 3
[.,[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => [2,2,2,1] => 4
[.,[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [2,2,1,1,1] => 3
[.,[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [2,2,1,1,1] => 3
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [2,1,1,1,1,1] => 2
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [2,2,1,1,1] => 3
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [2,2,1,1,1] => 3
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [2,2,1,1,1] => 3
[.,[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [2,2,1,1,1] => 3
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [2,1,1,1,1,1] => 2
[.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [2,2,1,1,1] => 3
[.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [2,2,1,1,1] => 3
[.,[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [2,2,1,1,1] => 3
[.,[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [2,2,1,1,1] => 3
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [2,1,1,1,1,1] => 2
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [2,2,1,1,1] => 3
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [2,1,1,1,1,1] => 2
[.,[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => [2,2,1,1,1] => 3
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [2,2,1,1,1] => 3
[.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => [2,2,2,1] => 4
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [2,1,1,1,1,1] => 2
[.,[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [2,2,1,1,1] => 3
[.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [2,1,1,1,1,1] => 2
[.,[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [2,2,1,1,1] => 3
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [2,1,1,1,1,1] => 2
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => [2,1,1,1,1,1] => 2
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [2,2,1,1,1] => 3
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => [2,1,1,1,1,1] => 2
[.,[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [2,1,1,1,1,1] => 2
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [2,2,1,1,1] => 3
[.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => [2,2,1,1,1] => 3
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [2,2,1,1,1] => 3
[.,[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [2,2,1,1,1] => 3
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [2,1,1,1,1,1] => 2
[.,[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => [2,1,1,1,1,1] => 2
[.,[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => [2,2,1,1,1] => 3
[.,[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => [2,1,1,1,1,1] => 2
[.,[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [2,1,1,1,1,1] => 2
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [2,1,1,1,1,1] => 2
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => [2,1,1,1,1,1] => 2
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => [2,2,1,1,1] => 3
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => [2,1,1,1,1,1] => 2
[.,[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [2,1,1,1,1,1] => 2
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [2,2,1,1,1] => 3
[.,[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => [2,2,1,1,1] => 3
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => [2,2,1,1,1] => 3
[.,[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => [2,2,1,1,1] => 3
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => [2,1,1,1,1,1] => 2
[.,[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [2,1,1,1,1,1] => 2
[.,[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [2,2,1,1,1] => 3
[.,[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [2,1,1,1,1,1] => 2
[.,[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [2,1,1,1,1,1] => 2
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [2,2,1,1,1] => 3
[.,[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => [2,2,1,1,1] => 3
[.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => [2,2,2,1] => 4
[.,[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [2,2,1,1,1] => 3
[.,[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => [2,2,1,1,1] => 3
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => [2,2,1,1,1] => 3
[.,[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [2,2,1,1,1] => 3
[.,[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [2,2,1,1,1] => 3
[.,[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => [2,2,1,1,1] => 3
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => [2,2,1,1,1] => 3
[.,[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [2,2,1,1,1] => 3
[.,[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => [2,2,2,1] => 4
[.,[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [2,2,1,1,1] => 3
[.,[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [2,2,1,1,1] => 3
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [2,1,1,1,1,1] => 2
[.,[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [2,1,1,1,1,1] => 2
[.,[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => [2,2,1,1,1] => 3
[.,[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => [2,1,1,1,1,1] => 2
[.,[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => [2,1,1,1,1,1] => 2
[.,[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [2,2,1,1,1] => 3
[.,[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => [2,2,1,1,1] => 3
[.,[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => [2,2,1,1,1] => 3
[.,[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => [2,2,1,1,1] => 3
[.,[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => [2,1,1,1,1,1] => 2
[.,[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => [2,1,1,1,1,1] => 2
[.,[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => [2,2,1,1,1] => 3
[.,[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => [2,1,1,1,1,1] => 2
[.,[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 2
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => 2
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,2,1,1,1] => 3
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,2,1,1,1] => 3
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,2,1,1,1] => 3
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => [2,2,1,1,1] => 3
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,2,1,1,1] => 3
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,2,2,1] => 4
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,2,1,1,1] => 3
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => [2,2,1,1,1] => 3
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,2,1,1,1] => 3
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6] => [2,2,1,1,1] => 3
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,4,7,5] => [2,2,2,1] => 4
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => [2,2,1,1,1] => 3
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [2,2,1,1,1] => 3
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,2,1,1,1] => 3
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,2,2,1] => 4
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,2,2,1] => 4
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,2,2,1] => 4
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => [2,2,2,1] => 4
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,2,1,1,1] => 3
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,2,2,1] => 4
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [2,2,1,1,1] => 3
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => [2,2,2,1] => 4
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,2,1,1,1] => 3
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,7] => [2,2,1,1,1] => 3
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4,7] => [2,2,2,1] => 4
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [2,2,1,1,1] => 3
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => [2,2,1,1,1] => 3
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,2,1,1,1] => 3
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => [2,2,1,1,1] => 3
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => [2,2,2,1] => 4
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => [2,2,1,1,1] => 3
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => [2,2,1,1,1] => 3
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [2,2,2,1] => 4
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6] => [2,2,2,1] => 4
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => [2,2,2,1] => 4
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,3,4,7,5] => [2,2,2,1] => 4
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [2,2,1,1,1] => 3
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6] => [2,2,1,1,1] => 3
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,7,4,5] => [2,2,2,1] => 4
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => [2,2,1,1,1] => 3
[[.,.],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => [2,2,1,1,1] => 3
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,1,1,1,1,1] => 2
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [2,2,1,1,1] => 3
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [2,2,1,1,1] => 3
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [2,2,1,1,1] => 3
[[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [2,2,1,1,1] => 3
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [2,2,1,1,1] => 3
[[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [2,2,2,1] => 4
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [2,2,1,1,1] => 3
[[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [2,2,1,1,1] => 3
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [2,2,1,1,1] => 3
[[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [2,2,1,1,1] => 3
[[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [2,2,2,1] => 4
[[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [2,2,1,1,1] => 3
[[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [2,2,1,1,1] => 3
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [2,1,1,1,1,1] => 2
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => [2,2,1,1,1] => 3
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => [2,2,1,1,1] => 3
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => [2,2,1,1,1] => 3
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => [2,2,1,1,1] => 3
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => [2,2,1,1,1] => 3
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => [2,2,2,1] => 4
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => [2,2,1,1,1] => 3
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => [2,2,1,1,1] => 3
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => [2,2,1,1,1] => 3
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6] => [2,2,1,1,1] => 3
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,6,4,7,5] => [2,2,2,1] => 4
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [2,2,1,1,1] => 3
[[[.,.],.],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => [2,2,1,1,1] => 3
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,1,1,1,1,1] => 2
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [2,2,1,1,1] => 3
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [2,2,1,1,1] => 3
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [2,2,1,1,1] => 3
[[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [2,2,1,1,1] => 3
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => [2,1,1,1,1,1] => 2
[[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => [2,2,1,1,1] => 3
[[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,7] => [2,2,1,1,1] => 3
[[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => [2,2,1,1,1] => 3
[[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,7,5,6] => [2,2,1,1,1] => 3
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => [2,2,1,1,1] => 3
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => [2,2,2,1] => 4
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,7] => [2,2,2,1] => 4
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => [2,2,2,1] => 4
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,7,5,6] => [2,2,2,1] => 4
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => [2,1,1,1,1,1] => 2
[[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => [2,2,1,1,1] => 3
[[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => [2,2,1,1,1] => 3
[[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [2,2,1,1,1] => 3
[[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [2,2,1,1,1] => 3
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => [2,1,1,1,1,1] => 2
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => [2,2,1,1,1] => 3
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => [2,2,1,1,1] => 3
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => [2,2,1,1,1] => 3
[[[[.,.],.],.],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => [2,2,1,1,1] => 3
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,1,1,1,1,1] => 2
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [2,2,1,1,1] => 3
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => [2,1,1,1,1,1] => 2
[[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => [2,2,1,1,1] => 3
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => [2,2,1,1,1] => 3
[[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => [2,2,2,1] => 4
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => [2,1,1,1,1,1] => 2
[[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => [2,2,1,1,1] => 3
[[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => [2,1,1,1,1,1] => 2
[[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [2,2,1,1,1] => 3
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => [2,2,1,1,1] => 3
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [2,2,2,1] => 4
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [2,2,1,1,1] => 3
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => [2,2,2,1] => 4
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => [2,2,1,1,1] => 3
[[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => [2,2,2,1] => 4
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => [2,2,1,1,1] => 3
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => [2,2,2,1] => 4
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => [2,1,1,1,1,1] => 2
[[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [2,2,1,1,1] => 3
[[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,6,7] => [2,1,1,1,1,1] => 2
[[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [2,2,1,1,1] => 3
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [2,2,1,1,1] => 3
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6] => [2,2,2,1] => 4
[[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => [2,1,1,1,1,1] => 2
[[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [2,2,1,1,1] => 3
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => [2,1,1,1,1,1] => 2
[[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => [2,2,1,1,1] => 3
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,1,1,1,1,1] => 2
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => [2,1,1,1,1,1] => 2
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => [2,2,1,1,1] => 3
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => [2,1,1,1,1,1] => 2
[[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => [2,1,1,1,1,1] => 2
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [2,2,1,1,1] => 3
[[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => [2,2,1,1,1] => 3
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => [2,2,1,1,1] => 3
[[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => [2,2,1,1,1] => 3
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => [2,1,1,1,1,1] => 2
[[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,7] => [2,1,1,1,1,1] => 2
[[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [2,2,1,1,1] => 3
[[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [2,1,1,1,1,1] => 2
[[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [2,1,1,1,1,1] => 2
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [2,2,1,1,1] => 3
