Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001732: Dyck paths ⟶ ℤ
Values
[.,.] => [1] => [1] => [1,0] => 1
[.,[.,.]] => [2,1] => [2,1] => [1,1,0,0] => 1
[[.,.],.] => [1,2] => [1,2] => [1,0,1,0] => 1
[.,[.,[.,.]]] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0] => 1
[.,[[.,.],.]] => [2,3,1] => [2,3,1] => [1,1,0,1,0,0] => 1
[[.,.],[.,.]] => [3,1,2] => [1,3,2] => [1,0,1,1,0,0] => 2
[[.,[.,.]],.] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 1
[[[.,.],.],.] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 1
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => 1
[.,[.,[[.,.],.]]] => [3,4,2,1] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 1
[.,[[.,.],[.,.]]] => [4,2,3,1] => [2,4,3,1] => [1,1,0,1,1,0,0,0] => 2
[.,[[.,[.,.]],.]] => [3,2,4,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 1
[.,[[[.,.],.],.]] => [2,3,4,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 1
[[.,.],[.,[.,.]]] => [4,3,1,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => 2
[[.,.],[[.,.],.]] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[[.,[.,.]],[.,.]] => [4,2,1,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => 2
[[[.,.],.],[.,.]] => [4,1,2,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 2
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[.,[[.,.],.]],.] => [2,3,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 1
[[[.,.],[.,.]],.] => [3,1,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 2
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 1
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 1
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 1
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 1
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => 2
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 2
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 2
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 2
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => 2
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => 3
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => 2
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 2
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => 2
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => 2
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 2
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0] => 2
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => 2
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => 3
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 2
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 2
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => 1
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => 2
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => 1
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 1
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => 2
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 2
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 2
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 2
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 1
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 1
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 2
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 1
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 2
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 2
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2
>>> Load all 972 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 2
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [1,5,6,4,3,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [1,4,6,5,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [1,5,4,6,3,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [1,3,6,5,4,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [1,4,6,3,5,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [1,4,5,3,6,2] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [2,6,5,4,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [2,5,6,4,1,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [2,4,6,5,1,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [2,5,4,6,1,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [3,6,5,2,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [3,5,6,2,1,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [1,3,6,5,2,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [2,1,6,5,3,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [4,6,3,2,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [3,4,6,2,1,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [2,4,6,3,1,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [3,2,6,4,1,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [1,4,6,3,2,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [2,4,5,3,1,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [3,5,2,4,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => 2
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [1,4,5,3,2,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => 2
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [2,5,4,1,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [3,5,2,1,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [5,7,6,4,3,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [6,5,7,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [4,7,6,5,3,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [4,6,7,5,3,2,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [5,7,4,6,3,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [4,5,7,6,3,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [6,5,4,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [5,6,4,7,3,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [4,6,5,7,3,2,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [5,4,6,7,3,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [4,5,6,7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [3,7,6,5,4,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [3,6,7,5,4,2,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [3,5,7,6,4,2,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [3,6,5,7,4,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [3,5,6,7,4,2,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [4,7,6,3,5,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [4,6,7,3,5,2,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [3,4,7,6,5,2,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [3,4,6,7,5,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => [5,7,4,3,6,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => [4,5,7,3,6,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [3,5,7,4,6,2,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => [4,3,7,5,6,2,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [3,4,5,7,6,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [6,5,4,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [5,6,4,3,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [4,6,5,3,7,2,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [5,4,6,3,7,2,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 1
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [4,5,6,3,7,2,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [3,6,5,4,7,2,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [3,5,6,4,7,2,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 2
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [4,6,3,5,7,2,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [3,4,6,5,7,2,1] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [5,4,3,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [4,5,3,6,7,2,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [3,5,4,6,7,2,1] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 2
