Identifier
-
Mp00020:
Binary trees
—to Tamari-corresponding Dyck path⟶
Dyck paths
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
St000142: Integer partitions ⟶ ℤ
Values
[.,.] => [1,0] => [1] => [1] => 0
[.,[.,.]] => [1,1,0,0] => [2,1] => [2] => 1
[[.,.],.] => [1,0,1,0] => [1,2] => [1,1] => 0
[.,[.,[.,.]]] => [1,1,1,0,0,0] => [3,1,2] => [2,1] => 1
[.,[[.,.],.]] => [1,1,0,1,0,0] => [2,3,1] => [2,1] => 1
[[.,.],[.,.]] => [1,0,1,1,0,0] => [1,3,2] => [2,1] => 1
[[.,[.,.]],.] => [1,1,0,0,1,0] => [2,1,3] => [2,1] => 1
[[[.,.],.],.] => [1,0,1,0,1,0] => [1,2,3] => [1,1,1] => 0
[.,[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => [2,1,1] => 1
[.,[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => [2,1,1] => 1
[.,[[.,.],[.,.]]] => [1,1,0,1,1,0,0,0] => [2,4,1,3] => [2,1,1] => 1
[.,[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => [2,2] => 2
[.,[[[.,.],.],.]] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,1,1] => 1
[[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => [2,1,1] => 1
[[.,.],[[.,.],.]] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,1,1] => 1
[[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,2] => 2
[[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => [2,1,1] => 1
[[.,[.,[.,.]]],.] => [1,1,1,0,0,0,1,0] => [3,1,2,4] => [2,1,1] => 1
[[.,[[.,.],.]],.] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,1,1] => 1
[[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,1,1] => 1
[[[.,[.,.]],.],.] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,1] => 1
[[[[.,.],.],.],.] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,1,1,1] => 0
[.,[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [2,1,1,1] => 1
[.,[.,[.,[[.,.],.]]]] => [1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [2,1,1,1] => 1
[.,[.,[[.,.],[.,.]]]] => [1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [2,1,1,1] => 1
[.,[.,[[.,[.,.]],.]]] => [1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [2,2,1] => 2
[.,[.,[[[.,.],.],.]]] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [2,1,1,1] => 1
[.,[[.,.],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [2,1,1,1] => 1
[.,[[.,.],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [2,1,1,1] => 1
[.,[[.,[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [2,2,1] => 2
[.,[[[.,.],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [2,1,1,1] => 1
[.,[[.,[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [2,2,1] => 2
[.,[[.,[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [2,2,1] => 2
[.,[[[.,.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [2,2,1] => 2
[.,[[[.,[.,.]],.],.]] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [2,2,1] => 2
[.,[[[[.,.],.],.],.]] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,1,1,1] => 1
[[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [2,1,1,1] => 1
[[.,.],[.,[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [2,1,1,1] => 1
[[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [2,1,1,1] => 1
[[.,.],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [2,2,1] => 2
[[.,.],[[[.,.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,1,1,1] => 1
[[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [2,2,1] => 2
[[.,[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,2,1] => 2
[[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [2,1,1,1] => 1
[[[.,.],.],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [2,1,1,1] => 1
[[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [2,2,1] => 2
[[.,[[.,.],.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,2,1] => 2
[[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,2,1] => 2
[[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,2,1] => 2
[[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [2,1,1,1] => 1
[[.,[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [2,1,1,1] => 1
[[.,[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [2,1,1,1] => 1
[[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [2,1,1,1] => 1
[[.,[[.,[.,.]],.]],.] => [1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [2,2,1] => 2
[[.,[[[.,.],.],.]],.] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,1,1,1] => 1
[[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [2,1,1,1] => 1
[[[.,.],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [2,1,1,1] => 1
[[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,2,1] => 2
[[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,1,1,1] => 1
[[[.,[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [2,1,1,1] => 1
[[[.,[[.,.],.]],.],.] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,1,1,1] => 1
[[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,1,1,1] => 1
[[[[.,[.,.]],.],.],.] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,1,1] => 1
[[[[[.,.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [2,1,1,1,1] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [2,1,1,1,1] => 1
[.,[.,[.,[[.,.],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [2,1,1,1,1] => 1
[.,[.,[.,[[.,[.,.]],.]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [2,2,1,1] => 2
[.,[.,[.,[[[.,.],.],.]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [2,1,1,1,1] => 1
[.,[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [2,1,1,1,1] => 1
[.,[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [2,1,1,1,1] => 1
[.,[.,[[.,[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [2,2,1,1] => 2
[.,[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [2,1,1,1,1] => 1
[.,[.,[[.,[.,[.,.]]],.]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [2,2,1,1] => 2
[.,[.,[[.,[[.,.],.]],.]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [2,2,1,1] => 2
[.,[.,[[[.,.],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [2,2,1,1] => 2
[.,[.,[[[.,[.,.]],.],.]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [2,2,1,1] => 2
[.,[.,[[[[.,.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [2,1,1,1,1] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [2,1,1,1,1] => 1
[.,[[.,.],[.,[[.,.],.]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [2,1,1,1,1] => 1
[.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [2,1,1,1,1] => 1
[.,[[.,.],[[.,[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [2,2,1,1] => 2
[.,[[.,.],[[[.,.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [2,1,1,1,1] => 1
[.,[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [2,2,1,1] => 2
[.,[[.,[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [2,2,1,1] => 2
[.,[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [2,1,1,1,1] => 1
[.,[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [2,1,1,1,1] => 1
[.,[[.,[.,[.,.]]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [2,2,1,1] => 2
[.,[[.,[[.,.],.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [2,2,1,1] => 2
[.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [2,2,1,1] => 2
[.,[[[.,[.,.]],.],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [2,2,1,1] => 2
[.,[[[[.,.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [2,1,1,1,1] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [2,2,1,1] => 2
[.,[[.,[.,[[.,.],.]]],.]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [2,2,1,1] => 2
[.,[[.,[[.,.],[.,.]]],.]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [2,2,1,1] => 2
[.,[[.,[[.,[.,.]],.]],.]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [2,2,2] => 3
[.,[[.,[[[.,.],.],.]],.]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [2,2,1,1] => 2
[.,[[[.,.],[.,[.,.]]],.]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [2,2,1,1] => 2
[.,[[[.,.],[[.,.],.]],.]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [2,2,1,1] => 2
[.,[[[.,[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [2,2,2] => 3
[.,[[[[.,.],.],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [2,2,1,1] => 2
>>> Load all 1951 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [2,2,1,1] => 2
[.,[[[.,[[.,.],.]],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [2,2,1,1] => 2
[.,[[[[.,.],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [2,2,1,1] => 2
[.,[[[[.,[.,.]],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [2,2,1,1] => 2
[.,[[[[[.,.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,1,1,1,1] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [2,1,1,1,1] => 1
[[.,.],[.,[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [2,1,1,1,1] => 1
[[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [2,1,1,1,1] => 1
[[.,.],[.,[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [2,2,1,1] => 2
[[.,.],[.,[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [2,1,1,1,1] => 1
[[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [2,1,1,1,1] => 1
[[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [2,1,1,1,1] => 1
[[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [2,2,1,1] => 2
[[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [2,1,1,1,1] => 1
[[.,.],[[.,[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [2,2,1,1] => 2
[[.,.],[[.,[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [2,2,1,1] => 2
[[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [2,2,1,1] => 2
[[.,.],[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [2,2,1,1] => 2
[[.,.],[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,1,1,1,1] => 1
[[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [2,2,1,1] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [2,2,1,1] => 2
[[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [2,2,1,1] => 2
[[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [2,2,2] => 3
[[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,2,1,1] => 2
[[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [2,1,1,1,1] => 1
[[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [2,1,1,1,1] => 1
[[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [2,1,1,1,1] => 1
[[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [2,2,1,1] => 2
[[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [2,1,1,1,1] => 1
[[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [2,2,1,1] => 2
[[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [2,2,1,1] => 2
[[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [2,2,1,1] => 2
[[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,2,1,1] => 2
[[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [2,2,1,1] => 2
[[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [2,2,1,1] => 2
[[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [2,2,1,1] => 2
[[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,2,1,1] => 2
[[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [2,1,1,1,1] => 1
[[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [2,1,1,1,1] => 1
[[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [2,2,1,1] => 2
[[.,[.,[[.,.],.]]],[.,.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [2,2,1,1] => 2
[[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [2,2,1,1] => 2
[[.,[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [2,2,2] => 3
[[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [2,2,1,1] => 2
[[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [2,2,1,1] => 2
[[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [2,2,1,1] => 2
[[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,2,2] => 3
[[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [2,2,1,1] => 2
[[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [2,2,1,1] => 2
[[[.,[[.,.],.]],.],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,2,1,1] => 2
[[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,2,1,1] => 2
[[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,2,1,1] => 2
[[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [2,1,1,1,1] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [2,1,1,1,1] => 1
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [2,1,1,1,1] => 1
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [2,1,1,1,1] => 1
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [2,2,1,1] => 2
[[.,[.,[[[.,.],.],.]]],.] => [1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [2,1,1,1,1] => 1
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [2,1,1,1,1] => 1
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [2,1,1,1,1] => 1
[[.,[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [2,2,1,1] => 2
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [2,1,1,1,1] => 1
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [2,2,1,1] => 2
[[.,[[.,[[.,.],.]],.]],.] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [2,2,1,1] => 2
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [2,2,1,1] => 2
[[.,[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [2,2,1,1] => 2
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,1,1,1,1] => 1
[[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [2,1,1,1,1] => 1
[[[.,.],[.,[[.,.],.]]],.] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [2,1,1,1,1] => 1
[[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [2,1,1,1,1] => 1
[[[.,.],[[.,[.,.]],.]],.] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [2,2,1,1] => 2
[[[.,.],[[[.,.],.],.]],.] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [2,1,1,1,1] => 1
[[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [2,2,1,1] => 2
[[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,2,1,1] => 2
[[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [2,1,1,1,1] => 1
[[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [2,1,1,1,1] => 1
[[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [2,2,1,1] => 2
[[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,2,1,1] => 2
[[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,2,1,1] => 2
[[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,2,1,1] => 2
[[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,1,1,1,1] => 1
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [2,1,1,1,1] => 1
[[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [2,1,1,1,1] => 1
[[[.,[[.,.],[.,.]]],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [2,1,1,1,1] => 1
[[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [2,2,1,1] => 2
[[[.,[[[.,.],.],.]],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,1,1,1,1] => 1
[[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [2,1,1,1,1] => 1
[[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [2,1,1,1,1] => 1
[[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,2,1,1] => 2
[[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,1,1,1,1] => 1
[[[[.,[.,[.,.]]],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [2,1,1,1,1] => 1
[[[[.,[[.,.],.]],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,1,1,1,1] => 1
[[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,1,1,1,1] => 1
[[[[[.,[.,.]],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,1,1,1] => 1
[[[[[[.,.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [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] => 1
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [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] => 1
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [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] => 1
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [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] => 2
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [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] => 1
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [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] => 1
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [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] => 1
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [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] => 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] => 1
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [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] => 2
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [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] => 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] => 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] => 2
[.,[.,[.,[[[[.,.],.],.],.]]]] => [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] => 1
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [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] => 1
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [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] => 1
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [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] => 1
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [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] => 2
[.,[.,[[.,.],[[[.,.],.],.]]]] => [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] => 1
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [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] => 2
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [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] => 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] => 1
[.,[.,[[[.,.],.],[[.,.],.]]]] => [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] => 1
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [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] => 2
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [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] => 2
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [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] => 2
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [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] => 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] => 1
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [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] => 2
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [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] => 2
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [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] => 2
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [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] => 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] => 2
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [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] => 2
[.,[.,[[[.,.],[[.,.],.]],.]]] => [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] => 2
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [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] => 3
[.,[.,[[[[.,.],.],[.,.]],.]]] => [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] => 2
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [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] => 2
[.,[.,[[[.,[[.,.],.]],.],.]]] => [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] => 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] => 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] => 2
[.,[.,[[[[[.,.],.],.],.],.]]] => [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] => 1
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [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] => 1
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [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] => 1
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [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] => 1
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [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] => 2
[.,[[.,.],[.,[[[.,.],.],.]]]] => [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] => 1
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [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] => 1
[.,[[.,.],[[.,.],[[.,.],.]]]] => [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] => 1
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [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] => 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] => 1
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [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] => 2
[.,[[.,.],[[.,[[.,.],.]],.]]] => [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] => 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] => 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] => 2
[.,[[.,.],[[[[.,.],.],.],.]]] => [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] => 1
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [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] => 2
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [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] => 2
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [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] => 2
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [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] => 3
[.,[[.,[.,.]],[[[.,.],.],.]]] => [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] => 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] => 1
[.,[[[.,.],.],[.,[[.,.],.]]]] => [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] => 1
[.,[[[.,.],.],[[.,.],[.,.]]]] => [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] => 1
[.,[[[.,.],.],[[.,[.,.]],.]]] => [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] => 2
[.,[[[.,.],.],[[[.,.],.],.]]] => [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] => 1
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [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] => 2
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [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] => 2
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [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] => 2
[.,[[.,[[.,.],.]],[[.,.],.]]] => [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] => 2
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [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] => 2
[.,[[[.,.],[.,.]],[[.,.],.]]] => [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] => 2
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [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] => 2
[.,[[[.,[.,.]],.],[[.,.],.]]] => [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] => 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] => 1
[.,[[[[.,.],.],.],[[.,.],.]]] => [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] => 1
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [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] => 2
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [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] => 2
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [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] => 2
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [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] => 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] => 2
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [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] => 2
[.,[[[.,.],[[.,.],.]],[.,.]]] => [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] => 2
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [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] => 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] => 2
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [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] => 2
[.,[[[.,[[.,.],.]],.],[.,.]]] => [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] => 2