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => [2,2,1,1,1] => 3
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => [2,2,2,1] => 4
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => [2,2,1,1,1] => 3
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => [2,2,1,1,1] => 3
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [2,2,1,1,1] => 3
[[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => [2,2,1,1,1] => 3
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => [2,2,1,1,1] => 3
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => [2,2,1,1,1] => 3
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [2,2,1,1,1] => 3
[[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => [2,2,1,1,1] => 3
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3,7] => [2,2,2,1] => 4
[[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => [2,2,1,1,1] => 3
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => [2,2,1,1,1] => 3
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [2,1,1,1,1,1] => 2
[[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => [2,1,1,1,1,1] => 2
[[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => [2,2,1,1,1] => 3
[[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => [2,1,1,1,1,1] => 2
[[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => [2,1,1,1,1,1] => 2
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [2,2,1,1,1] => 3
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => [2,2,1,1,1] => 3
[[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => [2,2,1,1,1] => 3
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => [2,2,1,1,1] => 3
[[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => [2,1,1,1,1,1] => 2
[[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => [2,1,1,1,1,1] => 2
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => [2,2,1,1,1] => 3
[[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => [2,1,1,1,1,1] => 2
[[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [2,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,1,1,1,1,1] => 2
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => [2,1,1,1,1,1] => 2
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [2,2,1,1,1] => 3
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => [2,1,1,1,1,1] => 2
[[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [2,1,1,1,1,1] => 2
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [2,2,1,1,1] => 3
[[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => [2,2,1,1,1] => 3
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [2,2,1,1,1] => 3
[[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => [2,2,1,1,1] => 3
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => [2,1,1,1,1,1] => 2
[[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [2,1,1,1,1,1] => 2
[[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [2,2,1,1,1] => 3
[[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => [2,1,1,1,1,1] => 2
[[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6] => [2,1,1,1,1,1] => 2
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [2,2,1,1,1] => 3
[[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => [2,2,1,1,1] => 3
[[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => [2,2,2,1] => 4
[[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => [2,2,1,1,1] => 3
[[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,3,5,6] => [2,2,1,1,1] => 3
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [2,2,1,1,1] => 3
[[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => [2,2,1,1,1] => 3
[[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => [2,2,1,1,1] => 3
[[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6] => [2,2,1,1,1] => 3
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [2,2,1,1,1] => 3
[[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => [2,2,1,1,1] => 3
[[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => [2,2,2,1] => 4
[[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => [2,2,1,1,1] => 3
[[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,7,5] => [2,2,1,1,1] => 3
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,1,3] => [2,1,1,1,1,1] => 2
[[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [2,1,1,1,1,1] => 2
[[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [2,2,1,1,1] => 3
[[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => [2,1,1,1,1,1] => 2
[[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => [2,1,1,1,1,1] => 2
[[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => [2,2,1,1,1] => 3
[[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6] => [2,2,1,1,1] => 3
[[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [2,2,1,1,1] => 3
[[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => [2,2,1,1,1] => 3
[[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [2,1,1,1,1,1] => 2
[[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => [2,1,1,1,1,1] => 2
[[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => [2,2,1,1,1] => 3
[[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,1,3,4,5] => [2,1,1,1,1,1] => 2
[[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => [2,1,1,1,1,1] => 2
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [2,2,1,1,1] => 3
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => [2,2,1,1,1] => 3
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => [2,2,2,1] => 4
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [2,2,1,1,1] => 3
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,4,7,2,5,6] => [2,2,1,1,1] => 3
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => [2,2,2,1] => 4
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6] => [2,2,2,1] => 4
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => [2,2,2,1] => 4
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,2,4,7,5] => [2,2,2,1] => 4
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => [2,2,1,1,1] => 3
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6] => [2,2,1,1,1] => 3
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => [2,2,2,1] => 4
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,6,7,2,4,5] => [2,2,1,1,1] => 3
[[[.,.],[[[[.,.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6] => [2,2,1,1,1] => 3
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [2,2,1,1,1] => 3
[[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => [2,2,1,1,1] => 3
[[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => [2,2,2,1] => 4
[[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => [2,2,1,1,1] => 3
[[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => [2,2,1,1,1] => 3
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,3] => [2,2,1,1,1] => 3
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6] => [2,2,1,1,1] => 3
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,7,5] => [2,2,2,1] => 4
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => [2,2,1,1,1] => 3
[[[[.,.],.],[[[.,.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,7,3,5,6] => [2,2,1,1,1] => 3
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [2,2,1,1,1] => 3
[[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => [2,2,1,1,1] => 3
[[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => [2,2,1,1,1] => 3
[[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6] => [2,2,1,1,1] => 3
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => [2,2,2,1] => 4
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6] => [2,2,2,1] => 4
[[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,1,2,6,7,3] => [2,2,1,1,1] => 3
[[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6] => [2,2,1,1,1] => 3
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => [2,2,1,1,1] => 3
[[[[[.,.],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => [2,2,1,1,1] => 3
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [2,2,1,1,1] => 3
[[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => [2,2,1,1,1] => 3
[[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => [2,2,2,1] => 4
[[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => [2,2,1,1,1] => 3
[[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,7,5] => [2,2,1,1,1] => 3
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => [2,2,2,1] => 4
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,7,5] => [2,2,2,1] => 4
[[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => [2,2,2,1] => 4
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,6,3,7,4] => [2,2,2,1] => 4
[[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,1,2,7,3] => [2,2,1,1,1] => 3
[[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => [2,2,1,1,1] => 3
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => [2,2,2,1] => 4
[[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => [2,2,1,1,1] => 3
[[[[[[.,.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => [2,2,1,1,1] => 3
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [2,1,1,1,1,1] => 2
[[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [2,1,1,1,1,1] => 2
[[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [2,2,1,1,1] => 3
[[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => [2,1,1,1,1,1] => 2
[[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6] => [2,1,1,1,1,1] => 2
[[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [2,2,1,1,1] => 3
[[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6] => [2,2,1,1,1] => 3
[[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [2,2,1,1,1] => 3
[[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => [2,2,1,1,1] => 3
[[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [2,1,1,1,1,1] => 2
[[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6] => [2,1,1,1,1,1] => 2
[[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => [2,2,1,1,1] => 3
[[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,1,2,4,5] => [2,1,1,1,1,1] => 2
[[[.,[[[[.,.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6] => [2,1,1,1,1,1] => 2
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [2,2,1,1,1] => 3
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6] => [2,2,1,1,1] => 3
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,7,3,5] => [2,2,2,1] => 4
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,7,2,3,5] => [2,2,1,1,1] => 3
[[[[.,.],[[[.,.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => [2,2,1,1,1] => 3
[[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => [2,2,1,1,1] => 3
[[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6] => [2,2,1,1,1] => 3
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,6,7,3,4] => [2,2,1,1,1] => 3
[[[[[.,.],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6] => [2,2,1,1,1] => 3
[[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [2,2,1,1,1] => 3
[[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => [2,2,1,1,1] => 3
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,6,2,7,3,4] => [2,2,2,1] => 4
[[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,1,2,7,3,4] => [2,2,1,1,1] => 3
[[[[[[.,.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => [2,2,1,1,1] => 3
[[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => [2,1,1,1,1,1] => 2
[[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,1,2,3,6] => [2,1,1,1,1,1] => 2
[[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,7,2,3,5] => [2,2,1,1,1] => 3
[[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,1,2,3,5] => [2,1,1,1,1,1] => 2
[[[[.,[[[.,.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6] => [2,1,1,1,1,1] => 2
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,6,7,2,3,4] => [2,2,1,1,1] => 3
[[[[[.,.],[[.,.],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6] => [2,2,1,1,1] => 3
[[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,1,7,2,3,4] => [2,2,1,1,1] => 3
[[[[[[.,.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => [2,2,1,1,1] => 3
[[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => [2,1,1,1,1,1] => 2
[[[[[.,[[.,.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6] => [2,1,1,1,1,1] => 2
[[[[[[.,.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1,7,2,3,4,5] => [2,2,1,1,1] => 3
[[[[[[.,[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => [2,1,1,1,1,1] => 2
[[[[[[[.,.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [2,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 1
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [2,2,1,1,1,1] => 3
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,5,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,5,8,6] => [2,2,1,1,1,1] => 3
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,5,6] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,4,5,7,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,4,6,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5,8] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,4,5,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,4,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,4,8,6] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,4,6] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,4,6,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,4,7,8,5] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,4,8,5,7] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,4,8,5] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,4,5,8,6] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,4,5] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,4,5,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,4,8,5,6] => [2,2,1,1,1,1] => 3
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,4,5,6] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [2,2,1,1,1,1] => 3
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [2,2,1,1,1,1] => 3
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [2,2,1,1,1,1] => 3
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => [2,2,1,1,1,1] => 3
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [2,2,1,1,1,1] => 3
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [2,2,2,1,1] => 4
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [2,2,1,1,1,1] => 3
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => [2,2,1,1,1,1] => 3
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [2,2,1,1,1,1] => 3
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,5,7] => [2,2,1,1,1,1] => 3
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [2,2,1,1,1,1] => 3
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => [2,2,1,1,1,1] => 3
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [2,2,1,1,1,1] => 3
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [2,2,1,1,1,1] => 3
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,6,7] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,3,4,6,7,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,3,4,7,8,6] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => [2,2,1,1,1,1] => 3
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [2,2,1,1,1,1] => 3
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,3,5,7,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,3,5,8,7] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,4,7,8] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,8,7] => [2,2,2,1,1] => 4
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,3,4,7,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,3,4,5,7,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => [2,2,1,1,1,1] => 3
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,3,6,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,6,7,3,5,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,3,5,6,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,3,6,7,4,8] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,2,5,3,7,4,6,8] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,3,7,4,8] => [2,2,1,1,1,1] => 3
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,6,3,4,7,5,8] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,3,4,6,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,6,3,7,4,5,8] => [2,2,1,1,1,1] => 3