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [4,3,5,6,7,2,1] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [3,4,5,6,7,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [2,7,6,5,4,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [2,6,7,5,4,3,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [2,5,7,6,4,3,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [2,6,5,7,4,3,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [2,5,6,7,4,3,1] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [2,4,7,6,5,3,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [2,4,6,7,5,3,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [2,5,7,4,6,3,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [2,4,5,7,6,3,1] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [2,6,5,4,7,3,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [2,5,6,4,7,3,1] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [2,4,6,5,7,3,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 3
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => [2,5,4,6,7,3,1] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [2,4,5,6,7,3,1] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [3,7,6,5,2,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [3,6,7,5,2,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => [3,5,7,6,2,4,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => [3,6,5,7,2,4,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => [3,5,6,7,2,4,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [2,3,7,6,5,4,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [2,3,6,7,5,4,1] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [2,3,5,7,6,4,1] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [2,3,6,5,7,4,1] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [2,3,5,6,7,4,1] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [4,7,6,3,2,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => [4,6,7,3,2,5,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [3,4,7,6,2,5,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => [3,4,6,7,2,5,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [2,4,7,6,3,5,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [2,4,6,7,3,5,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [3,2,7,6,4,5,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => [3,2,6,7,4,5,1] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [2,3,4,7,6,5,1] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [2,3,4,6,7,5,1] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [5,7,4,3,2,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [4,5,7,3,2,6,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [3,5,7,4,2,6,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [4,3,7,5,2,6,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [3,4,5,7,2,6,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [2,5,7,4,3,6,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [2,4,5,7,3,6,1] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [3,5,7,2,4,6,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [2,3,5,7,4,6,1] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [4,3,7,2,5,6,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [3,4,2,7,5,6,1] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [2,4,3,7,5,6,1] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [3,2,4,7,5,6,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [2,3,4,5,7,6,1] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [5,6,4,3,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [4,6,5,3,2,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [5,4,6,3,2,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [4,5,6,3,2,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [3,6,5,4,2,7,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [3,5,6,4,2,7,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [4,6,3,5,2,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [3,4,6,5,2,7,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [5,4,3,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [4,5,3,6,2,7,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => [3,5,4,6,2,7,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 2
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [4,3,5,6,2,7,1] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 1
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [3,4,5,6,2,7,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [2,6,5,4,3,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [2,5,6,4,3,7,1] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 2
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [2,4,6,5,3,7,1] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [2,5,4,6,3,7,1] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [2,4,5,6,3,7,1] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 2
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [3,6,5,2,4,7,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => [3,5,6,2,4,7,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [2,3,6,5,4,7,1] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [2,3,5,6,4,7,1] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 2
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [4,6,3,2,5,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => [3,4,6,2,5,7,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => [2,4,6,3,5,7,1] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => [3,2,6,4,5,7,1] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [2,3,4,6,5,7,1] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 2
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [4,5,3,2,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [3,5,4,2,6,7,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 2
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [4,3,5,2,6,7,1] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [2,5,4,3,6,7,1] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [2,4,5,3,6,7,1] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 2
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 2
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [2,3,5,4,6,7,1] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 2
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [3,4,2,5,6,7,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 2
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [1,6,7,5,4,3,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,5,7,6,4,3,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [1,6,5,7,4,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [1,5,6,7,4,3,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,4,7,6,5,3,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [1,4,6,7,5,3,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [1,5,7,4,6,3,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [1,4,5,7,6,3,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [1,6,5,4,7,3,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [1,5,6,4,7,3,2] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [1,4,6,5,7,3,2] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => [1,5,4,6,7,3,2] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [1,4,5,6,7,3,2] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,3,7,6,5,4,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [1,3,6,7,5,4,2] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,3,5,7,6,4,2] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [1,3,6,5,7,4,2] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [1,3,5,6,7,4,2] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [1,4,7,6,3,5,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [1,4,6,7,3,5,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [1,3,4,7,6,5,2] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [1,3,4,6,7,5,2] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [1,5,7,4,3,6,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [1,4,5,7,3,6,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [1,3,5,7,4,6,2] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [1,4,3,7,5,6,2] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [1,3,4,5,7,6,2] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [1,6,5,4,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [1,5,6,4,3,7,2] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [1,4,6,5,3,7,2] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => [1,5,4,6,3,7,2] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [1,4,5,6,3,7,2] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [1,3,6,5,4,7,2] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [1,3,5,6,4,7,2] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => [1,4,6,3,5,7,2] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [1,3,4,6,5,7,2] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => [1,5,4,3,6,7,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [1,4,5,3,6,7,2] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [1,3,5,4,6,7,2] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [1,4,3,5,6,7,2] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [1,3,4,5,6,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [2,7,6,5,4,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [2,6,7,5,4,1,3] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => [2,5,7,6,4,1,3] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => [2,6,5,7,4,1,3] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => [2,5,6,7,4,1,3] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [2,4,7,6,5,1,3] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => [2,4,6,7,5,1,3] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => [2,5,7,4,6,1,3] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [2,4,5,7,6,1,3] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [2,6,5,4,7,1,3] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => [2,5,6,4,7,1,3] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => [2,4,6,5,7,1,3] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 3
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => [2,5,4,6,7,1,3] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [2,4,5,6,7,1,3] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [1,2,6,7,5,4,3] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [1,2,5,7,6,4,3] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [1,2,6,5,7,4,3] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [1,2,5,6,7,4,3] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [1,2,4,7,6,5,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [1,2,4,6,7,5,3] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [1,2,5,7,4,6,3] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [1,2,4,5,7,6,3] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [1,2,6,5,4,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [1,2,5,6,4,7,3] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [1,2,4,6,5,7,3] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => [1,2,5,4,6,7,3] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [3,7,6,5,2,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => [3,6,7,5,2,1,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => [3,5,7,6,2,1,4] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => [3,6,5,7,2,1,4] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => [3,5,6,7,2,1,4] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [2,3,7,6,5,1,4] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => [2,3,6,7,5,1,4] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => [2,3,5,7,6,1,4] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => [2,3,6,5,7,1,4] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => [2,3,5,6,7,1,4] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [1,3,7,6,5,2,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [1,3,6,7,5,2,4] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [1,3,5,7,6,2,4] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [1,3,6,5,7,2,4] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [1,3,5,6,7,2,4] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [2,1,7,6,5,3,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => [2,1,6,7,5,3,4] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => [2,1,5,7,6,3,4] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 3
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => [2,1,6,5,7,3,4] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => [2,1,5,6,7,3,4] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [1,2,3,6,7,5,4] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [1,2,3,5,7,6,4] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [1,2,3,6,5,7,4] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [4,7,6,3,2,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [4,6,7,3,2,1,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [3,4,7,6,2,1,5] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [3,4,6,7,2,1,5] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [2,4,7,6,3,1,5] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [2,4,6,7,3,1,5] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [3,2,7,6,4,1,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [3,2,6,7,4,1,5] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [2,3,4,7,6,1,5] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [2,3,4,6,7,1,5] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [1,4,7,6,3,2,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [1,4,6,7,3,2,5] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [1,3,4,7,6,2,5] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [1,3,4,6,7,2,5] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [2,4,7,6,1,3,5] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [2,4,6,7,1,3,5] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [1,2,4,7,6,3,5] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [1,2,4,6,7,3,5] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [3,2,7,6,1,4,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [3,2,6,7,1,4,5] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [2,3,1,7,6,4,5] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [2,3,1,6,7,4,5] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [1,3,2,7,6,4,5] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [1,3,2,6,7,4,5] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [2,1,3,7,6,4,5] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => [2,1,3,6,7,4,5] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [1,2,3,4,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [5,7,4,3,2,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [4,5,7,3,2,1,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [3,5,7,4,2,1,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [4,3,7,5,2,1,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [3,4,5,7,2,1,6] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [2,5,7,4,3,1,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [2,4,5,7,3,1,6] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [3,5,7,2,4,1,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [2,3,5,7,4,1,6] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [4,3,7,2,5,1,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [3,4,2,7,5,1,6] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [2,4,3,7,5,1,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [3,2,4,7,5,1,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [2,3,4,5,7,1,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [1,5,7,4,3,2,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [1,4,5,7,3,2,6] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [1,3,5,7,4,2,6] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [1,4,3,7,5,2,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [1,3,4,5,7,2,6] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [2,5,7,4,1,3,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [2,4,5,7,1,3,6] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [1,2,5,7,4,3,6] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [1,2,4,5,7,3,6] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [3,5,7,2,1,4,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [2,3,5,7,1,4,6] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [1,3,5,7,2,4,6] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => [2,1,5,7,3,4,6] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 3
