Identifier
-
Mp00024:
Dyck paths
—to 321-avoiding permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
St001786: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [.,.] => [1,0] => 1
[1,0,1,0] => [2,1] => [[.,.],.] => [1,1,0,0] => 1
[1,1,0,0] => [1,2] => [.,[.,.]] => [1,0,1,0] => 1
[1,0,1,0,1,0] => [2,1,3] => [[.,.],[.,.]] => [1,1,0,0,1,0] => 1
[1,0,1,1,0,0] => [2,3,1] => [[.,.],[.,.]] => [1,1,0,0,1,0] => 1
[1,1,0,0,1,0] => [3,1,2] => [[.,[.,.]],.] => [1,1,0,1,0,0] => 2
[1,1,0,1,0,0] => [1,3,2] => [.,[[.,.],.]] => [1,0,1,1,0,0] => 1
[1,1,1,0,0,0] => [1,2,3] => [.,[.,[.,.]]] => [1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
>>> Load all 1240 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,7,1,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,5,6,7,1,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,5,1,7,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,5,7,1,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,1,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,6,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,4,6,1,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,1,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,4,7,1,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,6,1,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,5,7,1,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,1,6,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 16
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 16
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 16
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,4,5,1,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,4,5,6,1,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,4,5,6,7,1,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,5,1,3,6,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5,6,1,3,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,7,3,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5,6,7,1,3,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,5,6,7,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5,1,6,7,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5,6,1,7,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5,6,7,1,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5,6,7,8,1,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,3,4,6,1,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,7,8,1,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,4,5,7,1,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,5,7,8,1,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,8,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,1,8,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,8,1,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,1,4,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,3,4,1,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,3,4,5,1,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,3,4,5,8,1,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [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
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,2,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,2,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,4,5,1,2,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,4,5,8,2,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,4,1,5,8,2,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [3,4,1,5,6,8,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,4,5,6,1,8,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,6,8,1,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,5,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,4,5,1,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,4,5,6,1,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,5,2,6,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,5,1,2,6,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,5,6,2,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5,1,6,2,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5,6,1,2,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,5,6,7,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5,1,6,7,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5,6,1,7,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,5,6,7,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5,1,6,7,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5,6,7,1,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5,6,7,8,1,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,7,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,7,2,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,7,1,2,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,7,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,7,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,7,8,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,7,8,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,7,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,7,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,7,4,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,7,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,7,8,2,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,5,6,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,6,1,2,7,4,8,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,6,1,7,2,4,8,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,6,7,1,2,4,8,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,6,1,2,7,8,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,6,7,2,8,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,6,1,7,2,8,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,6,7,1,2,8,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,6,1,7,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,7,8,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,7,8,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,7,8,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,6,7,4,8,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,2,6,7,8,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,2,4,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,3,4,2,5,8,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,3,4,5,2,8,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,3,4,5,8,2,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,3,4,5,6,8,2,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,6,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [4,5,1,6,2,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [4,5,6,1,2,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [4,1,5,6,7,2,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5,1,6,7,2,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5,6,1,7,2,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,1,5,6,7,8,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,5,1,6,7,8,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [4,5,6,1,7,8,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,8,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,8,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,8,2,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [4,5,8,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,8,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,8,3,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,5,6,8,3,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,5,2,6,8,3,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,5,6,8,2,3,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,5,2,6,7,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,5,6,2,7,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,5,6,7,2,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,5,6,7,8,2,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,6,7,2,3,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,6,7,1,2,3,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,6,1,2,7,8,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,6,1,7,2,8,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,6,7,1,2,8,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,6,7,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,6,1,7,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,6,7,3,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,8,5,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,8,5,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,8,3,5,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,6,7,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,7,2,8,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,7,1,2,8,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,7,8,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,7,1,8,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,7,8,1,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,7,2,3,8,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [4,7,1,2,3,8,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,7,8,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,7,2,3,5,8,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,7,1,2,3,5,8,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,2,7,3,5,8,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,2,3,7,5,8,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,3,7,8,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,8,2,3,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 16
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,8,1,2,3,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 16
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,8,3,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 16
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,3,8,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 16