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,3,4,5,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,3,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,4,5,7,3,8,6] => [2,2,1,1,1,1] => 3
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,3,6] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,3,6,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,4,6,3,7,8,5] => [2,2,1,1,1,1] => 3
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,6,7,3,8,5] => [2,2,1,1,1,1] => 3
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,3,5,8,6] => [2,2,1,1,1,1] => 3
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,3,5] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,3,5,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,3,8,5,6] => [2,2,1,1,1,1] => 3
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,3,5,6] => [2,1,1,1,1,1,1] => 2
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,3,5,6,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,3,6,7,8,4] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,8,6] => [2,2,2,1,1] => 4
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,3,8,4,6,7] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,3,7,8,4] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,5,6,3,8,4,7] => [2,2,1,1,1,1] => 3
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,3,4,7,8,5] => [2,2,1,1,1,1] => 3
[.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,3,4,8,5,7] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,3,8,4] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,3,4,8,6] => [2,2,1,1,1,1] => 3
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,8,5] => [2,2,2,1,1] => 4
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,3,4,5,8,6] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,3,4] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,3,8,4,6] => [2,2,1,1,1,1] => 3
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,3,4,6] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,3,4,6,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [2,2,1,1,1,1] => 3
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,3,8,4,5,7] => [2,2,1,1,1,1] => 3
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,6,7,3,8,4,5] => [2,2,1,1,1,1] => 3
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [2,2,1,1,1,1] => 3
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,3,4,5] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,6,8,3,4,5,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,3,8,4,5,6] => [2,2,1,1,1,1] => 3
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,3,4,5,6] => [2,1,1,1,1,1,1] => 2
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [2,1,1,1,1,1,1] => 2
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [2,2,1,1,1,1] => 3
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [2,2,1,1,1,1] => 3
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [2,2,1,1,1,1] => 3
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => [2,2,1,1,1,1] => 3
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [2,2,1,1,1,1] => 3
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [2,2,2,1,1] => 4
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [2,2,1,1,1,1] => 3
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,5,7] => [2,2,1,1,1,1] => 3
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,5,8,6] => [2,2,2,1,1] => 4
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,7,8,5,6] => [2,2,1,1,1,1] => 3
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [2,2,2,1,1] => 4
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [2,2,2,1,1] => 4
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => [2,2,2,1,1] => 4
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [2,2,2,1,1] => 4
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,4,6,8] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5,8] => [2,2,2,1,1] => 4
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,4,5,8] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,8,6] => [2,2,2,1,1] => 4
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,4,6] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,4,6,7] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,7,8,5] => [2,2,2,1,1] => 4
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,8,5,7] => [2,2,2,1,1] => 4
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,4,8,5] => [2,2,2,1,1] => 4
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,4,5] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,4,5,7] => [2,2,1,1,1,1] => 3
[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,8,5,6] => [2,2,2,1,1] => 4
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => [2,2,1,1,1,1] => 3
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [2,2,1,1,1,1] => 3
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [2,2,1,1,1,1] => 3
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [2,2,1,1,1,1] => 3
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,6,7] => [2,2,1,1,1,1] => 3
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [2,2,2,1,1] => 4
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [2,2,1,1,1,1] => 3
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [2,2,1,1,1,1] => 3
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,8,6] => [2,2,2,1,1] => 4
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,5,6] => [2,2,1,1,1,1] => 3
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,5,6,7] => [2,2,1,1,1,1] => 3
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => [2,2,1,1,1,1] => 3
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => [2,2,1,1,1,1] => 3
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,2,3,5,7,8,6] => [2,2,1,1,1,1] => 3
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => [2,2,1,1,1,1] => 3
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => [2,2,1,1,1,1] => 3
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => [2,2,2,1,1] => 4
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,2,3,6,7,5,8] => [2,2,1,1,1,1] => 3
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => [2,2,1,1,1,1] => 3
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,2,3,6,7,8,5] => [2,2,1,1,1,1] => 3
[.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,2,3,7,5,8,6] => [2,2,2,1,1] => 4
[.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,2,3,7,8,5,6] => [2,2,1,1,1,1] => 3
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => [2,2,1,1,1,1] => 3
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => [2,2,1,1,1,1] => 3
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [2,2,1,1,1,1] => 3
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [2,2,1,1,1,1] => 3
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,6,7] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,2,4,6,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,2,4,6,8,7] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,8] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,2,4,7,8,6] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,2,4,8,6,7] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,3,6,7,8] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,3,6,8,7] => [2,2,2,1,1] => 4
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,8] => [2,2,2,1,1] => 4
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,3,7,8,6] => [2,2,2,1,1] => 4
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,8,6,7] => [2,2,2,1,1] => 4
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,2,3,6,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,2,3,7,6,8] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,2,3,7,8,6] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,2,3,4,7,8,6] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => [2,2,1,1,1,1] => 3
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [2,2,1,1,1,1] => 3
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,2,5,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,2,5,8,7] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,2,6,4,7,8] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,2,4,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,5,6,2,4,8,7] => [2,2,1,1,1,1] => 3
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,2,4,5,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,2,4,5,8,7] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,6,3,5,7,8] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,6,3,5,8,7] => [2,2,2,1,1] => 4
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,2,6,3,7,8] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,8,7] => [2,2,2,1,1] => 4
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,2,3,6,4,7,8] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2,3,6,4,8,7] => [2,2,2,1,1] => 4
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,2,3,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,4,5,6,2,3,8,7] => [2,2,1,1,1,1] => 3
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,2,3,5,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,4,6,2,3,5,8,7] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,6,3,4,7,8] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,6,3,4,8,7] => [2,2,2,1,1] => 4
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,2,3,4,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,2,3,4,8,7] => [2,2,1,1,1,1] => 3
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => [2,1,1,1,1,1,1] => 2
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => [2,2,1,1,1,1] => 3
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,2,6,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,2,7,5,8] => [2,2,1,1,1,1] => 3
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,2,5,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,3,4,7,2,5,6,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,2,6,7,4,8] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,2,7,4,6,8] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,2,7,4,8] => [2,2,1,1,1,1] => 3
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,2,4,7,5,8] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,2,4,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,2,4,6,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,2,7,4,5,8] => [2,2,1,1,1,1] => 3
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,2,4,5,6,8] => [2,1,1,1,1,1,1] => 2
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,2,5,6,7,3,8] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,2,5,7,3,6,8] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5,8] => [2,2,2,1,1] => 4
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,2,6,7,3,5,8] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,7,3,5,6,8] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,7,3,8] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,4,5,2,7,3,6,8] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,2,3,6,7,4,8] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,5,2,3,7,4,6,8] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,2,7,3,8] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4,8] => [2,2,2,1,1] => 4
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,2,3,4,7,5,8] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,2,3,8] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,2,3,6,8] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,2,7,3,5,8] => [2,2,1,1,1,1] => 3
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,2,3,5,8] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,2,3,5,6,8] => [2,1,1,1,1,1,1] => 2
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,2,6,7,3,4,8] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,7,3,4,6,8] => [2,2,1,1,1,1] => 3
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,5,6,2,7,3,4,8] => [2,2,1,1,1,1] => 3
[.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,2,3,7,4,5,8] => [2,2,1,1,1,1] => 3
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,2,3,4,8] => [2,1,1,1,1,1,1] => 2
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,5,7,2,3,4,6,8] => [2,1,1,1,1,1,1] => 2
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,7,3,4,5,8] => [2,2,1,1,1,1] => 3
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,2,3,4,5,8] => [2,1,1,1,1,1,1] => 2
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,2,7] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,2,8,6] => [2,2,1,1,1,1] => 3
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,2,6] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,2,6,7] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,2,8,5] => [2,2,1,1,1,1] => 3
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,8,2,5,7] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,7,8,2,5,6] => [2,1,1,1,1,1,1] => 2
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,2,5,6,7] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,2,6,7,8,4] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,2,6,8,4,7] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,8,6] => [2,2,2,1,1] => 4
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,2,8,4,6,7] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,2,7,8,4] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,6,2,8,4,7] => [2,2,1,1,1,1] => 3
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,6,2,4,7,8,5] => [2,2,1,1,1,1] => 3
[.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,2,4,8,5,7] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,2,8,4] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,2,4,8,6] => [2,2,1,1,1,1] => 3
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,2,7,4,8,5] => [2,2,2,1,1] => 4
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,7,2,4,5,8,6] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,2,4] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,2,4,7] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,2,8,4,6] => [2,2,1,1,1,1] => 3
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,2,4,6] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,2,4,6,7] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => [2,2,1,1,1,1] => 3
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,2,4,8,5,6] => [2,2,1,1,1,1] => 3
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,2,4,5] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,7,2,8,4,5,6] => [2,2,1,1,1,1] => 3
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,2,4,5,6] => [2,1,1,1,1,1,1] => 2
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [2,1,1,1,1,1,1] => 2
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,8,3] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,2,5,6,8,3,7] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [2,2,2,1,1] => 4
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,2,5,7,8,3,6] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,2,5,8,3,6,7] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,8,5,7] => [2,2,2,1,1] => 4
[.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,7,3,5,8,6] => [2,2,2,1,1] => 4
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,2,6,7,8,3,5] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,2,6,8,3,5,7] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,8,5,6] => [2,2,2,1,1] => 4
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,2,7,8,3,5,6] => [2,2,1,1,1,1] => 3
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,8,3,5,6,7] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,2,6,7,8,3] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,6,8,3,7] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,8,6] => [2,2,2,1,1] => 4
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,7,8,3,6] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,2,8,3,6,7] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,3,6,7,8,4] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,2,3,6,8,4,7] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,3,7,4,8,6] => [2,2,2,1,1] => 4