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [1,2,3,5,7,4,6] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [4,3,7,2,1,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [3,4,2,7,1,5,6] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [2,4,3,7,1,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [3,2,4,7,1,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [2,3,4,1,7,5,6] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [1,4,3,7,2,5,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [1,3,4,2,7,5,6] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => [2,4,1,7,3,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [1,2,4,3,7,5,6] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => [3,2,1,7,4,5,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [2,3,1,4,7,5,6] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [1,3,2,4,7,5,6] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [2,1,3,4,7,5,6] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [4,6,5,3,2,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [3,6,5,4,2,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [3,5,6,4,2,1,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [4,6,3,5,2,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [3,4,6,5,2,1,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 1
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => [3,5,4,6,2,1,7] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 1
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => [2,6,5,4,3,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [2,5,6,4,3,1,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [2,4,6,5,3,1,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 3
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => [2,5,4,6,3,1,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => [2,4,5,6,3,1,7] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [3,6,5,2,4,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => [3,5,6,2,4,1,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [2,3,6,5,4,1,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => [2,3,5,6,4,1,7] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [4,6,3,2,5,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => [3,4,6,2,5,1,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [2,4,6,3,5,1,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 3
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => [3,2,6,4,5,1,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => [2,3,4,6,5,1,7] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 1
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [3,5,4,2,6,1,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 1
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1,7] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 1
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [2,5,4,3,6,1,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [2,4,5,3,6,1,7] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [3,5,2,4,6,1,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [2,3,5,4,6,1,7] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1,7] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 1
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [2,4,3,5,6,1,7] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [1,5,6,4,3,2,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [1,4,6,5,3,2,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => [1,5,4,6,3,2,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [1,4,5,6,3,2,7] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [1,3,6,5,4,2,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [1,3,5,6,4,2,7] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => [1,4,6,3,5,2,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [1,3,4,6,5,2,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => [1,5,4,3,6,2,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [1,4,5,3,6,2,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [1,3,5,4,6,2,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [1,4,3,5,6,2,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [2,6,5,4,1,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => [2,5,6,4,1,3,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => [2,4,6,5,1,3,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 3
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => [2,5,4,6,1,3,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [2,4,5,6,1,3,7] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [1,2,5,6,4,3,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [1,2,4,6,5,3,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [1,2,5,4,6,3,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [3,6,5,2,1,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => [3,5,6,2,1,4,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => [2,3,6,5,1,4,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => [2,3,5,6,1,4,7] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [1,3,6,5,2,4,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => [1,3,5,6,2,4,7] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => [2,1,6,5,3,4,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => [2,1,5,6,3,4,7] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [1,2,3,6,5,4,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [4,6,3,2,1,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [3,4,6,2,1,5,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [2,4,6,3,1,5,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 3
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [3,2,6,4,1,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [2,3,4,6,1,5,7] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [1,4,6,3,2,5,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [1,3,4,6,2,5,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => [2,4,6,1,3,5,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 3
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [1,2,4,6,3,5,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => [3,2,6,1,4,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => [2,3,1,6,4,5,7] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [1,3,2,6,4,5,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [2,1,3,6,4,5,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [3,5,4,2,1,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 1
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [2,5,4,3,1,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [2,4,5,3,1,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 2
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [3,5,2,4,1,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [2,3,5,4,1,6,7] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 1
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6,7] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 1
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [2,4,3,5,1,6,7] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 1
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [1,4,5,3,2,6,7] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [1,3,5,4,2,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [1,4,3,5,2,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [1,3,4,5,2,6,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => [2,5,4,1,3,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => [2,4,5,1,3,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 2
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [1,2,5,4,3,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [3,5,2,1,4,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [2,3,5,1,4,6,7] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [1,3,5,2,4,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [2,1,5,3,4,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [2,4,3,1,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 2