[.,[[[[.,.],[.,.]],.],[.,.]]] => [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] => 2
[.,[[[[.,[.,.]],.],.],[.,.]]] => [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] => 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] => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [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] => 2
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [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] => 2
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [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] => 2
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [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] => 3
[.,[[.,[.,[[[.,.],.],.]]],.]] => [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] => 2
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [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] => 2
[.,[[.,[[.,.],[[.,.],.]]],.]] => [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] => 2
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [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] => 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] => 2
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [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] => 3
[.,[[.,[[.,[[.,.],.]],.]],.]] => [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] => 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] => 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] => 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] => 2
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [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] => 2
[.,[[[.,.],[.,[[.,.],.]]],.]] => [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] => 2
[.,[[[.,.],[[.,.],[.,.]]],.]] => [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] => 2
[.,[[[.,.],[[.,[.,.]],.]],.]] => [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] => 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] => 2
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [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] => 3
[.,[[[.,[.,.]],[[.,.],.]],.]] => [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] => 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] => 2
[.,[[[[.,.],.],[[.,.],.]],.]] => [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] => 2
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [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] => 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] => 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] => 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] => 3
[.,[[[[[.,.],.],.],[.,.]],.]] => [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] => 2
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [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] => 2
[.,[[[.,[.,[[.,.],.]]],.],.]] => [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] => 2
[.,[[[.,[[.,.],[.,.]]],.],.]] => [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] => 2
[.,[[[.,[[.,[.,.]],.]],.],.]] => [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] => 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] => 2
[.,[[[[.,.],[.,[.,.]]],.],.]] => [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] => 2
[.,[[[[.,.],[[.,.],.]],.],.]] => [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] => 2
[.,[[[[.,[.,.]],[.,.]],.],.]] => [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] => 3
[.,[[[[[.,.],.],[.,.]],.],.]] => [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] => 2
[.,[[[[.,[.,[.,.]]],.],.],.]] => [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] => 2
[.,[[[[.,[[.,.],.]],.],.],.]] => [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] => 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] => 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] => 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] => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [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] => 1
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [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] => 1
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [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] => 1
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [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] => 2
[[.,.],[.,[.,[[[.,.],.],.]]]] => [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] => 1
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [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] => 1
[[.,.],[.,[[.,.],[[.,.],.]]]] => [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] => 1
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [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] => 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] => 1
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [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] => 2
[[.,.],[.,[[.,[[.,.],.]],.]]] => [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] => 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] => 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] => 2
[[.,.],[.,[[[[.,.],.],.],.]]] => [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] => 1
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [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] => 1
[[.,.],[[.,.],[.,[[.,.],.]]]] => [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] => 1
[[.,.],[[.,.],[[.,.],[.,.]]]] => [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] => 1
[[.,.],[[.,.],[[.,[.,.]],.]]] => [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] => 2
[[.,.],[[.,.],[[[.,.],.],.]]] => [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] => 1
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [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] => 2
[[.,.],[[.,[.,.]],[[.,.],.]]] => [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] => 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] => 1
[[.,.],[[[.,.],.],[[.,.],.]]] => [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] => 1
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [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] => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => [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] => 2
[[.,.],[[[.,.],[.,.]],[.,.]]] => [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] => 2
[[.,.],[[[.,[.,.]],.],[.,.]]] => [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] => 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] => 1
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [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] => 2
[[.,.],[[.,[.,[[.,.],.]]],.]] => [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] => 2
[[.,.],[[.,[[.,.],[.,.]]],.]] => [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] => 2
[[.,.],[[.,[[.,[.,.]],.]],.]] => [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] => 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] => 2
[[.,.],[[[.,.],[.,[.,.]]],.]] => [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] => 2
[[.,.],[[[.,.],[[.,.],.]],.]] => [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] => 2
[[.,.],[[[.,[.,.]],[.,.]],.]] => [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] => 3
[[.,.],[[[[.,.],.],[.,.]],.]] => [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] => 2
[[.,.],[[[.,[.,[.,.]]],.],.]] => [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] => 2
[[.,.],[[[.,[[.,.],.]],.],.]] => [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] => 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] => 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] => 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] => 1
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [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] => 2
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [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] => 2
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [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] => 2
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [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] => 3
[[.,[.,.]],[.,[[[.,.],.],.]]] => [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] => 2
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [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] => 2
[[.,[.,.]],[[.,.],[[.,.],.]]] => [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] => 2
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [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] => 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] => 2
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [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] => 3
[[.,[.,.]],[[.,[[.,.],.]],.]] => [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] => 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] => 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] => 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] => 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] => 1
[[[.,.],.],[.,[.,[[.,.],.]]]] => [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] => 1
[[[.,.],.],[.,[[.,.],[.,.]]]] => [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] => 1
[[[.,.],.],[.,[[.,[.,.]],.]]] => [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] => 2
[[[.,.],.],[.,[[[.,.],.],.]]] => [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] => 1
[[[.,.],.],[[.,.],[.,[.,.]]]] => [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] => 1
[[[.,.],.],[[.,.],[[.,.],.]]] => [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] => 1
[[[.,.],.],[[.,[.,.]],[.,.]]] => [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] => 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] => 1
[[[.,.],.],[[.,[.,[.,.]]],.]] => [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] => 2
[[[.,.],.],[[.,[[.,.],.]],.]] => [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] => 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] => 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] => 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] => 1
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [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] => 2
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [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] => 2
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [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] => 2
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [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] => 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] => 2
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [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] => 2
[[.,[[.,.],.]],[.,[[.,.],.]]] => [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] => 2
[[.,[[.,.],.]],[[.,.],[.,.]]] => [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] => 2
[[.,[[.,.],.]],[[.,[.,.]],.]] => [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] => 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] => 2
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [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] => 2
[[[.,.],[.,.]],[.,[[.,.],.]]] => [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] => 2
[[[.,.],[.,.]],[[.,.],[.,.]]] => [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] => 2
[[[.,.],[.,.]],[[.,[.,.]],.]] => [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] => 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] => 2
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [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] => 2
[[[.,[.,.]],.],[.,[[.,.],.]]] => [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] => 2
[[[.,[.,.]],.],[[.,.],[.,.]]] => [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] => 2
[[[.,[.,.]],.],[[.,[.,.]],.]] => [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] => 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] => 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] => 1
[[[[.,.],.],.],[.,[[.,.],.]]] => [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] => 1
[[[[.,.],.],.],[[.,.],[.,.]]] => [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] => 1
[[[[.,.],.],.],[[.,[.,.]],.]] => [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] => 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] => 1
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [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] => 2
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [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] => 2
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [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] => 2
[[.,[.,[[.,.],.]]],[[.,.],.]] => [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] => 2
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [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] => 2
[[.,[[.,.],[.,.]]],[[.,.],.]] => [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] => 2
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [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] => 3
[[.,[[.,[.,.]],.]],[[.,.],.]] => [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] => 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] => 2
[[.,[[[.,.],.],.]],[[.,.],.]] => [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] => 2
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [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] => 2
[[[.,.],[.,[.,.]]],[[.,.],.]] => [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] => 2
[[[.,.],[[.,.],.]],[.,[.,.]]] => [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] => 2
[[[.,.],[[.,.],.]],[[.,.],.]] => [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] => 2
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [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] => 3
[[[.,[.,.]],[.,.]],[[.,.],.]] => [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] => 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] => 2
[[[[.,.],.],[.,.]],[[.,.],.]] => [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] => 2
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [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] => 2
[[[.,[.,[.,.]]],.],[[.,.],.]] => [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] => 2
[[[.,[[.,.],.]],.],[.,[.,.]]] => [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] => 2
[[[.,[[.,.],.]],.],[[.,.],.]] => [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] => 2
[[[[.,.],[.,.]],.],[.,[.,.]]] => [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] => 2
[[[[.,.],[.,.]],.],[[.,.],.]] => [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] => 2
[[[[.,[.,.]],.],.],[.,[.,.]]] => [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] => 2
[[[[.,[.,.]],.],.],[[.,.],.]] => [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] => 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] => 1
[[[[[.,.],.],.],.],[[.,.],.]] => [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] => 1
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [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] => 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] => 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] => 2
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [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] => 3
[[.,[.,[[[.,.],.],.]]],[.,.]] => [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] => 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] => 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] => 2
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [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] => 3
[[.,[[[.,.],.],[.,.]]],[.,.]] => [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] => 2
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [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] => 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] => 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] => 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] => 3
[[.,[[[[.,.],.],.],.]],[.,.]] => [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] => 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] => 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] => 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] => 2
[[[.,.],[[.,[.,.]],.]],[.,.]] => [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] => 3
[[[.,.],[[[.,.],.],.]],[.,.]] => [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] => 2
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [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] => 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] => 3
[[[[.,.],.],[.,[.,.]]],[.,.]] => [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] => 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] => 2
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [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] => 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] => 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] => 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] => 3
[[[[[.,.],.],.],[.,.]],[.,.]] => [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] => 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] => 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] => 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] => 2
[[[.,[[.,[.,.]],.]],.],[.,.]] => [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] => 3
[[[.,[[[.,.],.],.]],.],[.,.]] => [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] => 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] => 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] => 2
[[[[.,[.,.]],[.,.]],.],[.,.]] => [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] => 3
[[[[[.,.],.],[.,.]],.],[.,.]] => [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] => 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] => 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] => 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] => 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] => 2
[[[[[[.,.],.],.],.],.],[.,.]] => [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] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [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] => 1
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [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] => 1
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [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] => 1
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [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] => 2
[[.,[.,[.,[[[.,.],.],.]]]],.] => [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] => 1
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [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] => 1
[[.,[.,[[.,.],[[.,.],.]]]],.] => [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] => 1
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [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] => 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] => 1
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [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] => 2
[[.,[.,[[.,[[.,.],.]],.]]],.] => [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] => 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] => 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] => 2
[[.,[.,[[[[.,.],.],.],.]]],.] => [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] => 1
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [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] => 1
[[.,[[.,.],[.,[[.,.],.]]]],.] => [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] => 1
[[.,[[.,.],[[.,.],[.,.]]]],.] => [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] => 1
[[.,[[.,.],[[.,[.,.]],.]]],.] => [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] => 2
[[.,[[.,.],[[[.,.],.],.]]],.] => [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] => 1
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [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] => 2
[[.,[[.,[.,.]],[[.,.],.]]],.] => [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] => 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] => 1
[[.,[[[.,.],.],[[.,.],.]]],.] => [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] => 1
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [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] => 2
[[.,[[.,[[.,.],.]],[.,.]]],.] => [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] => 2
[[.,[[[.,.],[.,.]],[.,.]]],.] => [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] => 2
[[.,[[[.,[.,.]],.],[.,.]]],.] => [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] => 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] => 1
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [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] => 2
[[.,[[.,[.,[[.,.],.]]],.]],.] => [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] => 2
[[.,[[.,[[.,.],[.,.]]],.]],.] => [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] => 2
[[.,[[.,[[.,[.,.]],.]],.]],.] => [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] => 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] => 2
[[.,[[[.,.],[.,[.,.]]],.]],.] => [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] => 2
[[.,[[[.,.],[[.,.],.]],.]],.] => [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] => 2
[[.,[[[.,[.,.]],[.,.]],.]],.] => [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] => 3
[[.,[[[[.,.],.],[.,.]],.]],.] => [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] => 2
[[.,[[[.,[.,[.,.]]],.],.]],.] => [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] => 2
[[.,[[[.,[[.,.],.]],.],.]],.] => [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] => 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] => 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] => 2
[[.,[[[[[.,.],.],.],.],.]],.] => [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] => 1
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [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] => 1
[[[.,.],[.,[.,[[.,.],.]]]],.] => [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] => 1
[[[.,.],[.,[[.,.],[.,.]]]],.] => [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] => 1
[[[.,.],[.,[[.,[.,.]],.]]],.] => [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] => 2
[[[.,.],[.,[[[.,.],.],.]]],.] => [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] => 1
[[[.,.],[[.,.],[.,[.,.]]]],.] => [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] => 1
[[[.,.],[[.,.],[[.,.],.]]],.] => [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] => 1
[[[.,.],[[.,[.,.]],[.,.]]],.] => [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] => 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] => 1
[[[.,.],[[.,[.,[.,.]]],.]],.] => [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] => 2