[.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,2,3,7,8,4,6] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,2,3,8,4,6,7] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,5,6,2,7,8,3] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,5,6,2,8,3,7] => [2,2,1,1,1,1] => 3
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,6,2,3,7,8,5] => [2,2,1,1,1,1] => 3
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [2,2,2,1,1] => 4
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,8,4,7] => [2,2,2,1,1] => 4
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,6,2,3,7,8,4] => [2,2,1,1,1,1] => 3
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [2,2,1,1,1,1] => 3
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,3,4,7,8,5] => [2,2,1,1,1,1] => 3
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,2,3,4,8,5,7] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,2,8,3] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,5,7,2,3,8,6] => [2,2,1,1,1,1] => 3
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,2,7,3,8,5] => [2,2,2,1,1] => 4
[.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,7,2,3,5,8,6] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,7,3,4,8,6] => [2,2,2,1,1] => 4
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,8,5] => [2,2,2,1,1] => 4
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,2,3,8,4] => [2,2,1,1,1,1] => 3
[.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,7,2,3,4,8,6] => [2,2,1,1,1,1] => 3
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,7,3,4,8,5] => [2,2,2,1,1] => 4
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [2,2,1,1,1,1] => 3
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,2,3] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,4,5,6,8,2,3,7] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,2,3,6] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,4,6,2,7,8,3,5] => [2,2,1,1,1,1] => 3
[.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,2,8,3,5,7] => [2,2,1,1,1,1] => 3
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,2,8,3,5] => [2,2,1,1,1,1] => 3
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,2,3,8,5,6] => [2,2,1,1,1,1] => 3
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,2,3,5] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,2,3,5,7] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,4,7,2,8,3,5,6] => [2,2,1,1,1,1] => 3
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,2,3,5,6] => [2,1,1,1,1,1,1] => 2
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [2,1,1,1,1,1,1] => 2
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,2,6,7,8,3,4] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,2,6,8,3,4,7] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,8,4,6] => [2,2,2,1,1] => 4
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,2,7,8,3,4,6] => [2,2,1,1,1,1] => 3
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,8,3,4,6,7] => [2,2,1,1,1,1] => 3
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [2,2,1,1,1,1] => 3
[.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,5,6,2,8,3,4,7] => [2,2,1,1,1,1] => 3
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,2,3,7,8,4,5] => [2,2,1,1,1,1] => 3
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,6,2,3,8,4,5,7] => [2,2,1,1,1,1] => 3
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,5,6,7,2,8,3,4] => [2,2,1,1,1,1] => 3
[.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,5,7,2,3,8,4,6] => [2,2,1,1,1,1] => 3
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,8,4,5] => [2,2,2,1,1] => 4
[.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,6,7,2,3,8,4,5] => [2,2,1,1,1,1] => 3
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,2,3,4,8,5,6] => [2,2,1,1,1,1] => 3
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,2,3,4] => [2,1,1,1,1,1,1] => 2
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,5,6,8,2,3,4,7] => [2,1,1,1,1,1,1] => 2
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,2,8,3,4,6] => [2,2,1,1,1,1] => 3
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,5,7,8,2,3,4,6] => [2,1,1,1,1,1,1] => 2
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [2,1,1,1,1,1,1] => 2
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,2,7,8,3,4,5] => [2,2,1,1,1,1] => 3
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,8,3,4,5,7] => [2,2,1,1,1,1] => 3
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,2,8,3,4,5] => [2,2,1,1,1,1] => 3
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,2,3,8,4,5,6] => [2,2,1,1,1,1] => 3
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,2,3,4,5] => [2,1,1,1,1,1,1] => 2
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [2,1,1,1,1,1,1] => 2
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,8,3,4,5,6] => [2,2,1,1,1,1] => 3
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [2,1,1,1,1,1,1] => 2
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 2
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,2,1,1,1,1] => 3
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,2,1,1,1,1] => 3
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,2,1,1,1,1] => 3
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,6,7] => [2,2,1,1,1,1] => 3
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,2,1,1,1,1] => 3
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,2,2,1,1] => 4
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => [2,2,1,1,1,1] => 3
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => [2,2,1,1,1,1] => 3
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,2,1,1,1,1] => 3
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,5,8,6] => [2,2,2,1,1] => 4
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,5,6] => [2,2,1,1,1,1] => 3
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => [2,2,1,1,1,1] => 3
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,2,2,1,1] => 4
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [2,2,2,1,1] => 4
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [2,2,2,1,1] => 4
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,4,5,7,8] => [2,2,1,1,1,1] => 3
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => [2,2,2,1,1] => 4
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,2,1,1,1,1] => 3
[[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,4,6,7] => [2,2,1,1,1,1] => 3
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,6,7,4,8,5] => [2,2,2,1,1] => 4
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,4,5] => [2,2,1,1,1,1] => 3
[[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,7,4,8,5,6] => [2,2,2,1,1] => 4
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,4,5,6] => [2,2,1,1,1,1] => 3
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => [2,2,1,1,1,1] => 3
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,2,1,1,1,1] => 3
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,2,2,1,1] => 4
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,2,2,1,1] => 4
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => [2,2,2,1,1] => 4
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,2,2,1,1] => 4
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => 5
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,2,2,1,1] => 4
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,5,7] => [2,2,2,1,1] => 4
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6] => [2,2,2,2] => 5
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => [2,2,2,1,1] => 4
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => [2,2,2,1,1] => 4
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [2,2,1,1,1,1] => 3
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [2,2,2,1,1] => 4
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [2,2,1,1,1,1] => 3
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => [2,2,2,1,1] => 4
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,2,2,1,1] => 4
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,3,5,7,8] => [2,2,1,1,1,1] => 3
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,3,5,8,7] => [2,2,2,1,1] => 4
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,8,7] => [2,2,2,2] => 5
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,3,4,7,8] => [2,2,1,1,1,1] => 3
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,3,4,8,7] => [2,2,2,1,1] => 4
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => [2,2,2,1,1] => 4
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [2,2,1,1,1,1] => 3
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,4,6,3,7,5,8] => [2,2,2,1,1] => 4
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,3,5,8] => [2,2,1,1,1,1] => 3
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,3,6,7,4,8] => [2,2,2,1,1] => 4
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,4,8] => [2,2,2,1,1] => 4
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,3,4,8] => [2,2,1,1,1,1] => 3
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,5,7,3,4,6,8] => [2,2,1,1,1,1] => 3
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,7,4,5,8] => [2,2,2,1,1] => 4
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => [2,2,1,1,1,1] => 3
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,2,1,1,1,1] => 3
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,3,7] => [2,2,1,1,1,1] => 3
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,3,8,6] => [2,2,2,1,1] => 4
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,3,6] => [2,2,1,1,1,1] => 3
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,3,6,7] => [2,2,1,1,1,1] => 3
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,3,7,8,5] => [2,2,2,1,1] => 4
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,3,8,5,7] => [2,2,2,1,1] => 4
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,3,8,5] => [2,2,2,1,1] => 4
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,3,5,8,6] => [2,2,2,1,1] => 4
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,3,5] => [2,2,1,1,1,1] => 3
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,3,5,7] => [2,2,1,1,1,1] => 3
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,3,5,6] => [2,2,1,1,1,1] => 3
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,3,5,6,7] => [2,2,1,1,1,1] => 3
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,3,6,7,8,4] => [2,2,2,1,1] => 4
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,3,6,8,4,7] => [2,2,2,1,1] => 4
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,8,6] => [2,2,2,2] => 5
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,3,7,8,4,6] => [2,2,2,1,1] => 4
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,8,4,6,7] => [2,2,2,1,1] => 4
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,3,7,8,4] => [2,2,2,1,1] => 4
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,3,4,7,8,5] => [2,2,2,1,1] => 4
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,3,4,8,5,7] => [2,2,2,1,1] => 4
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,3,8,4] => [2,2,2,1,1] => 4
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,3,4,8,6] => [2,2,2,1,1] => 4
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,8,5] => [2,2,2,2] => 5
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,3,4,8,5] => [2,2,2,1,1] => 4
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,3,4,5,8,6] => [2,2,2,1,1] => 4
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,3,4] => [2,2,1,1,1,1] => 3
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,3,4,7] => [2,2,1,1,1,1] => 3
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,3,8,4,6] => [2,2,2,1,1] => 4
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,3,4,6] => [2,2,1,1,1,1] => 3
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,3,4,6,7] => [2,2,1,1,1,1] => 3
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,3,7,8,4,5] => [2,2,2,1,1] => 4
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,8,4,5,7] => [2,2,2,1,1] => 4
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,3,8,4,5] => [2,2,2,1,1] => 4
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,3,4,8,5,6] => [2,2,2,1,1] => 4
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,3,4,5] => [2,2,1,1,1,1] => 3
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,3,4,5,7] => [2,2,1,1,1,1] => 3
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,8,4,5,6] => [2,2,2,1,1] => 4
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,3,4,5,6] => [2,2,1,1,1,1] => 3
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,6,7] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [2,2,2,1,1] => 4
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,7,5,6,8] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,5,6] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,5,6,7] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [2,2,2,1,1] => 4
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,4,5,7,8] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5,8] => [2,2,2,1,1] => 4
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,4,7] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,4,6] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,8,5,7] => [2,2,2,1,1] => 4
[[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,4,5,8,6] => [2,2,2,1,1] => 4
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,4,5] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,4,5,7] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,8,5,6] => [2,2,2,1,1] => 4
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,4,5,6] => [2,2,1,1,1,1] => 3
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,4,5,6,7] => [2,2,1,1,1,1] => 3
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,8,7] => [2,2,1,1,1,1] => 3
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,2,4,5,7,6,8] => [2,2,1,1,1,1] => 3
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,2,4,5,7,8,6] => [2,2,1,1,1,1] => 3
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => [2,2,1,1,1,1] => 3
[[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,4,6,5,8,7] => [2,2,2,1,1] => 4
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,4,6,7,5,8] => [2,2,1,1,1,1] => 3
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [2,2,1,1,1,1] => 3
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,4,6,7,8,5] => [2,2,1,1,1,1] => 3
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,4,6,8,5,7] => [2,2,1,1,1,1] => 3
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,2,4,7,5,8,6] => [2,2,2,1,1] => 4
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,2,4,7,8,5,6] => [2,2,1,1,1,1] => 3
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,2,4,8,5,6,7] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => [2,2,2,1,1] => 4
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [2,2,2,1,1] => 4
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,2,5,6,4,7,8] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => [2,2,2,1,1] => 4
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,6,7,4,8] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5,8] => [2,2,2,1,1] => 4
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,5,6,7,8,4] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,1,2,5,6,8,4,7] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,2,5,7,4,8,6] => [2,2,2,1,1] => 4
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,2,5,7,8,4,6] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,2,5,8,4,6,7] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,2,6,4,7,8,5] => [2,2,2,1,1] => 4
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,2,6,7,4,8,5] => [2,2,2,1,1] => 4
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,1,2,6,7,8,4,5] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,1,2,6,8,4,5,7] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,2,7,4,8,5,6] => [2,2,2,1,1] => 4
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,2,7,8,4,5,6] => [2,2,1,1,1,1] => 3
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => [2,2,1,1,1,1] => 3
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [2,2,1,1,1,1] => 3
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [2,2,1,1,1,1] => 3
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [2,2,1,1,1,1] => 3