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 1
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [1,4,3,2,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [1,3,4,2,5,6,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [2,4,1,3,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 2
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,8,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [1,7,8,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,6,8,7,5,4,3,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,3,1,2] => [1,7,6,8,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => [1,6,7,8,5,4,3,2] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,5,8,7,6,4,3,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 3
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,3,1,2] => [1,6,8,5,7,4,3,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,3,1,2] => [1,7,6,5,8,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,3,1,2] => [1,6,7,5,8,4,3,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => [1,5,7,6,8,4,3,2] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 3
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => [1,6,5,7,8,4,3,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [1,5,6,7,8,4,3,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,4,8,7,6,5,3,2] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [1,4,7,8,6,5,3,2] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 3
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => [1,4,6,8,7,5,3,2] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => [1,4,6,7,8,5,3,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,3,1,2] => [1,5,8,7,4,6,3,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 3
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,3,1,2] => [1,4,5,8,7,6,3,2] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => [1,4,5,7,8,6,3,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 3
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,3,1,2] => [1,5,6,8,4,7,3,2] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 3
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => [1,4,6,8,5,7,3,2] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,3,1,2] => [1,7,6,5,4,8,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => [1,4,7,6,5,8,3,2] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 3
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,3,1,2] => [1,4,6,7,5,8,3,2] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [7,5,4,6,8,3,1,2] => [1,5,7,4,6,8,3,2] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 3
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,3,1,2] => [1,6,5,4,7,8,3,2] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [5,4,6,7,8,3,1,2] => [1,5,4,6,7,8,3,2] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => [1,4,5,6,7,8,3,2] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,3,8,7,6,5,4,2] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [1,3,7,8,6,5,4,2] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 3
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,3,4,1,2] => [1,3,6,8,7,5,4,2] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 4
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => [1,3,6,7,8,5,4,2] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,3,5,8,7,6,4,2] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 4
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [1,3,5,7,8,6,4,2] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,4,1,2] => [1,3,5,6,8,7,4,2] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 4
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => [1,3,6,7,5,8,4,2] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [1,3,5,7,6,8,4,2] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 4
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => [1,3,6,5,7,8,4,2] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [1,3,5,6,7,8,4,2] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,3,5,1,2] => [1,4,8,7,6,3,5,2] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [7,8,6,4,3,5,1,2] => [1,4,7,8,6,3,5,2] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 3
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [8,6,7,4,3,5,1,2] => [1,4,6,8,7,3,5,2] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [7,6,8,4,3,5,1,2] => [1,4,7,6,8,3,5,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 3
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [6,7,8,4,3,5,1,2] => [1,4,6,7,8,3,5,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => [1,3,4,8,7,6,5,2] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 3
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [6,7,8,3,4,5,1,2] => [1,3,4,6,7,8,5,2] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,3,6,1,2] => [1,5,8,7,4,3,6,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 3
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => [1,5,7,8,4,3,6,2] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [8,7,4,5,3,6,1,2] => [1,4,5,8,7,3,6,2] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => [1,4,5,7,8,3,6,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 3
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => [1,3,5,7,8,4,6,2] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [8,7,4,3,5,6,1,2] => [1,4,3,8,7,5,6,2] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => [1,4,3,7,8,5,6,2] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [8,7,3,4,5,6,1,2] => [1,3,4,5,8,7,6,2] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [1,3,4,5,7,8,6,2] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,3,7,1,2] => [1,6,8,5,4,3,7,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [8,5,4,6,3,7,1,2] => [1,5,4,8,6,3,7,2] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 3
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [8,5,6,3,4,7,1,2] => [1,3,5,6,8,4,7,2] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 4
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [8,6,4,3,5,7,1,2] => [1,4,6,8,3,5,7,2] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => [1,4,3,5,8,6,7,2] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 3
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [1,3,4,5,6,8,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [1,7,6,5,4,3,8,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [6,7,5,4,3,8,1,2] => [1,6,7,5,4,3,8,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2] => [1,6,5,7,4,3,8,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => [1,4,6,7,5,3,8,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => [1,5,6,4,7,3,8,2] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [6,4,5,7,3,8,1,2] => [1,4,6,5,7,3,8,2] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [5,4,6,7,3,8,1,2] => [1,5,4,6,7,3,8,2] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => [1,4,5,6,7,3,8,2] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => [1,3,5,7,6,4,8,2] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 4
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [6,5,7,3,4,8,1,2] => [1,3,6,5,7,4,8,2] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [5,6,7,3,4,8,1,2] => [1,3,5,6,7,4,8,2] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 3
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [6,7,4,3,5,8,1,2] => [1,4,6,7,3,5,8,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => [1,3,4,7,6,5,8,2] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [6,7,3,4,5,8,1,2] => [1,3,4,6,7,5,8,2] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [7,4,5,3,6,8,1,2] => [1,4,5,7,3,6,8,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [7,5,3,4,6,8,1,2] => [1,3,5,7,4,6,8,2] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 4