[[[.,.],[[.,[[.,.],.]],.]],.] => [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] => 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] => 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] => 2
[[[.,.],[[[[.,.],.],.],.]],.] => [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] => 1
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [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] => 2
[[[.,[.,.]],[.,[[.,.],.]]],.] => [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] => 2
[[[.,[.,.]],[[.,.],[.,.]]],.] => [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] => 2
[[[.,[.,.]],[[.,[.,.]],.]],.] => [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] => 3
[[[.,[.,.]],[[[.,.],.],.]],.] => [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] => 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] => 1
[[[[.,.],.],[.,[[.,.],.]]],.] => [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] => 1
[[[[.,.],.],[[.,.],[.,.]]],.] => [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] => 1
[[[[.,.],.],[[.,[.,.]],.]],.] => [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] => 2
[[[[.,.],.],[[[.,.],.],.]],.] => [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] => 1
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [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] => 2
[[[.,[.,[.,.]]],[[.,.],.]],.] => [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] => 2
[[[.,[[.,.],.]],[.,[.,.]]],.] => [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] => 2
[[[.,[[.,.],.]],[[.,.],.]],.] => [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] => 2
[[[[.,.],[.,.]],[.,[.,.]]],.] => [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] => 2
[[[[.,.],[.,.]],[[.,.],.]],.] => [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] => 2
[[[[.,[.,.]],.],[.,[.,.]]],.] => [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] => 2
[[[[.,[.,.]],.],[[.,.],.]],.] => [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] => 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] => 1
[[[[[.,.],.],.],[[.,.],.]],.] => [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] => 1
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [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] => 2
[[[.,[.,[[.,.],.]]],[.,.]],.] => [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] => 2
[[[.,[[.,.],[.,.]]],[.,.]],.] => [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] => 2
[[[.,[[.,[.,.]],.]],[.,.]],.] => [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] => 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] => 2
[[[[.,.],[.,[.,.]]],[.,.]],.] => [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] => 2
[[[[.,.],[[.,.],.]],[.,.]],.] => [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] => 2
[[[[.,[.,.]],[.,.]],[.,.]],.] => [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] => 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] => 2
[[[[.,[.,[.,.]]],.],[.,.]],.] => [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] => 2
[[[[.,[[.,.],.]],.],[.,.]],.] => [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] => 2
[[[[[.,.],[.,.]],.],[.,.]],.] => [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] => 2
[[[[[.,[.,.]],.],.],[.,.]],.] => [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] => 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] => 1
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [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] => 1
[[[.,[.,[.,[[.,.],.]]]],.],.] => [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] => 1
[[[.,[.,[[.,.],[.,.]]]],.],.] => [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] => 1
[[[.,[.,[[.,[.,.]],.]]],.],.] => [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] => 2
[[[.,[.,[[[.,.],.],.]]],.],.] => [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] => 1
[[[.,[[.,.],[.,[.,.]]]],.],.] => [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] => 1
[[[.,[[.,.],[[.,.],.]]],.],.] => [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] => 1
[[[.,[[.,[.,.]],[.,.]]],.],.] => [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] => 2
[[[.,[[[.,.],.],[.,.]]],.],.] => [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] => 1
[[[.,[[.,[.,[.,.]]],.]],.],.] => [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] => 2
[[[.,[[.,[[.,.],.]],.]],.],.] => [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] => 2
[[[.,[[[.,.],[.,.]],.]],.],.] => [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] => 2
[[[.,[[[.,[.,.]],.],.]],.],.] => [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] => 2
[[[.,[[[[.,.],.],.],.]],.],.] => [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] => 1
[[[[.,.],[.,[.,[.,.]]]],.],.] => [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] => 1
[[[[.,.],[.,[[.,.],.]]],.],.] => [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] => 1
[[[[.,.],[[.,.],[.,.]]],.],.] => [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] => 1
[[[[.,.],[[.,[.,.]],.]],.],.] => [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] => 2
[[[[.,.],[[[.,.],.],.]],.],.] => [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] => 1
[[[[.,[.,.]],[.,[.,.]]],.],.] => [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] => 2
[[[[.,[.,.]],[[.,.],.]],.],.] => [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] => 2
[[[[[.,.],.],[.,[.,.]]],.],.] => [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] => 1
[[[[[.,.],.],[[.,.],.]],.],.] => [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] => 1
[[[[.,[.,[.,.]]],[.,.]],.],.] => [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] => 2
[[[[.,[[.,.],.]],[.,.]],.],.] => [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] => 2
[[[[[.,.],[.,.]],[.,.]],.],.] => [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] => 2
[[[[[.,[.,.]],.],[.,.]],.],.] => [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] => 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] => 1
[[[[.,[.,[.,[.,.]]]],.],.],.] => [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] => 1
[[[[.,[.,[[.,.],.]]],.],.],.] => [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] => 1
[[[[.,[[.,.],[.,.]]],.],.],.] => [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] => 1
[[[[.,[[.,[.,.]],.]],.],.],.] => [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] => 2
[[[[.,[[[.,.],.],.]],.],.],.] => [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] => 1
[[[[[.,.],[.,[.,.]]],.],.],.] => [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] => 1
[[[[[.,.],[[.,.],.]],.],.],.] => [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] => 1
[[[[[.,[.,.]],[.,.]],.],.],.] => [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] => 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] => 1
[[[[[.,[.,[.,.]]],.],.],.],.] => [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] => 1
[[[[[.,[[.,.],.]],.],.],.],.] => [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] => 1
[[[[[[.,.],[.,.]],.],.],.],.] => [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] => 1
[[[[[[.,[.,.]],.],.],.],.],.] => [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] => 1
[[[[[[[.,.],.],.],.],.],.],.] => [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] => 0
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [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] => 1
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [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] => 1
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [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] => 1
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [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] => 2
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [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] => 1
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [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] => 1
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [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] => 1
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [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] => 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] => 1
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [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] => 2
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [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] => 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] => 2
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [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] => 1
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [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] => 1
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [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] => 1
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [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] => 1
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [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] => 2
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [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] => 1
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [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] => 2
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [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] => 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] => 1
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [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] => 1
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [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] => 2
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [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] => 2
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [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] => 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] => 1
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [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] => 2
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [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] => 2
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [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] => 2
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [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] => 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] => 2
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [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] => 2
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [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] => 2
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [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] => 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] => 2
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [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] => 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] => 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] => 2
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [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] => 1
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [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] => 1
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [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] => 1
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [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] => 1
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [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] => 2
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [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] => 1
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [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] => 1
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [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] => 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] => 1
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [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] => 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] => 2
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [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] => 1
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [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] => 2
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [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] => 2
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [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] => 2
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [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] => 3
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [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] => 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] => 1
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [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] => 1
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [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] => 1
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [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] => 2
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [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] => 1
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [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] => 2
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [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] => 2
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [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] => 2
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [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] => 2
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [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] => 2
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [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] => 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] => 1
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [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] => 1
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [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] => 2
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [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] => 2
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [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] => 2
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [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] => 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] => 2
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [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] => 2
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [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] => 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] => 2
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [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] => 2
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [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] => 2
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [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] => 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] => 1
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [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] => 2
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [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] => 2
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [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] => 3
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [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] => 2
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [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] => 2
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [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] => 2
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [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] => 2
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [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] => 3
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [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] => 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] => 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] => 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] => 2
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [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] => 2
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [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] => 2
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [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] => 2
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => [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] => 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] => 2
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [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] => 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] => 2
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [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] => 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] => 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] => 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] => 3
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [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] => 2
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [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] => 2
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => [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] => 2
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => [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] => 2
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => [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] => 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] => 2
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [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] => 2
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [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] => 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] => 2
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [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] => 2
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [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] => 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] => 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] => 2
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [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] => 1
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [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] => 1
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [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] => 1
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [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] => 1
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [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] => 2
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [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] => 1
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [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] => 1
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [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] => 1
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [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] => 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] => 1
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [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] => 2
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [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] => 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] => 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] => 2
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [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] => 1
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [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] => 1
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [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] => 1
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [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] => 1
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [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] => 2
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [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] => 1
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [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] => 2
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [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] => 2
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [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] => 1
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [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] => 2
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [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] => 2
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [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] => 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] => 1
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [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] => 2
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [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] => 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] => 2
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [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] => 2
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [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] => 2
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [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] => 3
[.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [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] => 2
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [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] => 2
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [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] => 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] => 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] => 2
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [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] => 1
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [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] => 2
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [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] => 2
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [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] => 2