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,6,7] => [2,2,1,1,1,1] => 3
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [2,2,1,1,1,1] => 3
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [2,2,2,1,1] => 4
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [2,2,1,1,1,1] => 3
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,5,6,8] => [2,2,1,1,1,1] => 3
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [2,2,1,1,1,1] => 3
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,5,7] => [2,2,1,1,1,1] => 3
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,8,6] => [2,2,2,1,1] => 4
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,5,6] => [2,2,1,1,1,1] => 3
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,5,6,7] => [2,2,1,1,1,1] => 3
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,1,3,6,5,7,8] => [2,2,1,1,1,1] => 3
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [2,2,2,1,1] => 4
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,1,3,6,7,8,5] => [2,2,1,1,1,1] => 3
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,1,3,6,8,5,7] => [2,2,1,1,1,1] => 3
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,1,3,7,5,8,6] => [2,2,2,1,1] => 4
[[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,1,3,7,8,5,6] => [2,2,1,1,1,1] => 3
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,1,3,8,5,6,7] => [2,2,1,1,1,1] => 3
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => [2,2,1,1,1,1] => 3
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,2,5,7,8,6] => [2,2,2,1,1] => 4
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,2,5,8,6,7] => [2,2,2,1,1] => 4
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,5,7,8] => [2,2,2,1,1] => 4
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7] => [2,2,2,2] => 5
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,2,6,7,5,8] => [2,2,2,1,1] => 4
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,7,5,6,8] => [2,2,2,1,1] => 4
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,2,6,7,8,5] => [2,2,2,1,1] => 4
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,2,6,8,5,7] => [2,2,2,1,1] => 4
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6] => [2,2,2,2] => 5
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,2,7,8,5,6] => [2,2,2,1,1] => 4
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,8,5,6,7] => [2,2,2,1,1] => 4
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,5,6,8,7] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,4,1,2,5,7,6,8] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,4,1,2,5,7,8,6] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,1,2,5,8,6,7] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,4,1,2,6,5,7,8] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [2,2,2,1,1] => 4
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,4,1,2,6,7,5,8] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,4,1,2,7,5,6,8] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,1,2,6,7,8,5] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,1,2,6,8,5,7] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,1,2,7,5,8,6] => [2,2,2,1,1] => 4
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,1,2,7,8,5,6] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,1,2,8,5,6,7] => [2,2,1,1,1,1] => 3
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,3,5,6,8,7] => [2,2,1,1,1,1] => 3
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,3,5,7,6,8] => [2,2,1,1,1,1] => 3
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,3,5,7,8,6] => [2,2,1,1,1,1] => 3
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,3,5,8,6,7] => [2,2,1,1,1,1] => 3
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,3,6,5,7,8] => [2,2,1,1,1,1] => 3
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => [2,2,2,1,1] => 4
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,3,6,7,5,8] => [2,2,1,1,1,1] => 3
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => [2,2,1,1,1,1] => 3
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,3,6,7,8,5] => [2,2,1,1,1,1] => 3
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,3,6,8,5,7] => [2,2,1,1,1,1] => 3
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,3,7,5,8,6] => [2,2,2,1,1] => 4
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,1,2,3,7,8,5,6] => [2,2,1,1,1,1] => 3
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,6,7] => [2,2,1,1,1,1] => 3
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,1,4,6,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,4,7,6,8] => [2,2,1,1,1,1] => 3
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,4,8,6,7] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,3,6,7,8] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,3,6,8,7] => [2,2,2,1,1] => 4
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,8] => [2,2,2,1,1] => 4
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,3,7,8,6] => [2,2,2,1,1] => 4
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,8,6,7] => [2,2,2,1,1] => 4
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,1,3,6,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,1,3,7,6,8] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,1,3,7,8,6] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,1,3,4,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,2,6,7,8] => [2,2,1,1,1,1] => 3
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6,8] => [2,2,2,1,1] => 4
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,5,2,7,8,6] => [2,2,2,1,1] => 4
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,4,6,7,8] => [2,2,1,1,1,1] => 3
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,5,2,4,6,8,7] => [2,2,2,1,1] => 4
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,8] => [2,2,2,1,1] => 4
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,5,2,4,7,8,6] => [2,2,2,1,1] => 4
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,5,2,4,8,6,7] => [2,2,2,1,1] => 4
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,2,6,7,8] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6,8] => [2,2,2,1,1] => 4
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,8,6,7] => [2,2,2,1,1] => 4
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,2,5,3,6,7,8] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6,8] => [2,2,2,1,1] => 4
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,5,3,7,8,6] => [2,2,2,1,1] => 4
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,2,5,3,8,6,7] => [2,2,2,1,1] => 4
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,1,2,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,1,2,6,8,7] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,1,2,7,8,6] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,1,2,4,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,1,2,4,6,8,7] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,1,2,4,7,6,8] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,1,2,4,7,8,6] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,1,2,4,8,6,7] => [2,2,1,1,1,1] => 3
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => [2,2,1,1,1,1] => 3
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,5,2,3,7,6,8] => [2,2,2,1,1] => 4
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,5,2,3,7,8,6] => [2,2,2,1,1] => 4
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,5,2,3,8,6,7] => [2,2,2,1,1] => 4
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,1,2,3,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,1,2,3,7,6,8] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,1,2,3,8,6,7] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,4,6,8,7] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,4,7,8,6] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,1,5,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,8,7] => [2,2,2,1,1] => 4
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,1,4,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,1,4,8,7] => [2,2,1,1,1,1] => 3
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,1,4,5,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,1,4,5,8,7] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3,7,8] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,1,5,6,3,8,7] => [2,2,2,1,1] => 4
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,1,6,3,5,7,8] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7] => [2,2,2,1,1] => 4
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,4,5,1,6,3,7,8] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,8,7] => [2,2,2,1,1] => 4
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,1,3,6,4,7,8] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => [2,2,2,1,1] => 4
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,1,3,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,4,5,6,1,3,8,7] => [2,2,1,1,1,1] => 3
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,1,3,5,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,1,3,5,8,7] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,1,6,3,4,7,8] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,5,1,6,3,4,8,7] => [2,2,2,1,1] => 4
[[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,1,3,4,8,7] => [2,2,1,1,1,1] => 3
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,6,1,3,4,5,7,8] => [2,1,1,1,1,1,1] => 2
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,1,3,4,5,8,7] => [2,2,1,1,1,1] => 3
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,6,2,8,7] => [2,2,2,1,1] => 4
[[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,5,8,7] => [2,2,2,1,1] => 4
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7] => [2,2,2,2] => 5
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,5,6,2,4,7,8] => [2,2,1,1,1,1] => 3
[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,1,5,6,2,4,8,7] => [2,2,2,1,1] => 4
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => [2,2,1,1,1,1] => 3
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,6,2,4,5,8,7] => [2,2,2,1,1] => 4
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2,7,8] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,6,2,8,7] => [2,2,2,1,1] => 4
[[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,1,6,2,5,8,7] => [2,2,2,1,1] => 4
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,2,5,6,3,7,8] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,2,5,6,3,8,7] => [2,2,2,1,1] => 4
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,1,2,6,3,5,8,7] => [2,2,2,1,1] => 4
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,1,6,2,7,8] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,8,7] => [2,2,2,1,1] => 4
[[[.,[[.,.],.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => [2,2,2,1,1] => 4
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,3,7,8] => [2,2,2,1,1] => 4
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7] => [2,2,2,2] => 5
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [2,2,2,1,1] => 4
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,2,3,6,4,7,8] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,1,2,7,8] => [2,1,1,1,1,1,1] => 2
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,1,2,8,7] => [2,2,1,1,1,1] => 3
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,1,2,5,8,7] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,5,1,6,2,4,7,8] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,1,6,2,4,8,7] => [2,2,2,1,1] => 4
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,5,6,1,2,4,7,8] => [2,1,1,1,1,1,1] => 2
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,1,2,4,8,7] => [2,2,1,1,1,1] => 3
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,1,2,4,5,7,8] => [2,1,1,1,1,1,1] => 2
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,1,2,4,5,8,7] => [2,2,1,1,1,1] => 3
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,5,6,2,3,7,8] => [2,2,1,1,1,1] => 3
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,5,6,2,3,8,7] => [2,2,2,1,1] => 4
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [2,2,1,1,1,1] => 3
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,1,6,2,3,5,8,7] => [2,2,2,1,1] => 4
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,5,1,6,2,3,7,8] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,1,6,2,3,8,7] => [2,2,2,1,1] => 4
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,2,6,3,4,7,8] => [2,2,1,1,1,1] => 3
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,1,2,3,7,8] => [2,1,1,1,1,1,1] => 2
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,1,2,3,8,7] => [2,2,1,1,1,1] => 3
[[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,6,1,2,3,5,7,8] => [2,1,1,1,1,1,1] => 2
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7] => [2,2,1,1,1,1] => 3
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => [2,2,1,1,1,1] => 3
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,6,2,3,4,8,7] => [2,2,2,1,1] => 4
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4,8,7] => [2,2,1,1,1,1] => 3
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,7,8] => [2,1,1,1,1,1,1] => 2
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,1,6,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,1,5,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,1,5,6,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,1,7,4,8] => [2,2,1,1,1,1] => 3
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,6,1,4,7,5,8] => [2,2,1,1,1,1] => 3
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,1,4,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,1,4,6,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,1,4,5,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,1,4,5,6,8] => [2,1,1,1,1,1,1] => 2
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,1,5,6,7,3,8] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5,8] => [2,2,2,1,1] => 4
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,4,1,6,7,3,5,8] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,4,5,1,6,7,3,8] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,4,5,1,7,3,6,8] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,1,7,3,8] => [2,2,1,1,1,1] => 3
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,4,6,1,3,7,5,8] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4,8] => [2,2,2,1,1] => 4
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,5,6,1,3,7,4,8] => [2,2,1,1,1,1] => 3
[[.,[[[[.,.],.],.],[.,.]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,1,3,4,7,5,8] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,1,3,8] => [2,1,1,1,1,1,1] => 2
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,1,3,5,8] => [2,1,1,1,1,1,1] => 2
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,1,6,7,3,4,8] => [2,2,1,1,1,1] => 3
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,1,7,3,4,8] => [2,2,1,1,1,1] => 3
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,6,1,7,3,4,5,8] => [2,2,1,1,1,1] => 3
[[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,1,3,4,5,8] => [2,1,1,1,1,1,1] => 2
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,1,3,4,5,6,8] => [2,1,1,1,1,1,1] => 2
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,7,2,8] => [2,2,1,1,1,1] => 3
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,6,8] => [2,2,2,1,1] => 4
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,5,7,2,4,6,8] => [2,2,1,1,1,1] => 3
[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,7,4,5,8] => [2,2,2,1,1] => 4
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,6,7,2,4,5,8] => [2,2,1,1,1,1] => 3
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,7,2,4,5,6,8] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,1,5,6,7,2,8] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,1,5,7,2,6,8] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5,8] => [2,2,2,1,1] => 4
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,1,6,7,2,5,8] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,6,7,3,8] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6,8] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => [2,2,2,1,1] => 4