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,2,3,5,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,4,3,5,8,6,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,4,5,3,8,6,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,4,5,8,3,6,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,4,5,6,8,3,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [5,6,1,2,7,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,6,7,2,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [5,6,1,7,2,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,1,2,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,6,1,2,7,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [5,1,6,7,2,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,6,7,1,2,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,1,6,7,8,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [5,6,1,7,8,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [5,6,1,2,3,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [5,1,2,6,3,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [5,1,2,6,7,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,6,2,8,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,6,1,2,8,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,6,1,8,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,6,8,1,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,8,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,8,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,8,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,1,2,6,8,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,6,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,7,2,8,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,7,1,2,8,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,1,7,8,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,7,1,8,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,7,8,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,7,2,3,8,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,7,1,2,3,8,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,7,3,8,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,7,8,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,7,2,3,4,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,7,3,4,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,7,4,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,7,8,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,8,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,8,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,8,3,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,3,8,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,2,3,4,8,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,5,6,8,4,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,7,1,2,8,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [6,1,7,8,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,7,1,8,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,7,2,3,8,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,7,1,2,3,8,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [6,1,2,7,3,8,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [6,1,2,7,8,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,7,2,3,4,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,7,1,2,3,4,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [6,1,2,7,3,4,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [6,1,2,3,7,4,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [6,1,2,3,7,8,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,8,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 16
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,8,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 16
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,8,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 16
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,8,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 16
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,8,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 16
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 16
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 32
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 32
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,8,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 32
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1,2,3,8,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 32
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1,2,3,4,8,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 32
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 32
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 32
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6,8] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 64
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 128
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 256
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 64
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 512
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 64
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,1,2,3,4,5,9,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 64
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 32
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,1,2,3,4,9,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 64
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 32
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1,2,3,9,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 64
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1,2,9,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 64
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 64
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,9,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 64
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,9,1,2,3,4,5,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 32
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,9,2,3,4,5,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 32
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,9,6,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,9,3,4,5,6,7,8] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,8] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,1,9,3,4,5,6,7,8] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,9,1,3,4,5,6,7,8] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,6,7,8,9,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,1,5,6,7,8,9,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,1,6,7,8,9,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,1,7,8,9,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,8,2,9,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [7,1,8,9,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,10,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,9,6,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,8,2,3,9,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,9,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,6,8,5,10,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,3,8,5,10,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,9,4,6,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,7,2,9,4,10,6,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,6,7,8,1,9,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,8,1,9,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [6,7,8,1,9,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,5,6,7,8,1,9,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,9,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,4,1,5,6,7,8,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,5,6,1,7,8,9,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,5,6,7,8,9,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0] => [5,6,1,7,8,9,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0] => [5,6,7,1,8,2,3,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,9,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,8,9,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
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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 9,4,0,1 21,15,0,5,0,0,0,1 51,50,0,24,0,0,0,6,0,0,0,0,0,0,0,1 127,161,0,98,0,0,0,35,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 4\ q + q^{2}$
$F_{4} = 9\ q + 4\ q^{2} + q^{4}$
$F_{5} = 21\ q + 15\ q^{2} + 5\ q^{4} + q^{8}$
$F_{6} = 51\ q + 50\ q^{2} + 24\ q^{4} + 6\ q^{8} + q^{16}$
$F_{7} = 127\ q + 161\ q^{2} + 98\ q^{4} + 35\ q^{8} + 7\ q^{16} + q^{32}$
Description
The number of total orderings of the north steps of a Dyck path such that steps after the k-th east step are not among the first k positions in the order.
Alternatively, remark that the monomials of the polynomial $\prod_{k=1}^n (z_1+\dots +z_k)$ are in bijection with Dyck paths, regarded as superdiagonal paths, with $n$ east steps: the exponent of $z_i$ is the number of north steps before the $i$-th east step, see [2]. Thus, this statistic records the coefficients of the monomials.
A formula for the coefficient of $z_1^{a_1}\dots z_n^{a_n}$ is provided in [3]:
$$ c_{(a_1,\dots,a_n)} = \prod_{k=1}^{n-1} \frac{n-k+1 - \sum_{i=k+1}^n a_i}{a_k!}. $$
This polynomial arises in a partial symmetrization process as follows, see [1]. For $w\in\frak{S}_n$, let $w\cdot F(x_1,\dots,x_n)=F(x_{w(1)},\dots,x_{w(n)})$. Furthermore, let
$$G(\mathbf{x},\mathbf{z}) = \prod_{k=1}^n\frac{x_1z_1+x_2z_2+\cdots+x_kz_k}{x_k-x_{k+1}}.$$
Then $\sum_{w\in\frak{S}_{n+1}}w\cdot G = \prod_{k=1}^n (z_1+\dots +z_k)$.
Alternatively, remark that the monomials of the polynomial $\prod_{k=1}^n (z_1+\dots +z_k)$ are in bijection with Dyck paths, regarded as superdiagonal paths, with $n$ east steps: the exponent of $z_i$ is the number of north steps before the $i$-th east step, see [2]. Thus, this statistic records the coefficients of the monomials.
A formula for the coefficient of $z_1^{a_1}\dots z_n^{a_n}$ is provided in [3]:
$$ c_{(a_1,\dots,a_n)} = \prod_{k=1}^{n-1} \frac{n-k+1 - \sum_{i=k+1}^n a_i}{a_k!}. $$
This polynomial arises in a partial symmetrization process as follows, see [1]. For $w\in\frak{S}_n$, let $w\cdot F(x_1,\dots,x_n)=F(x_{w(1)},\dots,x_{w(n)})$. Furthermore, let
$$G(\mathbf{x},\mathbf{z}) = \prod_{k=1}^n\frac{x_1z_1+x_2z_2+\cdots+x_kz_k}{x_k-x_{k+1}}.$$
Then $\sum_{w\in\frak{S}_{n+1}}w\cdot G = \prod_{k=1}^n (z_1+\dots +z_k)$.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
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