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [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] => 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] => 2
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [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] => 2
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [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] => 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] => 2
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [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] => 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] => 3
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [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] => 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] => 1
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [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] => 1
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [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] => 1
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [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] => 1
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [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] => 1
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [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] => 1
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [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] => 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] => 1
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [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] => 2
[.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [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] => 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] => 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] => 2
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [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] => 1
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [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] => 2
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [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] => 2
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [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] => 2
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [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] => 2
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [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] => 2
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [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] => 2
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [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] => 2
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [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] => 2
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [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] => 3
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [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] => 2
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [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] => 2
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [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] => 2
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [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] => 3
[.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [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] => 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] => 1
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [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] => 1
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [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] => 1
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [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] => 2
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [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] => 1
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [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] => 2
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [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] => 2
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [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] => 2
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [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] => 2
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [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] => 2
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [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] => 2
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [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] => 3
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [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] => 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] => 2
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [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] => 2
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [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] => 2
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [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] => 2
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [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] => 2
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [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] => 3
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [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] => 3
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [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] => 2
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [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] => 2
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [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] => 2
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [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] => 2
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [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] => 2
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [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] => 2
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [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] => 2
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [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] => 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] => 1
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [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] => 1
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [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] => 2
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [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] => 2
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [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] => 2
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [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] => 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] => 2
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [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] => 2
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [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] => 2
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [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] => 3
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [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] => 3
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [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] => 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] => 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] => 2
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [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] => 2
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [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] => 2
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [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] => 2
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [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] => 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] => 2
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [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] => 3
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [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] => 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] => 2
[.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [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] => 2
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [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] => 3
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [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] => 3
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [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] => 3
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [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] => 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] => 2
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [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] => 2
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [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] => 2
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [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] => 2
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [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] => 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] => 2
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [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] => 2
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [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] => 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] => 2
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [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] => 2
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [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] => 2
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [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] => 2
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [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] => 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] => 1
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [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] => 2
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [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] => 2
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [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] => 2
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [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] => 3
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [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] => 2
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [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] => 2
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [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] => 2
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [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] => 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] => 2
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [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] => 3
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]] => [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] => 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] => 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] => 3
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [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] => 2
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [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] => 2
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => [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] => 2
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [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] => 2
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [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] => 3
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [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] => 2
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [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] => 3
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [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] => 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] => 2
[.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [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] => 2
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [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] => 3
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [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] => 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] => 2
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [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] => 3
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [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] => 3
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [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] => 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] => 3
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [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] => 3
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [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] => 3
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [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] => 4
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [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] => 3
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [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] => 3
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [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] => 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] => 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] => 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] => 2
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [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] => 2
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [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] => 2
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [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] => 2
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [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] => 3
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [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] => 2
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [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] => 2
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [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] => 2
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [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] => 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] => 2
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [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] => 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] => 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] => 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] => 2
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [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] => 3
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [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] => 3
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [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] => 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] => 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] => 2
[.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [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] => 2
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [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] => 2
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [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] => 2
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [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] => 3
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [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] => 3
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [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] => 3
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [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] => 3
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [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] => 3
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [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] => 3
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [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] => 3
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [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] => 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] => 2
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [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] => 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] => 3
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [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] => 4
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [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] => 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] => 3
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [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] => 4
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [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] => 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] => 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] => 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] => 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] => 3
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [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] => 2
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [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] => 2
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [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] => 2
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [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] => 3
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [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] => 2
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [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] => 2
[.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [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] => 2
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [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] => 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] => 2
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [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] => 3
[.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [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] => 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] => 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] => 2
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [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] => 2
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [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] => 2
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [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] => 2
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [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] => 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] => 2
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [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] => 3
[.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [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] => 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] => 2
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [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] => 2
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [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] => 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] => 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] => 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] => 3
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [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] => 2
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [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] => 2
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [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] => 2
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [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] => 2
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [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] => 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] => 2
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [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] => 2
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [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] => 2
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [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] => 3
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [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] => 2
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [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] => 2
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [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] => 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] => 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] => 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] => 1
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [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] => 1
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [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] => 1
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [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] => 1
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [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] => 2
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [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] => 1
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [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] => 1