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,6,7,3,5,8] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,7,3,5,6,8] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,1,6,7,2,8] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,5,1,7,2,6,8] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,1,2,6,7,4,8] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,1,2,7,4,6,8] => [2,2,1,1,1,1] => 3
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,7,3,6,8] => [2,2,2,1,1] => 4
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,5,1,2,6,7,3,8] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,1,2,7,3,6,8] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,2,3,6,7,4,8] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,1,7,2,8] => [2,2,1,1,1,1] => 3
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,1,2,7,5,8] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4,8] => [2,2,2,1,1] => 4
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,1,2,7,4,8] => [2,2,1,1,1,1] => 3
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,1,2,4,7,5,8] => [2,2,1,1,1,1] => 3
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,1,6,2,3,7,5,8] => [2,2,2,1,1] => 4
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3,8] => [2,2,2,1,1] => 4
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => [2,2,2,1,1] => 4
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,5,6,1,2,7,3,8] => [2,2,1,1,1,1] => 3
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,6,1,2,3,7,5,8] => [2,2,1,1,1,1] => 3
[[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,6,2,3,7,4,8] => [2,2,2,1,1] => 4
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,2,3,4,7,5,8] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,1,2,8] => [2,1,1,1,1,1,1] => 2
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,5,7,1,2,6,8] => [2,1,1,1,1,1,1] => 2
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,4,6,7,1,2,5,8] => [2,1,1,1,1,1,1] => 2
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,5,1,6,7,2,4,8] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,1,7,2,4,6,8] => [2,2,1,1,1,1] => 3
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,1,7,2,4,8] => [2,2,1,1,1,1] => 3
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,1,2,4,8] => [2,1,1,1,1,1,1] => 2
[[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,1,2,4,6,8] => [2,1,1,1,1,1,1] => 2
[[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,6,7,1,2,4,5,8] => [2,1,1,1,1,1,1] => 2
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,7,1,2,4,5,6,8] => [2,1,1,1,1,1,1] => 2
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,5,6,7,2,3,8] => [2,2,1,1,1,1] => 3
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,5,7,2,3,6,8] => [2,2,1,1,1,1] => 3
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,7,3,5,8] => [2,2,2,1,1] => 4
[[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,1,6,7,2,3,5,8] => [2,2,1,1,1,1] => 3
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,1,7,2,3,5,6,8] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,5,1,6,7,2,3,8] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,5,1,7,2,3,6,8] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,4,8] => [2,2,1,1,1,1] => 3
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,5,6,1,7,2,3,8] => [2,2,1,1,1,1] => 3
[[[[.,[[.,.],.]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,6,1,2,7,3,5,8] => [2,2,1,1,1,1] => 3
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,7,3,4,8] => [2,2,2,1,1] => 4
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,1,2,7,3,4,8] => [2,2,1,1,1,1] => 3
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5,8] => [2,2,1,1,1,1] => 3
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,1,2,3,8] => [2,1,1,1,1,1,1] => 2
[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,1,7,2,3,5,8] => [2,2,1,1,1,1] => 3
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,1,2,3,5,8] => [2,1,1,1,1,1,1] => 2
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,1,2,3,5,6,8] => [2,1,1,1,1,1,1] => 2
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,1,7,2,3,4,8] => [2,2,1,1,1,1] => 3
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,2,7,3,4,5,8] => [2,2,1,1,1,1] => 3
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,1,2,3,4,8] => [2,1,1,1,1,1,1] => 2
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,1,2,3,4,6,8] => [2,1,1,1,1,1,1] => 2
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,7,2,3,4,5,8] => [2,2,1,1,1,1] => 3
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,1,2,3,4,5,8] => [2,1,1,1,1,1,1] => 2
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,1,8,6] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,1,6] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,1,6,7] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,1,7,8,5] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,1,8,5,7] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,1,5,8,6] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,1,5] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,1,5,7] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,1,8,5,6] => [2,2,1,1,1,1] => 3
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,1,5,6] => [2,1,1,1,1,1,1] => 2
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,1,5,6,7] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,1,6,7,8,4] => [2,2,1,1,1,1] => 3
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,3,5,1,6,8,4,7] => [2,2,1,1,1,1] => 3
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,8,6] => [2,2,2,1,1] => 4
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,1,8,4,6,7] => [2,2,1,1,1,1] => 3
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,1,7,8,4] => [2,2,1,1,1,1] => 3
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,1,8,4,7] => [2,2,1,1,1,1] => 3
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,1,4,7,8,5] => [2,2,1,1,1,1] => 3
[[.,[.,[[[.,.],.],[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,1,4,8,5,7] => [2,2,1,1,1,1] => 3
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,1,8,4] => [2,2,1,1,1,1] => 3
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,1,4,8,6] => [2,2,1,1,1,1] => 3
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,6,7,1,4,8,5] => [2,2,1,1,1,1] => 3
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,1,4,5,8,6] => [2,2,1,1,1,1] => 3
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,1,4] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,1,4,7] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,1,8,4,6] => [2,2,1,1,1,1] => 3
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,1,4,6] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,1,4,6,7] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => [2,2,1,1,1,1] => 3
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,1,8,4,5,7] => [2,2,1,1,1,1] => 3
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,1,8,4,5] => [2,2,1,1,1,1] => 3
[[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,1,4,8,5,6] => [2,2,1,1,1,1] => 3
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,1,4,5] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,6,8,1,4,5,7] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[[[.,[.,.]],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,7,8,1,4,5,6] => [2,1,1,1,1,1,1] => 2
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [2,1,1,1,1,1,1] => 2
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,3] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,1,5,6,8,3,7] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,8,6] => [2,2,2,1,1] => 4
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,1,5,8,3,6,7] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => [2,2,2,1,1] => 4
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7] => [2,2,2,1,1] => 4
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => [2,2,2,1,1] => 4
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,1,7,3,5,8,6] => [2,2,2,1,1] => 4
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,1,6,7,8,3,5] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,1,6,8,3,5,7] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,8,5,6] => [2,2,2,1,1] => 4
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,1,7,8,3,5,6] => [2,2,1,1,1,1] => 3
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,1,8,3,5,6,7] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,1,6,7,8,3] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,1,6,8,3,7] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,8,6] => [2,2,2,1,1] => 4
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,1,7,8,3,6] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,1,8,3,6,7] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,1,3,6,7,8,4] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,1,3,6,8,4,7] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,1,3,7,4,8,6] => [2,2,2,1,1] => 4
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,1,3,7,8,4,6] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,1,3,8,4,6,7] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,1,7,8,3] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,1,8,3,7] => [2,2,1,1,1,1] => 3
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,1,3,7,8,5] => [2,2,1,1,1,1] => 3
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => [2,2,2,1,1] => 4
[[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,8,4,7] => [2,2,2,1,1] => 4
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,1,3,7,8,4] => [2,2,1,1,1,1] => 3
[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,5,6,1,3,8,4,7] => [2,2,1,1,1,1] => 3
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,1,3,4,7,8,5] => [2,2,1,1,1,1] => 3
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,1,3,4,8,5,7] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,1,8,3] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,4,5,7,1,3,8,6] => [2,2,1,1,1,1] => 3
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,1,7,3,8,5] => [2,2,2,1,1] => 4
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,1,3,8,5] => [2,2,1,1,1,1] => 3
[[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,4,7,1,3,5,8,6] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => [2,2,2,1,1] => 4
[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,1,7,3,4,8,6] => [2,2,2,1,1] => 4
[[.,[[[[.,.],.],[.,.]],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,6,1,3,7,4,8,5] => [2,2,2,1,1] => 4
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,1,3,8,4] => [2,2,1,1,1,1] => 3
[[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,5,7,1,3,4,8,6] => [2,2,1,1,1,1] => 3
[[.,[[[[.,.],[.,.]],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,1,7,3,4,8,5] => [2,2,2,1,1] => 4
[[.,[[[[.,[.,.]],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,6,7,1,3,4,8,5] => [2,2,1,1,1,1] => 3
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,1,3,4,5,8,6] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,1,3] => [2,1,1,1,1,1,1] => 2
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,1,3,7] => [2,1,1,1,1,1,1] => 2
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,4,5,7,1,8,3,6] => [2,2,1,1,1,1] => 3
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,1,3,6] => [2,1,1,1,1,1,1] => 2
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,1,7,8,3,5] => [2,2,1,1,1,1] => 3
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,1,8,3,5,7] => [2,2,1,1,1,1] => 3
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,1,8,3,5] => [2,2,1,1,1,1] => 3
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,4,7,1,3,8,5,6] => [2,2,1,1,1,1] => 3
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,1,3,5] => [2,1,1,1,1,1,1] => 2
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7] => [2,1,1,1,1,1,1] => 2
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,4,7,1,8,3,5,6] => [2,2,1,1,1,1] => 3
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,1,3,5,6] => [2,1,1,1,1,1,1] => 2
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [2,1,1,1,1,1,1] => 2
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,1,6,7,8,3,4] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,5,1,6,8,3,4,7] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,8,4,6] => [2,2,2,1,1] => 4
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,1,7,8,3,4,6] => [2,2,1,1,1,1] => 3
[[.,[[[.,.],[[[.,.],.],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,1,8,3,4,6,7] => [2,2,1,1,1,1] => 3
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,1,7,8,3,4] => [2,2,1,1,1,1] => 3
[[.,[[[[.,.],.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,1,3,7,8,4,5] => [2,2,1,1,1,1] => 3
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,1,3,8,4,5,7] => [2,2,1,1,1,1] => 3
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,1,8,3,4] => [2,2,1,1,1,1] => 3
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,5,7,1,3,8,4,6] => [2,2,1,1,1,1] => 3
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,6,1,7,3,8,4,5] => [2,2,2,1,1] => 4
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,1,3,4] => [2,1,1,1,1,1,1] => 2
[[.,[[[.,[.,[[.,.],.]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,5,6,8,1,3,4,7] => [2,1,1,1,1,1,1] => 2
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,5,7,1,8,3,4,6] => [2,2,1,1,1,1] => 3
[[.,[[[.,[[.,[.,.]],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,5,7,8,1,3,4,6] => [2,1,1,1,1,1,1] => 2
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,1,3,4,6,7] => [2,1,1,1,1,1,1] => 2
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,6,1,7,8,3,4,5] => [2,2,1,1,1,1] => 3
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,1,8,3,4,5,7] => [2,2,1,1,1,1] => 3
[[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,1,8,3,4,5] => [2,2,1,1,1,1] => 3
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,1,3,8,4,5,6] => [2,2,1,1,1,1] => 3
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,1,3,4,5] => [2,1,1,1,1,1,1] => 2
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [2,1,1,1,1,1,1] => 2
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,1,8,3,4,5,6] => [2,2,1,1,1,1] => 3
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [2,1,1,1,1,1,1] => 2
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [2,1,1,1,1,1,1] => 2
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,2] => [2,2,1,1,1,1] => 3
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,6,8,2,7] => [2,2,1,1,1,1] => 3
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,4,5,7,2,8,6] => [2,2,2,1,1] => 4
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,4,5,7,8,2,6] => [2,2,1,1,1,1] => 3
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,4,5,8,2,6,7] => [2,2,1,1,1,1] => 3
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,4,6,2,7,8,5] => [2,2,2,1,1] => 4
[[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,4,6,2,8,5,7] => [2,2,2,1,1] => 4
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,4,6,7,2,8,5] => [2,2,2,1,1] => 4
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,4,7,2,5,8,6] => [2,2,2,1,1] => 4
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,4,6,7,8,2,5] => [2,2,1,1,1,1] => 3
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,4,6,8,2,5,7] => [2,2,1,1,1,1] => 3
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,1,4,7,2,8,5,6] => [2,2,2,1,1] => 4
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4,8,2,5,6,7] => [2,2,1,1,1,1] => 3
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,2,6,7,8,4] => [2,2,2,1,1] => 4
[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,2,6,8,4,7] => [2,2,2,1,1] => 4
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,8,6] => [2,2,2,2] => 5
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,2,7,8,4,6] => [2,2,2,1,1] => 4
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,8,4,6,7] => [2,2,2,1,1] => 4
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,1,5,6,2,7,8,4] => [2,2,2,1,1] => 4
[[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,1,5,6,2,8,4,7] => [2,2,2,1,1] => 4
[[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,6,2,4,7,8,5] => [2,2,2,1,1] => 4