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [7,3,4,5,6,8,1,2] => [1,3,4,5,7,6,8,2] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [6,5,4,3,7,8,1,2] => [1,6,5,4,3,7,8,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => [1,5,4,6,3,7,8,2] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => [1,3,5,6,4,7,8,2] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 3
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => [1,4,6,3,5,7,8,2] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => [1,3,4,6,5,7,8,2] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => [1,5,4,3,6,7,8,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => [1,4,5,3,6,7,8,2] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [5,3,4,6,7,8,1,2] => [1,3,5,4,6,7,8,2] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => [1,4,3,5,6,7,8,2] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [1,3,4,5,6,7,8,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [1,2,8,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => [1,2,7,8,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => [1,2,6,7,8,5,4,3] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,1,2,3] => [1,2,6,8,5,7,4,3] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [1,2,5,6,8,7,4,3] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,1,2,3] => [1,2,7,6,5,8,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,1,2,3] => [1,2,5,7,6,8,4,3] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => [1,2,6,5,7,8,4,3] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => [1,2,5,6,7,8,4,3] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [1,2,4,8,7,6,5,3] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [7,8,6,4,5,1,2,3] => [1,2,4,7,8,6,5,3] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [1,2,4,6,8,7,5,3] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [6,7,8,4,5,1,2,3] => [1,2,4,6,7,8,5,3] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [8,7,5,4,6,1,2,3] => [1,2,5,8,7,4,6,3] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [7,8,5,4,6,1,2,3] => [1,2,5,7,8,4,6,3] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [1,2,4,5,8,7,6,3] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [1,2,4,5,7,8,6,3] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,1,2,3] => [1,2,6,8,5,4,7,3] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [8,5,6,4,7,1,2,3] => [1,2,5,6,8,4,7,3] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => [1,2,4,6,8,5,7,3] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [8,5,4,6,7,1,2,3] => [1,2,5,4,8,6,7,3] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => [1,2,4,5,6,8,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,1,2,3] => [1,2,7,6,5,4,8,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,1,2,3] => [1,2,5,6,7,4,8,3] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,1,2,3] => [1,2,4,7,6,5,8,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,1,2,3] => [1,2,5,7,4,6,8,3] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => [1,2,6,5,4,7,8,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,1,2,3] => [1,2,5,4,6,7,8,3] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => [1,2,4,5,6,7,8,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [1,3,8,7,6,5,2,4] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,1,2,4] => [1,3,6,8,7,5,2,4] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 4
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,1,2,4] => [1,3,7,6,8,5,2,4] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 3
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,1,2,4] => [1,3,6,7,8,5,2,4] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,1,2,4] => [1,3,5,8,7,6,2,4] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 4
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => [1,3,5,7,8,6,2,4] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,1,2,4] => [1,3,6,8,5,7,2,4] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 4
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,1,2,4] => [1,3,5,6,8,7,2,4] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 4
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,1,2,4] => [1,3,7,6,5,8,2,4] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 3
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => [1,3,6,7,5,8,2,4] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => [1,3,5,7,6,8,2,4] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 4
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,1,2,4] => [1,3,6,5,7,8,2,4] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => [1,3,5,6,7,8,2,4] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => [2,1,8,7,6,5,3,4] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => [2,1,7,8,6,5,3,4] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,1,3,4] => [2,1,6,8,7,5,3,4] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,1,3,4] => [2,1,7,6,8,5,3,4] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => [2,1,6,7,8,5,3,4] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,1,3,4] => [2,1,5,8,7,6,3,4] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => [2,1,5,7,8,6,3,4] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,1,3,4] => [2,1,6,8,5,7,3,4] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [8,5,6,7,2,1,3,4] => [2,1,5,6,8,7,3,4] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,1,3,4] => [2,1,7,6,5,8,3,4] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [6,7,5,8,2,1,3,4] => [2,1,6,7,5,8,3,4] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => [2,1,6,5,7,8,3,4] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => [2,1,5,6,7,8,3,4] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [1,2,3,8,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [1,2,3,7,8,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [1,2,3,6,8,7,5,4] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => [1,2,3,7,6,8,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => [1,2,3,6,7,8,5,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [1,2,3,5,8,7,6,4] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [1,2,3,5,7,8,6,4] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => [1,2,3,6,8,5,7,4] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [1,2,3,5,6,8,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => [1,2,3,7,6,5,8,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => [1,2,3,6,7,5,8,4] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => [1,2,3,5,7,6,8,4] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => [1,2,3,6,5,7,8,4] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [1,2,3,5,6,7,8,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [7,6,8,4,3,1,2,5] => [1,4,7,6,8,3,2,5] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 3
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => [1,4,6,7,8,3,2,5] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => [1,3,4,8,7,6,2,5] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [7,6,8,3,4,1,2,5] => [1,3,4,7,6,8,2,5] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [1,2,4,8,7,6,3,5] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => [1,2,4,7,8,6,3,5] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [7,6,8,4,1,2,3,5] => [1,2,4,7,6,8,3,5] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => [1,2,4,6,7,8,3,5] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [8,7,6,3,1,2,4,5] => [1,3,2,8,7,6,4,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [8,6,7,3,1,2,4,5] => [1,3,2,6,8,7,4,5] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 4
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [7,6,8,3,1,2,4,5] => [1,3,2,7,6,8,4,5] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 3
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [6,7,8,3,1,2,4,5] => [1,3,2,6,7,8,4,5] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => [2,1,3,8,7,6,4,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [7,8,6,2,1,3,4,5] => [2,1,3,7,8,6,4,5] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [8,6,7,2,1,3,4,5] => [2,1,3,6,8,7,4,5] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => [2,1,3,6,7,8,4,5] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [1,2,3,4,8,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [1,2,3,4,7,8,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [1,2,3,4,6,8,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => [1,2,3,4,7,6,8,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => [1,2,3,4,6,7,8,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => [1,5,8,7,4,3,2,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 3