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [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] => 1
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [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] => 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] => 1
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [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] => 2
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [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] => 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] => 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] => 2
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [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] => 1
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [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] => 1
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [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] => 1
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [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] => 1
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [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] => 2
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [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] => 1
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [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] => 2
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [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] => 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] => 1
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [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] => 2
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [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] => 2
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [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] => 2
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [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] => 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] => 1
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [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] => 2
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [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] => 2
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [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] => 2
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [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] => 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] => 2
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [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] => 2
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [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] => 2
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [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] => 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] => 2
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [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] => 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] => 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] => 2
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [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] => 1
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [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] => 1
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [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] => 1
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [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] => 2
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [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] => 1
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [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] => 1
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [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] => 1
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [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] => 1
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [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] => 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] => 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] => 2
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [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] => 1
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [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] => 2
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [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] => 2
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [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] => 2
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [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] => 3
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [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] => 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] => 1
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [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] => 1
[[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [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] => 1
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [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] => 2
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [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] => 2
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [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] => 2
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [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] => 2
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [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] => 2
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [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] => 2
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [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] => 2
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [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] => 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] => 1
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [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] => 1
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [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] => 2
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [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] => 2
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [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] => 2
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [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] => 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] => 2
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [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] => 2
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [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] => 2
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [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] => 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] => 2
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [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] => 2
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [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] => 2
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [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] => 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] => 1
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [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] => 2
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [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] => 2
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [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] => 3
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [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] => 2
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [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] => 2
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [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] => 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] => 2
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [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] => 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] => 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] => 2
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [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] => 2
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [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] => 2
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [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] => 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] => 2
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [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] => 3
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [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] => 2
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [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] => 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] => 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] => 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] => 3
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [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] => 2
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [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] => 2
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [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] => 2
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [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] => 2
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [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] => 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] => 2
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [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] => 2
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [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] => 2
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [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] => 2
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [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] => 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] => 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] => 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] => 1
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [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] => 2
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [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] => 2
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [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] => 2
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [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] => 3
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [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] => 2
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [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] => 2
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [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] => 2
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [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] => 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] => 2
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [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] => 3
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [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] => 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] => 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] => 3
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [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] => 2
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [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] => 2
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [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] => 2
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [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] => 2
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [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] => 2
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [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] => 3
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [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] => 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] => 2
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [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] => 2
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [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] => 3
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [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] => 3
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [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] => 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] => 2
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [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] => 3
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [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] => 3
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [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] => 3
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [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] => 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] => 3
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [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] => 3
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [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] => 3
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [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] => 4
[[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [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] => 3
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [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] => 3
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [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] => 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] => 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] => 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] => 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] => 1
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [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] => 1
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [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] => 1
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [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] => 2
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [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] => 1
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [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] => 1
[[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [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] => 1
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [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] => 2
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [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] => 2
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [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] => 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] => 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] => 2
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [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] => 1
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [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] => 1
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [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] => 1
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [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] => 1
[[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [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] => 2
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [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] => 1
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [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] => 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] => 1
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [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] => 1
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [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] => 2
[[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [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] => 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] => 1
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [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] => 2
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [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] => 2
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [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] => 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] => 2
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [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] => 2
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [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] => 2
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [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] => 3
[[[.,.],.],[[[[.,.],.],[.,.]],.]] => [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] => 2
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [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] => 2
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [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] => 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] => 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] => 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] => 1
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [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] => 2
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [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] => 2
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [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] => 2
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [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] => 3
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [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] => 2
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [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] => 2
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [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] => 2
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [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] => 2
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [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] => 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] => 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] => 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] => 2
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [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] => 2
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [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] => 2
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [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] => 2
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [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] => 3
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [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] => 2
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [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] => 2
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [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] => 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] => 2
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [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] => 3
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [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] => 2
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [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] => 2
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [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] => 2
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [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] => 3
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [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] => 2
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [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] => 2
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [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] => 2
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [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] => 3
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [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] => 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] => 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] => 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] => 2
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [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] => 2
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [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] => 2
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [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] => 3
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [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] => 2
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [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] => 2
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [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] => 3
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [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] => 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] => 1
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [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] => 1
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [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] => 1
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [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] => 2