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,6,2,4,8,5,7] => [2,2,2,1,1] => 4
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,1,5,6,7,2,8,4] => [2,2,2,1,1] => 4
[[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,1,5,7,2,4,8,6] => [2,2,2,1,1] => 4
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,8,5] => [2,2,2,2] => 5
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,7,2,4,5,8,6] => [2,2,2,1,1] => 4
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,1,5,6,7,8,2,4] => [2,2,1,1,1,1] => 3
[[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,1,5,6,8,2,4,7] => [2,2,1,1,1,1] => 3
[[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,1,5,7,2,8,4,6] => [2,2,2,1,1] => 4
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,1,5,7,8,2,4,6] => [2,2,1,1,1,1] => 3
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,1,5,8,2,4,6,7] => [2,2,1,1,1,1] => 3
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,8,4,5,7] => [2,2,2,1,1] => 4
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,1,6,7,2,8,4,5] => [2,2,2,1,1] => 4
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,1,6,8,2,4,5,7] => [2,2,1,1,1,1] => 3
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,8,4,5,6] => [2,2,2,1,1] => 4
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,7,8,2,4,5,6] => [2,2,1,1,1,1] => 3
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,2] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,1,5,6,8,2,7] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,8,6] => [2,2,2,1,1] => 4
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,1,5,7,8,2,6] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,1,5,8,2,6,7] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,2,7,8,5] => [2,2,2,1,1] => 4
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,8,5,7] => [2,2,2,1,1] => 4
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,1,6,7,2,8,5] => [2,2,2,1,1] => 4
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,1,7,2,5,8,6] => [2,2,2,1,1] => 4
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,4,1,6,7,8,2,5] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,4,1,6,8,2,5,7] => [2,2,1,1,1,1] => 3
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,1,8,2,5,6,7] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,3] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,2,5,6,8,3,7] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,5,7,3,8,6] => [2,2,2,1,1] => 4
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,5,7,8,3,6] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,2,5,8,3,6,7] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,1,2,6,3,7,8,5] => [2,2,2,1,1] => 4
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,1,2,6,3,8,5,7] => [2,2,2,1,1] => 4
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,1,2,6,7,3,8,5] => [2,2,2,1,1] => 4
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,1,2,7,3,5,8,6] => [2,2,2,1,1] => 4
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,1,2,7,8,3,5,6] => [2,2,1,1,1,1] => 3
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,2,8,3,5,6,7] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,1,6,7,8,2] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,1,7,8,2,6] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,1,2,6,7,8,4] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,1,2,6,8,4,7] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,1,2,7,4,8,6] => [2,2,2,1,1] => 4
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,1,2,7,8,4,6] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,5,1,2,8,4,6,7] => [2,2,1,1,1,1] => 3
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,2,6,7,8,3] => [2,2,2,1,1] => 4
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,2,6,8,3,7] => [2,2,2,1,1] => 4
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,8,6] => [2,2,2,2] => 5
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,2,7,8,3,6] => [2,2,2,1,1] => 4
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,8,3,6,7] => [2,2,2,1,1] => 4
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,1,2,6,7,8,3] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,5,1,2,6,8,3,7] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,5,1,2,7,8,3,6] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,1,2,8,3,6,7] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,4] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2,3,6,8,4,7] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,1,2,3,7,4,8,6] => [2,2,2,1,1] => 4
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,1,2,3,7,8,4,6] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,1,2,3,8,4,6,7] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,1,7,8,2] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,1,8,2,7] => [2,2,1,1,1,1] => 3
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,1,2,7,8,5] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,1,6,2,7,8,4] => [2,2,2,1,1] => 4
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,1,2,7,8,4] => [2,2,1,1,1,1] => 3
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,1,2,8,4,7] => [2,2,1,1,1,1] => 3
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,1,2,4,7,8,5] => [2,2,1,1,1,1] => 3
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,1,2,4,8,5,7] => [2,2,1,1,1,1] => 3
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,5,6,2,8,3,7] => [2,2,2,1,1] => 4
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,1,6,2,3,7,8,5] => [2,2,2,1,1] => 4
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,1,6,2,3,8,5,7] => [2,2,2,1,1] => 4
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,5,1,6,2,7,8,3] => [2,2,2,1,1] => 4
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,8,3,7] => [2,2,2,1,1] => 4
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,2,6,3,7,8,4] => [2,2,2,1,1] => 4
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2,6,3,8,4,7] => [2,2,2,1,1] => 4
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,1,2,7,8,3] => [2,2,1,1,1,1] => 3
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,1,2,8,3,7] => [2,2,1,1,1,1] => 3
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,1,2,3,8,5,7] => [2,2,1,1,1,1] => 3
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,6,2,3,7,8,4] => [2,2,2,1,1] => 4
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,6,2,3,8,4,7] => [2,2,2,1,1] => 4
[[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,6,1,2,3,7,8,4] => [2,2,1,1,1,1] => 3
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,8,4,7] => [2,2,1,1,1,1] => 3
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,2,3,4,7,8,5] => [2,2,1,1,1,1] => 3
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2,3,4,8,5,7] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,1,8,2] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,1,2,8,6] => [2,2,1,1,1,1] => 3
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,1,7,2,8,5] => [2,2,2,1,1] => 4
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,1,2,8,5] => [2,2,1,1,1,1] => 3
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,1,2,5,8,6] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,1,6,7,2,8,4] => [2,2,2,1,1] => 4
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,1,7,2,8,4] => [2,2,2,1,1] => 4
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,1,2,7,4,8,5] => [2,2,2,1,1] => 4
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,1,2,8,4] => [2,2,1,1,1,1] => 3
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,1,2,4,8,6] => [2,2,1,1,1,1] => 3
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,6,1,7,2,4,8,5] => [2,2,2,1,1] => 4
[[[.,[[[.,[.,.]],.],.]],[.,.]],.] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,6,7,1,2,4,8,5] => [2,2,1,1,1,1] => 3
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,7,1,2,4,5,8,6] => [2,2,1,1,1,1] => 3
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,5,6,7,2,8,3] => [2,2,2,1,1] => 4
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,8,5] => [2,2,2,2] => 5
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,1,6,7,2,3,8,5] => [2,2,2,1,1] => 4
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,1,7,2,3,5,8,6] => [2,2,2,1,1] => 4
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,1,6,7,2,8,3] => [2,2,2,1,1] => 4
[[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,1,7,2,3,8,6] => [2,2,2,1,1] => 4
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,2,6,7,3,8,4] => [2,2,2,1,1] => 4
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,1,2,7,3,4,8,6] => [2,2,2,1,1] => 4
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,1,7,2,8,3] => [2,2,2,1,1] => 4
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,8,4] => [2,2,2,2] => 5
[[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,1,2,7,3,8,4] => [2,2,2,1,1] => 4
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,2,3,7,4,8,5] => [2,2,2,1,1] => 4
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,1,2,8,3] => [2,2,1,1,1,1] => 3
[[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,5,7,1,2,3,8,6] => [2,2,1,1,1,1] => 3
[[[[.,[[.,.],[.,.]]],.],[.,.]],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,1,7,2,3,8,5] => [2,2,2,1,1] => 4
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,1,2,3,8,5] => [2,2,1,1,1,1] => 3
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,1,2,3,5,8,6] => [2,2,1,1,1,1] => 3
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,6,7,2,3,8,4] => [2,2,2,1,1] => 4
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,1,7,2,3,4,8,6] => [2,2,2,1,1] => 4
[[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,6,1,7,2,3,8,4] => [2,2,2,1,1] => 4
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,2,7,3,4,8,5] => [2,2,2,1,1] => 4
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,1,2,3,8,4] => [2,2,1,1,1,1] => 3
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,1,2,3,4,8,6] => [2,2,1,1,1,1] => 3
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,7,2,3,4,8,5] => [2,2,2,1,1] => 4
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,1,2,3,4,8,5] => [2,2,1,1,1,1] => 3
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,8,6] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,1,2] => [2,1,1,1,1,1,1] => 2
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,1,2,7] => [2,1,1,1,1,1,1] => 2
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,1,8,2,6] => [2,2,1,1,1,1] => 3
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,1,2,6] => [2,1,1,1,1,1,1] => 2
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,1,2,6,7] => [2,1,1,1,1,1,1] => 2
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,1,7,8,2,5] => [2,2,1,1,1,1] => 3
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,1,8,2,5] => [2,2,1,1,1,1] => 3
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,1,2,5] => [2,1,1,1,1,1,1] => 2
[[[.,[.,[[.,[[.,.],.]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,1,2,5,7] => [2,1,1,1,1,1,1] => 2
[[[.,[.,[[[.,.],[.,.]],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,4,7,1,8,2,5,6] => [2,2,1,1,1,1] => 3
[[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,1,2,5,6] => [2,1,1,1,1,1,1] => 2
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => [2,1,1,1,1,1,1] => 2
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,1,6,7,8,2,4] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],[.,[[.,.],.]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,5,1,6,8,2,4,7] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,8,4,6] => [2,2,2,1,1] => 4
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,1,7,8,2,4,6] => [2,2,1,1,1,1] => 3
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,5,1,8,2,4,6,7] => [2,2,1,1,1,1] => 3
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => [2,2,1,1,1,1] => 3
[[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,5,6,1,8,2,4,7] => [2,2,1,1,1,1] => 3
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,1,2,7,8,4,5] => [2,2,1,1,1,1] => 3
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,1,8,2,4] => [2,2,1,1,1,1] => 3
[[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,1,2,8,4,6] => [2,2,1,1,1,1] => 3
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,6,1,7,2,8,4,5] => [2,2,2,1,1] => 4
[[[.,[[[.,[.,.]],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,1,2,8,4,5] => [2,2,1,1,1,1] => 3
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,1,2,4,8,5,6] => [2,2,1,1,1,1] => 3
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,1,2,4] => [2,1,1,1,1,1,1] => 2
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,1,2,4,7] => [2,1,1,1,1,1,1] => 2
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,1,2,4,6] => [2,1,1,1,1,1,1] => 2
[[[.,[[[.,.],[.,[.,.]]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,1,7,8,2,4,5] => [2,2,1,1,1,1] => 3
[[[.,[[[.,.],[[.,.],.]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,6,1,8,2,4,5,7] => [2,2,1,1,1,1] => 3
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,1,2,8,4,5,6] => [2,2,1,1,1,1] => 3
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,1,2,4,5] => [2,1,1,1,1,1,1] => 2
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,1,2,4,5,7] => [2,1,1,1,1,1,1] => 2
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,1,8,2,4,5,6] => [2,2,1,1,1,1] => 3
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [2,1,1,1,1,1,1] => 2
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [2,1,1,1,1,1,1] => 2
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,8,2,3] => [2,2,1,1,1,1] => 3
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,5,6,8,2,3,7] => [2,2,1,1,1,1] => 3
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,5,7,2,8,3,6] => [2,2,2,1,1] => 4
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,8,3,5,7] => [2,2,2,1,1] => 4
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,1,7,2,3,8,5,6] => [2,2,2,1,1] => 4
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,1,6,7,8,2,3,5] => [2,2,1,1,1,1] => 3
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,1,6,8,2,3,5,7] => [2,2,1,1,1,1] => 3
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,8,3,5,6] => [2,2,2,1,1] => 4
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,1,7,8,2,3,5,6] => [2,2,1,1,1,1] => 3
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,1,6,7,8,2,3] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,1,6,8,2,3,7] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,8,3,6] => [2,2,2,1,1] => 4
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,1,7,8,2,3,6] => [2,2,1,1,1,1] => 3
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,1,8,2,3,6,7] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,2,6,7,8,3,4] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,1,2,6,8,3,4,7] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,1,2,7,3,8,4,6] => [2,2,2,1,1] => 4
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,1,2,7,8,3,4,6] => [2,2,1,1,1,1] => 3
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,1,2,8,3,4,6,7] => [2,2,1,1,1,1] => 3
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,5,6,1,7,8,2,3] => [2,2,1,1,1,1] => 3
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,1,8,2,3,7] => [2,2,1,1,1,1] => 3
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,6,1,2,7,8,3,5] => [2,2,1,1,1,1] => 3
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,1,2,8,3,5,7] => [2,2,1,1,1,1] => 3
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,6,2,7,8,3,4] => [2,2,2,1,1] => 4
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,8,3,4,7] => [2,2,2,1,1] => 4
[[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,1,2,7,8,3,4] => [2,2,1,1,1,1] => 3
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,1,2,8,3,4,7] => [2,2,1,1,1,1] => 3
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,2,3,7,8,4,5] => [2,2,1,1,1,1] => 3
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,1,2,3,8,4,5,7] => [2,2,1,1,1,1] => 3
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,1,8,2,3] => [2,2,1,1,1,1] => 3
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,5,7,1,2,8,3,6] => [2,2,1,1,1,1] => 3