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [7,8,5,4,3,1,2,6] => [1,5,7,8,4,3,2,6] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [7,8,5,3,4,1,2,6] => [1,3,5,7,8,4,2,6] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [7,8,4,3,5,1,2,6] => [1,4,3,7,8,5,2,6] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [8,7,3,4,5,1,2,6] => [1,3,4,5,8,7,2,6] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [7,8,3,4,5,1,2,6] => [1,3,4,5,7,8,2,6] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => [1,2,5,8,7,4,3,6] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => [1,2,5,7,8,4,3,6] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => [1,2,4,5,8,7,3,6] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => [1,2,4,5,7,8,3,6] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [8,7,5,3,1,2,4,6] => [1,3,5,8,7,2,4,6] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 4
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [7,8,5,3,1,2,4,6] => [1,3,5,7,8,2,4,6] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => [2,1,5,8,7,3,4,6] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => [2,1,5,7,8,3,4,6] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => [1,2,3,5,8,7,4,6] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [1,2,3,5,7,8,4,6] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [8,7,4,3,1,2,5,6] => [1,4,3,8,7,2,5,6] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [7,8,4,3,1,2,5,6] => [1,4,3,7,8,2,5,6] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => [1,3,4,2,7,8,5,6] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => [1,2,4,3,8,7,5,6] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [7,8,4,1,2,3,5,6] => [1,2,4,3,7,8,5,6] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [7,8,2,3,1,4,5,6] => [2,3,1,4,7,8,5,6] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [7,8,3,1,2,4,5,6] => [1,3,2,4,7,8,5,6] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [8,7,2,1,3,4,5,6] => [2,1,3,4,8,7,5,6] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => [2,1,3,4,7,8,5,6] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,8,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [1,2,3,4,5,7,8,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => [1,6,8,5,4,3,2,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [8,5,4,6,3,1,2,7] => [1,5,4,8,6,3,2,7] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 3
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [8,6,5,3,4,1,2,7] => [1,3,6,8,5,4,2,7] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 4
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [1,3,5,6,8,4,2,7] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 4
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [8,6,4,3,5,1,2,7] => [1,4,6,8,3,5,2,7] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [8,5,3,4,6,1,2,7] => [1,3,5,4,8,6,2,7] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 4
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => [1,3,4,5,6,8,2,7] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => [1,2,6,8,5,4,3,7] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [1,2,4,6,8,5,3,7] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [8,5,4,6,1,2,3,7] => [1,2,5,4,8,6,3,7] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [8,4,5,6,1,2,3,7] => [1,2,4,5,6,8,3,7] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [8,6,5,3,1,2,4,7] => [1,3,6,8,5,2,4,7] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 4
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [8,5,6,3,1,2,4,7] => [1,3,5,6,8,2,4,7] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 4
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [8,6,5,2,1,3,4,7] => [2,1,6,8,5,3,4,7] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => [2,1,5,6,8,3,4,7] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => [1,2,3,6,8,5,4,7] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => [1,2,3,5,6,8,4,7] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [8,6,4,3,1,2,5,7] => [1,4,6,8,3,2,5,7] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [8,6,3,4,1,2,5,7] => [1,3,4,6,8,2,5,7] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 4
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [8,6,4,1,2,3,5,7] => [1,2,4,6,8,3,5,7] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => [1,2,3,4,6,8,5,7] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [8,5,4,3,1,2,6,7] => [1,5,4,8,3,2,6,7] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 3
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [8,5,3,4,1,2,6,7] => [1,3,5,4,8,2,6,7] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 4
[[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [8,4,3,5,1,2,6,7] => [1,4,3,5,8,2,6,7] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 3
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [8,3,4,5,1,2,6,7] => [1,3,4,5,2,8,6,7] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [8,5,4,1,2,3,6,7] => [1,2,5,4,8,3,6,7] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [8,4,5,1,2,3,6,7] => [1,2,4,5,3,8,6,7] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [8,5,3,1,2,4,6,7] => [1,3,5,2,8,4,6,7] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 4
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [8,5,2,1,3,4,6,7] => [2,1,5,3,8,4,6,7] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => [1,2,3,5,4,8,6,7] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [8,4,3,1,2,5,6,7] => [1,4,3,2,8,5,6,7] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [8,3,4,1,2,5,6,7] => [1,3,4,2,5,8,6,7] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => [1,2,4,3,5,8,6,7] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => [2,3,1,4,5,8,6,7] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => [1,3,2,4,5,8,6,7] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => [2,1,3,4,5,8,6,7] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [1,7,6,5,4,3,2,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,3,1,2,8] => [1,6,7,5,4,3,2,8] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [6,5,7,4,3,1,2,8] => [1,6,5,7,4,3,2,8] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [5,6,7,4,3,1,2,8] => [1,5,6,7,4,3,2,8] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,3,1,2,8] => [1,4,7,6,5,3,2,8] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 3
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [7,5,4,6,3,1,2,8] => [1,5,7,4,6,3,2,8] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [5,4,6,7,3,1,2,8] => [1,5,4,6,7,3,2,8] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [7,6,5,3,4,1,2,8] => [1,3,7,6,5,4,2,8] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3
[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [6,7,5,3,4,1,2,8] => [1,3,6,7,5,4,2,8] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [7,5,6,3,4,1,2,8] => [1,3,5,7,6,4,2,8] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [6,5,7,3,4,1,2,8] => [1,3,6,5,7,4,2,8] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [5,6,7,3,4,1,2,8] => [1,3,5,6,7,4,2,8] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [6,7,4,3,5,1,2,8] => [1,4,6,7,3,5,2,8] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [6,7,3,4,5,1,2,8] => [1,3,4,6,7,5,2,8] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [7,5,4,3,6,1,2,8] => [1,5,7,4,3,6,2,8] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [7,5,3,4,6,1,2,8] => [1,3,5,7,4,6,2,8] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [7,3,4,5,6,1,2,8] => [1,3,4,5,7,6,2,8] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [6,5,3,4,7,1,2,8] => [1,3,6,5,4,7,2,8] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [5,6,3,4,7,1,2,8] => [1,3,5,6,4,7,2,8] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 3