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [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] => 1
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [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] => 1
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [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] => 1
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [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] => 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] => 1
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [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] => 2
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [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] => 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] => 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] => 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] => 1
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [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] => 2
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [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] => 2
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [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] => 2
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [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] => 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] => 2
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [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] => 2
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [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] => 2
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [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] => 2
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [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] => 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] => 2
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [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] => 2
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [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] => 2
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [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] => 2
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [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] => 3
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [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] => 2
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [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] => 3
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [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] => 3
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [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] => 3
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [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] => 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] => 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] => 2
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [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] => 2
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [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] => 2
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [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] => 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] => 2
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [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] => 2
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [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] => 2
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [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] => 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] => 2
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [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] => 2
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [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] => 2
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [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] => 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] => 2
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [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] => 3
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [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] => 3
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [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] => 3
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [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] => 4
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [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] => 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] => 2
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [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] => 2
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [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] => 2
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [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] => 2
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [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] => 2
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [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] => 2
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [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] => 2
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [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] => 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] => 2
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [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] => 2
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [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] => 2
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [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] => 2
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [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] => 2
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [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] => 2
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [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] => 2
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [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] => 3
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [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] => 2
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [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] => 2
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [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] => 2
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [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] => 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] => 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] => 1
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [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] => 1
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [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] => 1
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [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] => 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] => 1
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [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] => 2
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [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] => 2
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [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] => 2
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [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] => 2
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [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] => 2
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [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] => 3
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [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] => 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] => 2
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [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] => 2
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [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] => 3
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [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] => 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] => 2
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [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] => 3
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [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] => 3
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [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] => 3
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [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] => 3
[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [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] => 3
[[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [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] => 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] => 2
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [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] => 2
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [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] => 2
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [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] => 2
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [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] => 2
[[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [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] => 2
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [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] => 2
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [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] => 2
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [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] => 3
[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [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] => 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] => 2
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [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] => 2
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [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] => 2
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [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] => 2
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [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] => 2
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [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] => 2
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [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] => 3
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [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] => 3
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [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] => 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] => 2
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [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] => 2
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [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] => 2
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [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] => 2
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [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] => 2
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [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] => 2
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [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] => 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] => 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] => 2
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [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] => 2
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [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] => 2
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [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] => 2
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [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] => 2
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [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] => 2
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [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] => 3
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [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] => 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] => 2
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [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] => 2
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [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] => 2
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [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] => 2
[[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [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] => 2
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [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] => 2
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [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] => 2
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [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] => 2
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [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] => 2
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [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] => 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] => 1
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [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] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [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] => 2
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [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] => 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] => 2
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [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] => 3
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [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] => 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] => 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] => 2
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [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] => 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] => 2
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [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] => 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] => 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] => 3
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [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] => 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] => 2
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [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] => 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] => 2
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [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] => 3
[[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [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] => 2
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [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] => 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] => 3
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [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] => 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] => 2
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [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] => 3
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [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] => 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] => 3
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [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] => 3
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [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] => 3
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [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] => 3
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [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] => 4
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [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] => 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] => 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] => 3
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [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] => 4
[[.,[[[[.,.],.],[.,.]],.]],[.,.]] => [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] => 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] => 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] => 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] => 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] => 3
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [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] => 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] => 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] => 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] => 2
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [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] => 3
[[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [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] => 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] => 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] => 2
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [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] => 3
[[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [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] => 2
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [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] => 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] => 3
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [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] => 2
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [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] => 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] => 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] => 3
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [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] => 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] => 3
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [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] => 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] => 2
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [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] => 3
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [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] => 2
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [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] => 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] => 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] => 3
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [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] => 3
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [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] => 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] => 2
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [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] => 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] => 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] => 3
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [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] => 4
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [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] => 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] => 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] => 3
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [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] => 4
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [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] => 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] => 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] => 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] => 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] => 3
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [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] => 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] => 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] => 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] => 2
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [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] => 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] => 3
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [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] => 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] => 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] => 2
[[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [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] => 3
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [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] => 2
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [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] => 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] => 3
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [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] => 2
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [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] => 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] => 3
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [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] => 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] => 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] => 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] => 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] => 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] => 2
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [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] => 3