[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,6,1,7,2,8,3,5] => [2,2,2,1,1] => 4
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,6,7,1,2,8,3,5] => [2,2,1,1,1,1] => 3
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,1,2,3,8,5,6] => [2,2,1,1,1,1] => 3
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,6,7,2,8,3,4] => [2,2,2,1,1] => 4
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,6,1,7,2,8,3,4] => [2,2,2,1,1] => 4
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,2,7,3,8,4,5] => [2,2,2,1,1] => 4
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,1,2,8,3,4] => [2,2,1,1,1,1] => 3
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,7,2,3,8,4,5] => [2,2,2,1,1] => 4
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,1,2,3,8,4,5] => [2,2,1,1,1,1] => 3
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,8,5,6] => [2,2,1,1,1,1] => 3
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,1,2,3] => [2,1,1,1,1,1,1] => 2
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,1,2,3,7] => [2,1,1,1,1,1,1] => 2
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,1,2,3,6] => [2,1,1,1,1,1,1] => 2
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [2,1,1,1,1,1,1] => 2
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,1,7,8,2,3,5] => [2,2,1,1,1,1] => 3
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,1,8,2,3,5,7] => [2,2,1,1,1,1] => 3
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,1,8,2,3,5] => [2,2,1,1,1,1] => 3
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,1,2,8,3,5,6] => [2,2,1,1,1,1] => 3
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,1,2,3,5] => [2,1,1,1,1,1,1] => 2
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [2,1,1,1,1,1,1] => 2
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,1,8,2,3,5,6] => [2,2,1,1,1,1] => 3
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,1,2,3,5,6] => [2,1,1,1,1,1,1] => 2
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [2,1,1,1,1,1,1] => 2
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,6,7,8,2,3,4] => [2,2,1,1,1,1] => 3
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,8,3,4,6] => [2,2,2,1,1] => 4
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,1,7,8,2,3,4,6] => [2,2,1,1,1,1] => 3
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [2,2,1,1,1,1] => 3
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,1,7,8,2,3,4] => [2,2,1,1,1,1] => 3
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,1,8,2,3,4,7] => [2,2,1,1,1,1] => 3
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,2,7,8,3,4,5] => [2,2,1,1,1,1] => 3
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,1,2,8,3,4,5,7] => [2,2,1,1,1,1] => 3
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,1,8,2,3,4] => [2,2,1,1,1,1] => 3
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,1,2,8,3,4,6] => [2,2,1,1,1,1] => 3
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,7,2,8,3,4,5] => [2,2,2,1,1] => 4
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,1,2,8,3,4,5] => [2,2,1,1,1,1] => 3
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1,2,3,8,4,5,6] => [2,2,1,1,1,1] => 3
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4] => [2,1,1,1,1,1,1] => 2
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [2,1,1,1,1,1,1] => 2
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [2,1,1,1,1,1,1] => 2
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [2,1,1,1,1,1,1] => 2
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,7,8,2,3,4,5] => [2,2,1,1,1,1] => 3
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [2,2,1,1,1,1] => 3
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,1,8,2,3,4,5] => [2,2,1,1,1,1] => 3
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1,2,8,3,4,5,6] => [2,2,1,1,1,1] => 3
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [2,1,1,1,1,1,1] => 2
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [2,1,1,1,1,1,1] => 2
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [2,2,1,1,1,1] => 3
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [2,1,1,1,1,1,1] => 2
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 1
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,7,8] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 2
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 2
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 1
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [2,1,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => [2,1,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [2,2,1,1,1,1,1] => 3
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [2,1,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 2
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 2
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 2
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => [2,2,1,1,1,1,1] => 3
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 2
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [2,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [2,1,1,1,1,1,1,1,1] => 2
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,9,2] => [2,2,1,1,1,1,1] => 3
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,1,1,1,1,1,1,1,1] => 2
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,2,2,2,2] => 6
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9] => [2,2,2,2,1,1] => 5
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7,10,9] => [2,2,2,2,1,1] => 5
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,8,5,7,10,9] => [2,2,2,2,1,1] => 5
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,10,7,9] => [2,2,2,2,1,1] => 5
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [2,1,1,1,1,1,1,1,1] => 2
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,2,2,2,2,2] => 7
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,4,6,8,10,12,1,3,5,7,9,11] => [2,1,1,1,1,1,1,1,1,1,1] => 2
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => [2,1,1,1,1,1,1,1] => 2
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => [2,1,1,1,1,1,1,1,1] => 2
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,8,2,3,4,5,6,9] => [2,2,1,1,1,1,1] => 3
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,1,2,3,4,5,7,9] => [2,1,1,1,1,1,1,1] => 2
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,9,3,4,5,6,7] => [2,2,1,1,1,1,1] => 3
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,6,8,9] => [2,1,1,1,1,1,1,1] => 2
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,8,9,3,4,5,6,7] => [2,2,1,1,1,1,1] => 3
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => [2,2,1,1,1,1,1,1] => 3
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,1,8] => [2,1,1,1,1,1,1,1] => 2
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [2,1,1,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,1,9] => [2,1,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,1,7] => [2,1,1,1,1,1,1,1] => 2
[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [2,2,2,2,1,1] => 5
[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,12,10] => [2,2,2,2,2,1,1] => 6
[[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,9,8] => [2,2,2,2,1] => 5
[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [2,2,2,2,2] => 6
[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6,10,9] => [2,2,2,2,2] => 6
[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,8,5,10,7,9] => [2,2,2,2,1,1] => 5
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [2,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [2,1,1,1,1,1,1,1] => 2
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,1,2] => [2,1,1,1,1,1,1,1] => 2
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [2,1,1,1,1,1,1,1] => 2
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [2,1,1,1,1,1,1,1] => 2
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [2,1,1,1,1,1,1,1] => 2
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => [2,1,1,1,1,1,1,1] => 2
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [2,1,1,1,1,1,1,1] => 2
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [2,1,1,1,1,1,1,1,1] => 2
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [2,1,1,1,1,1,1,1,1] => 2
[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,8,9,2,3] => [2,2,1,1,1,1,1] => 3
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [2,1,1,1,1,1,1,1,1] => 2
[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,1,6,7,8,9,2,3,4] => [2,2,1,1,1,1,1] => 3
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [2,1,1,1,1,1,1,1,1] => 2
[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,1,7,8,9,2,3,4,5] => [2,2,1,1,1,1,1] => 3
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [2,1,1,1,1,1,1,1,1] => 2
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,1,8,9,2,3,4,5,6] => [2,2,1,1,1,1,1] => 3
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [2,1,1,1,1,1,1,1,1] => 2
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,1,9,2,3,4,5,6,7] => [2,2,1,1,1,1,1] => 3
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1,1] => 2
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [2,2,2,2,1,1] => 5
[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,9,8,10] => [2,2,2,2,1,1] => 5
[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,8,5,9,7,10] => [2,2,2,2,1,1] => 5
[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,7,5,9,8,10] => [2,2,2,2,1,1] => 5
[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8,10] => [2,2,2,2,1,1] => 5
[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [2,2,2,2,1,1] => 5
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,7,9] => [2,1,1,1,1,1,1,1] => 2
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,2,3,4,5,6,7,8,10] => [2,1,1,1,1,1,1,1,1] => 2
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [7,8,1,9,2,3,4,5,6] => [2,2,1,1,1,1,1] => 3
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,7,8,1,9,2,3,4,5] => [2,2,1,1,1,1,1] => 3
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,8,1,9,2,3,4] => [2,2,1,1,1,1,1] => 3
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,8,1,9,2,3] => [2,2,1,1,1,1,1] => 3
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,1,9,2] => [2,2,1,1,1,1,1] => 3
[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,6,8] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,5,7,8] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [2,1,1,1,1,1,1,1] => 2
[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [2,1,1,1,1,1,1,1] => 2
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,2,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 2
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 2
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,1,2,3,4,5,6,8] => [2,1,1,1,1,1,1,1] => 2
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,1,3,4,5,6,9,7] => [2,2,1,1,1,1,1] => 3
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,1,2,9,3,4,5,6,7] => [2,2,1,1,1,1,1] => 3
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,1,2,3,9,4,5,6,7] => [2,2,1,1,1,1,1] => 3
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,1,2,3,4,9,5,6,7] => [2,2,1,1,1,1,1] => 3
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,9,6,7] => [2,2,1,1,1,1,1] => 3
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,9,7] => [2,2,1,1,1,1,1] => 3
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => [2,2,1,1,1,1,1,1] => 3
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,1,2,3,4,10,5,6,7,8] => [2,2,1,1,1,1,1,1] => 3
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,1,2,3,4,5,6,10,7,8] => [2,2,1,1,1,1,1,1] => 3
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [2,2,1,1,1,1,1,1] => 3
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [2,1,1,1,1,1,1,1] => 2
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,2,3,4] => [2,1,1,1,1,1,1,1] => 2
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,7,8,2,9] => [2,2,1,1,1,1,1] => 3
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [2,2,1,1,1,1,1] => 3
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1,1] => 2
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9] => [2,2,1,1,1,1,1] => 3
[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7,10,9] => [2,2,2,2,2] => 6
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [6,7,1,9,2,3,4,5,8] => [2,2,1,1,1,1,1] => 3
[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7,9] => [2,2,2,2,1] => 5
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [2,1,1,1,1,1,1,1,1] => 2
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,4,5,6,7,8] => [2,2,1,1,1,1,1] => 3
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,9,2,4,5,6,7,8] => [2,2,1,1,1,1,1] => 3
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,7,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,1,7,8] => [2,1,1,1,1,1,1,1] => 2
[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,9,1,3,4] => [2,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => [2,1,1,1,1,1,1,1,1] => 2
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,2,3,4,5,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,2,3,4,5,8,6,9] => [2,2,1,1,1,1,1] => 3
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,1,2,3,4,7,5,8,9] => [2,2,1,1,1,1,1] => 3
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,2,3,6,4,7,8,9] => [2,2,1,1,1,1,1] => 3
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,3,6,7,8,9] => [2,2,1,1,1,1,1] => 3
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [2,1,1,1,1,1,1,1,1,1] => 2
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,2,8] => [2,1,1,1,1,1,1,1] => 2
[[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [3,5,1,2,6,4,8,7,9] => [2,2,2,1,1,1] => 4
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,9,1,2,3,4,8] => [2,1,1,1,1,1,1,1] => 2
[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,8,1,2,3,4,9] => [2,1,1,1,1,1,1,1] => 2
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,1,2,3,4,5,8,9,6] => [2,2,1,1,1,1,1] => 3
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,7,1,8,9,2] => [2,2,1,1,1,1,1] => 3
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,9,1,10,2] => [2,2,1,1,1,1,1,1] => 3
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [2,2,1,1,1,1,1] => 3
[[[.,[.,[.,[.,[[[.,.],.],.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,6,9,1,2,7,8] => [2,1,1,1,1,1,1,1] => 2
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,9,3] => [2,2,1,1,1,1,1] => 3
[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,9,4] => [2,2,1,1,1,1,1] => 3
[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,1,2,3,4,7,8,9,5] => [2,2,1,1,1,1,1] => 3
[[[.,[.,.]],[.,.]],[[.,.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6,9,8] => [2,2,2,2,1] => 5
[[[.,.],[[.,.],.]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,4,7,6,9,8] => [2,2,2,2,1] => 5
[[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,1,2,5,6,7,8,9,4] => [2,2,1,1,1,1,1] => 3
[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [2,1,1,1,1,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [2,2,1,1,1,1,1,1] => 3
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,4 1,11,2 1,26,15 1,57,69,5 1,120,252,56
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 4\ q^{2}$
$F_{4} = q + 11\ q^{2} + 2\ q^{3}$
$F_{5} = q + 26\ q^{2} + 15\ q^{3}$
$F_{6} = q + 57\ q^{2} + 69\ q^{3} + 5\ q^{4}$
$F_{7} = q + 120\ q^{2} + 252\ q^{3} + 56\ q^{4}$
Description
The number of ordered refinements of an integer partition.
This is, for an integer partition $\mu = (\mu_1,\ldots,\mu_n)$ the number of integer partition $\lambda = (\lambda_1,\ldots,\lambda_m)$ such that there are indices $1 = a_0 < \ldots < a_n = m$ with $\mu_j = \lambda_{a_{j-1}} + \ldots + \lambda_{a_j-1}$.
This is, for an integer partition $\mu = (\mu_1,\ldots,\mu_n)$ the number of integer partition $\lambda = (\lambda_1,\ldots,\lambda_m)$ such that there are indices $1 = a_0 < \ldots < a_n = m$ with $\mu_j = \lambda_{a_{j-1}} + \ldots + \lambda_{a_j-1}$.
Map
LLPS
Description
The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
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