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [6,3,4,5,7,1,2,8] => [1,3,4,6,5,7,2,8] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [4,5,3,6,7,1,2,8] => [1,4,5,3,6,7,2,8] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [5,3,4,6,7,1,2,8] => [1,3,5,4,6,7,2,8] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 3
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [4,3,5,6,7,1,2,8] => [1,4,3,5,6,7,2,8] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [3,4,5,6,7,1,2,8] => [1,3,4,5,6,7,2,8] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [1,2,7,6,5,4,3,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [6,7,5,4,1,2,3,8] => [1,2,6,7,5,4,3,8] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,1,2,3,8] => [1,2,5,7,6,4,3,8] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => [1,2,5,6,7,4,3,8] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [6,7,4,5,1,2,3,8] => [1,2,4,6,7,5,3,8] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => [1,2,5,6,4,7,3,8] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[[[[.,.],.],[[[.,.],[.,.]],.]],.] => [6,4,5,7,1,2,3,8] => [1,2,4,6,5,7,3,8] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => [1,2,5,4,6,7,3,8] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => [1,2,4,5,6,7,3,8] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [7,6,5,3,1,2,4,8] => [1,3,7,6,5,2,4,8] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [6,7,5,3,1,2,4,8] => [1,3,6,7,5,2,4,8] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [7,5,6,3,1,2,4,8] => [1,3,5,7,6,2,4,8] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => [1,3,5,6,7,2,4,8] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [7,6,5,2,1,3,4,8] => [2,1,7,6,5,3,4,8] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => [2,1,5,6,7,3,4,8] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [1,2,3,7,6,5,4,8] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => [1,2,3,6,7,5,4,8] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => [1,2,3,5,7,6,4,8] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => [1,2,3,6,5,7,4,8] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => [1,2,3,5,6,7,4,8] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => [1,4,7,6,3,2,5,8] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 3
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [6,7,3,4,1,2,5,8] => [1,3,4,6,7,2,5,8] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [7,6,3,1,2,4,5,8] => [1,3,2,7,6,4,5,8] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [6,7,3,1,2,4,5,8] => [1,3,2,6,7,4,5,8] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => [1,2,3,4,7,6,5,8] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => [1,2,3,4,6,7,5,8] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [7,4,5,3,1,2,6,8] => [1,4,5,7,3,2,6,8] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [7,5,3,4,1,2,6,8] => [1,3,5,7,4,2,6,8] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [7,3,4,5,1,2,6,8] => [1,3,4,5,7,2,6,8] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [7,5,4,1,2,3,6,8] => [1,2,5,7,4,3,6,8] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [7,4,5,1,2,3,6,8] => [1,2,4,5,7,3,6,8] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8] => [1,3,5,7,2,4,6,8] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [7,5,2,1,3,4,6,8] => [2,1,5,7,3,4,6,8] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [1,2,3,5,7,4,6,8] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [7,4,3,1,2,5,6,8] => [1,4,3,7,2,5,6,8] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 3
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [7,4,1,2,3,5,6,8] => [1,2,4,3,7,5,6,8] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [7,2,3,1,4,5,6,8] => [2,3,1,4,7,5,6,8] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => [2,1,3,4,7,5,6,8] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,7,6,8] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [6,5,4,3,1,2,7,8] => [1,6,5,4,3,2,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => [1,5,6,4,3,2,7,8] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [6,4,5,3,1,2,7,8] => [1,4,6,5,3,2,7,8] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => [1,5,4,6,3,2,7,8] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [4,5,6,3,1,2,7,8] => [1,4,5,6,3,2,7,8] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 2
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => [1,3,5,6,4,2,7,8] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => [1,5,4,3,6,2,7,8] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [4,5,3,6,1,2,7,8] => [1,4,5,3,6,2,7,8] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [5,3,4,6,1,2,7,8] => [1,3,5,4,6,2,7,8] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [4,3,5,6,1,2,7,8] => [1,4,3,5,6,2,7,8] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [3,4,5,6,1,2,7,8] => [1,3,4,5,6,2,7,8] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8] => [1,2,6,5,4,3,7,8] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [5,6,4,1,2,3,7,8] => [1,2,5,6,4,3,7,8] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [6,4,5,1,2,3,7,8] => [1,2,4,6,5,3,7,8] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => [1,2,4,5,6,3,7,8] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [6,5,3,1,2,4,7,8] => [1,3,6,5,2,4,7,8] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [5,6,3,1,2,4,7,8] => [1,3,5,6,2,4,7,8] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [5,6,2,1,3,4,7,8] => [2,1,5,6,3,4,7,8] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [6,5,1,2,3,4,7,8] => [1,2,3,6,5,4,7,8] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [5,6,1,2,3,4,7,8] => [1,2,3,5,6,4,7,8] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[[[[[.,.],[[.,.],.]],[.,.]],.],.] => [6,3,4,1,2,5,7,8] => [1,3,4,6,2,5,7,8] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => [1,2,4,6,3,5,7,8] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [6,3,1,2,4,5,7,8] => [1,3,2,6,4,5,7,8] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [6,2,1,3,4,5,7,8] => [2,1,3,6,4,5,7,8] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => [1,2,3,4,6,5,7,8] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [5,4,3,1,2,6,7,8] => [1,5,4,3,2,6,7,8] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [4,5,3,1,2,6,7,8] => [1,4,5,3,2,6,7,8] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 2
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [5,3,4,1,2,6,7,8] => [1,3,5,4,2,6,7,8] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [4,3,5,1,2,6,7,8] => [1,4,3,5,2,6,7,8] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [3,4,5,1,2,6,7,8] => [1,3,4,5,2,6,7,8] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 2
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [5,4,1,2,3,6,7,8] => [1,2,5,4,3,6,7,8] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [4,5,1,2,3,6,7,8] => [1,2,4,5,3,6,7,8] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => [1,3,5,2,4,6,7,8] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [5,2,1,3,4,6,7,8] => [2,1,5,3,4,6,7,8] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [4,3,1,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => [1,3,4,2,5,6,7,8] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,6 16,24,2 32,80,20 64,240,120,5
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 4\ q + q^{2}$
$F_{4} = 8\ q + 6\ q^{2}$
$F_{5} = 16\ q + 24\ q^{2} + 2\ q^{3}$
$F_{6} = 32\ q + 80\ q^{2} + 20\ q^{3}$
$F_{7} = 64\ q + 240\ q^{2} + 120\ q^{3} + 5\ q^{4}$
Description
The number of peaks visible from the left.
This is, the number of left-to-right maxima of the heights of the peaks of a Dyck path.
This is, the number of left-to-right maxima of the heights of the peaks of a Dyck path.
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
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