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [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] => 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] => 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] => 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] => 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] => 2
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [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] => 1
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [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] => 1
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [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] => 1
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [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] => 1
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [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] => 2
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [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] => 1
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [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] => 1
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [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] => 1
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [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] => 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] => 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] => 2
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [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] => 1
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [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] => 1
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [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] => 1
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [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] => 1
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [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] => 1
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [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] => 2
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [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] => 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] => 1
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [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] => 2
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [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] => 2
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [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] => 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] => 1
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [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] => 2
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [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] => 2
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [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] => 2
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [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] => 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] => 2
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [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] => 2
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [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] => 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] => 2
[[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [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] => 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] => 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] => 2
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [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] => 1
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [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] => 1
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [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] => 1
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.] => [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] => 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] => 1
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [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] => 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] => 2
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [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] => 1
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [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] => 2
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [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] => 2
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [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] => 2
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [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] => 3
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [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] => 1
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [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] => 1
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [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] => 1
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [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] => 1
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [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] => 2
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [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] => 2
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [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] => 2
[[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [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] => 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] => 1
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [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] => 1
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [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] => 2
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [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] => 2
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [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] => 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] => 2
[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [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] => 2
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [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] => 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] => 2
[[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [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] => 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] => 1
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [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] => 2
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => [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] => 2
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [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] => 3
[[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [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] => 2
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [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] => 2
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [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] => 2
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [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] => 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] => 2
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [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] => 3
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [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] => 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] => 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] => 2
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [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] => 2
[[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [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] => 2
[[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [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] => 2
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [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] => 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] => 2
[[.,[[[[.,.],.],[.,[.,.]]],.]],.] => [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] => 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] => 2
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [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] => 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] => 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] => 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] => 2
[[.,[[[.,[.,[[.,.],.]]],.],.]],.] => [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] => 2
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [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] => 2
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [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] => 2
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [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] => 2
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [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] => 2
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [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] => 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] => 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] => 2
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [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] => 1
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [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] => 1
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [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] => 1
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [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] => 1
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [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] => 2
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [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] => 1
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [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] => 1
[[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [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] => 1
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [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] => 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] => 1
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [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] => 2
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [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] => 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] => 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] => 2
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [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] => 1
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [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] => 1
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [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] => 1
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [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] => 2
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [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] => 1
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [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] => 2
[[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [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] => 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] => 1
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [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] => 1
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [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] => 2
[[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [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] => 2
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [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] => 2
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [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] => 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] => 1
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [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] => 2
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [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] => 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] => 2
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [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] => 2
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [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] => 2
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [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] => 3
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [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] => 2
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [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] => 2
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [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] => 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] => 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] => 2
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [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] => 1
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [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] => 2
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [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] => 2
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [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] => 3
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [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] => 2
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [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] => 2
[[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [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] => 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] => 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] => 3
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [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] => 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] => 1
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [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] => 1
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [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] => 1
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [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] => 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] => 1
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [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] => 1
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [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] => 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] => 1
[[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [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] => 2
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [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] => 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] => 2
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [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] => 1
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [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] => 2
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [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] => 2
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [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] => 3
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [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] => 2
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [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] => 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] => 2
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [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] => 2
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [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] => 2
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [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] => 2
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [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] => 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] => 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] => 1
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [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] => 1
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [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] => 1
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [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] => 2
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [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] => 1
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [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] => 2
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [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] => 2
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [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] => 2
[[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [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] => 2
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [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] => 3
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [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] => 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] => 2
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [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] => 2
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [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] => 2
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [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] => 2
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [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] => 2
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [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] => 2
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [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] => 2
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [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] => 2
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [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] => 2
[[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [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] => 2
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [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] => 2
[[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [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] => 2
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [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] => 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] => 1
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [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] => 1
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [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] => 2
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [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] => 2
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [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] => 3
[[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [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] => 2
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [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] => 3
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [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] => 2
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [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] => 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] => 3
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [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] => 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] => 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] => 2
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [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] => 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] => 2
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [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] => 2
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [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] => 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] => 2
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [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] => 2
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [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] => 2
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [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] => 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] => 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] => 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] => 2
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [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] => 2
[[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [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] => 2
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [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] => 2
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [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] => 2
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [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] => 2
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [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] => 2
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [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] => 2
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [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] => 2
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [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] => 2
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [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] => 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] => 1
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [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] => 1
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.] => [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] => 1
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [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] => 2
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [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] => 1
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [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] => 1
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [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] => 1
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [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] => 2
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [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] => 2
[[[.,[.,[[.,[[.,.],.]],.]]],.],.] => [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] => 2
[[[.,[.,[[[.,.],[.,.]],.]]],.],.] => [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] => 2
[[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [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] => 2
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [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] => 1
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [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] => 1
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [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] => 1
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [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] => 2
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [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] => 1
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [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] => 2
[[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [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] => 2
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [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] => 1
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [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] => 1
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [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] => 2
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [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] => 1
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [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] => 2
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [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] => 3
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [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] => 2
[[[.,[[[.,.],[.,[.,.]]],.]],.],.] => [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] => 2
[[[.,[[[.,.],[[.,.],.]],.]],.],.] => [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] => 2
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [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] => 2
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [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] => 2
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [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] => 2
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [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] => 1
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [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] => 1
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [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] => 1
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [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] => 1
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [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] => 2
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [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] => 1
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [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] => 1
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [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] => 1
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [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] => 2
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [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] => 1
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [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] => 2
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [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] => 2
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [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] => 2
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [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] => 1
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [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] => 2
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [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] => 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] => 1
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [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] => 1
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [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] => 1
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [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] => 2
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [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] => 1
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [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] => 2
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [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] => 2
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [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] => 2
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [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] => 2
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [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] => 2
[[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [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] => 2
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [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] => 1
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [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] => 1
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [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] => 2
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [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] => 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] => 2
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [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] => 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] => 2
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [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] => 2
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [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] => 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] => 2
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [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] => 2
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [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] => 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] => 1
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [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] => 1
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [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] => 1
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [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] => 1
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [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] => 2
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [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] => 1
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [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] => 1
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [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] => 1
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [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] => 2
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [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] => 1
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [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] => 2
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [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] => 2
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [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] => 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] => 2
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [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] => 1
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [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] => 1
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [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] => 1
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [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] => 1
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [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] => 2
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [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] => 1
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [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] => 2
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [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] => 2
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [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] => 1
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [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] => 2
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [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] => 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] => 1
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [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] => 1
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [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] => 1
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [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] => 1
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [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] => 2
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [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] => 1
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [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] => 1
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [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] => 1
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [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] => 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] => 1
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [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] => 1
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [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] => 1
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [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] => 1
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [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] => 1
[[[[[[[[.,.],.],.],.],.],.],.],.] => [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] => 0
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [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] => 1
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [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] => 1
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [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] => 1
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [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] => 1
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [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] => 1
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [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] => 1
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [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] => 1
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [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] => 1
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [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] => 0
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [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] => 1
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [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] => 1
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [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] => 1
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [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] => 1
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [6,8,9,1,2,3,4,5,7] => [2,1,1,1,1,1,1,1] => 1
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [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] => 1
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [5,7,8,9,1,2,3,4,6] => [2,1,1,1,1,1,1,1] => 1
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [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] => 1
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,9,1,2,3,5] => [2,1,1,1,1,1,1,1] => 1
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [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] => 1
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,9,1,2,4] => [2,1,1,1,1,1,1,1] => 1
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [2,1,1,1,1,1,1,1,1] => 1
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,1,3] => [2,1,1,1,1,1,1,1] => 1
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [2,1,1,1,1,1,1,1,1] => 1
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [2,1,1,1,1,1,1,1] => 1
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,1,1,1,1,1,1,1,1] => 1
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [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] => 2
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [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] => 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] => 1
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [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] => 1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [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] => 1
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [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] => 4
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,9,6,8,10] => [2,2,2,2,1,1] => 4
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [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] => 5
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [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] => 6
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [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] => 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] => 1
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => 2
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => 2
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,9,3] => [2,2,1,1,1,1,1] => 2
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,8,9,3] => [2,2,1,1,1,1,1] => 2
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [2,1,1,1,1,1,1,1,1] => 1
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [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] => 1
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,1,2,3,4,5,6,9] => [2,1,1,1,1,1,1,1] => 1
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [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] => 1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9,11] => [2,1,1,1,1,1,1,1,1,1] => 1
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,1,2,3,4,5,6,7,10] => [2,1,1,1,1,1,1,1,1] => 1
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [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] => 2
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,1,7,2,8,3,9,4,10,5] => [2,2,2,2,2] => 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] => 5
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,7,3,8,4,10,9] => [2,2,2,2,2] => 5
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [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] => 5
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [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] => 5
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7,10,9] => [2,2,2,2,2] => 5
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,10,9] => [2,2,2,2,2] => 5
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => [2,2,2,2,2,2] => 6
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [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] => 2
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => [2,2,1,1,1,1,1] => 2
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => [2,2,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => [2,2,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => [2,2,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => [2,2,1,1,1,1,1] => 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] => 1
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [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] => 1
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [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] => 1
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [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] => 1
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [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] => 1
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [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] => 1
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [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] => 1
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [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] => 1
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [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] => 1
[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,7,2,3,4,5,6,8,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [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] => 1
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [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] => 1
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [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] => 1
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [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] => 1
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [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] => 1
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [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] => 1
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [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] => 1
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [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] => 1
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [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] => 1
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,2,1,1,1,1,1] => 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] => 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] => 1
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [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] => 1
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,5,1,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,4,6,1,5,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,5,7,1,6,8,9] => [2,1,1,1,1,1,1,1] => 1
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,1,7,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [2,1,1,1,1,1,1,1,1] => 1
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,1,2,3,4,5,9,6,8] => [2,2,1,1,1,1,1] => 2
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [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] => 2
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => [2,2,1,1,1,1,1] => 2
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [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] => 1
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => [2,2,1,1,1,1,1] => 2
[.,[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,1,2,3,4,7,9,5,8] => [2,2,1,1,1,1,1] => 2
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [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] => 2
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [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] => 1
[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [6,7,8,1,2,3,4,9,5] => [2,2,1,1,1,1,1] => 2
[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,1,6,8,3,5,7,9] => [2,2,1,1,1,1,1] => 2
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,1,2,3,4,5,9] => [2,1,1,1,1,1,1,1] => 1
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [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] => 2
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1,1] => 1
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,1,2,3,4,5,9,6] => [2,2,1,1,1,1,1] => 2
[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8,9] => [2,2,1,1,1,1,1] => 2
[.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [7,1,8,9,10,2,3,4,5,6] => [2,2,1,1,1,1,1,1] => 2
[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,1,2,3,4,8,5,9,6] => [2,2,2,1,1,1] => 3
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,9,7] => [2,2,1,1,1,1,1] => 2
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
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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
F1=1
F2=1+q
F3=1+4 q
F4=1+11 q+2 q2
F5=1+26 q+15 q2
F6=1+57 q+69 q2+5 q3
F7=1+120 q+252 q2+56 q3
Description
The number of even parts of a partition.
Map
LLPS
Description
The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence u=(u1,u2,…) is an index i such that ui<ui+1. Let asc(u) denote the number of ascents of u, and let
asc∗(u):={0if u is empty,1+asc(u)otherwise.
Given a permutation w in the symmetric group Sn, define
A′k:=max
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=(u1,u2,…) is an index i such that ui<ui+1. Let asc(u) denote the number of ascents of u, and let
asc∗(u):={0if u is empty,1+asc(u)otherwise.
Given a permutation w in the symmetric group Sn, define
A′k:=max
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 Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
The bijection is defined recursively as follows:
- a leaf is associated with an empty Dyck path,
- a tree with children l,r is associated with the Dyck word T(l) 1 T(r) 0 where T(l) and T(r) are the images of this bijection to 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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