Identifier
Mp00034:
Dyck paths
—to binary tree: up step, left tree, down step, right tree⟶
Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
[1,0] => [.,.] => [1] => [.,.]
[1,0,1,0] => [.,[.,.]] => [2,1] => [[.,.],.]
[1,1,0,0] => [[.,.],.] => [1,2] => [.,[.,.]]
[1,0,1,0,1,0] => [.,[.,[.,.]]] => [3,2,1] => [[[.,.],.],.]
[1,0,1,1,0,0] => [.,[[.,.],.]] => [2,3,1] => [[.,.],[.,.]]
[1,1,0,0,1,0] => [[.,.],[.,.]] => [1,3,2] => [.,[[.,.],.]]
[1,1,0,1,0,0] => [[.,[.,.]],.] => [2,1,3] => [[.,.],[.,.]]
[1,1,1,0,0,0] => [[[.,.],.],.] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => [[[[.,.],.],.],.]
[1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => [3,4,2,1] => [[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0] => [.,[[.,.],[.,.]]] => [2,4,3,1] => [[.,.],[[.,.],.]]
[1,0,1,1,0,1,0,0] => [.,[[.,[.,.]],.]] => [3,2,4,1] => [[[.,.],.],[.,.]]
[1,0,1,1,1,0,0,0] => [.,[[[.,.],.],.]] => [2,3,4,1] => [[.,.],[.,[.,.]]]
[1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => [1,4,3,2] => [.,[[[.,.],.],.]]
[1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => [1,3,4,2] => [.,[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,.]] => [2,1,4,3] => [[.,.],[[.,.],.]]
[1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],.] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],.] => [2,3,1,4] => [[.,.],[.,[.,.]]]
[1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => [1,2,4,3] => [.,[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],.] => [1,3,2,4] => [.,[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],.] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,1,1,1,0,0,0,0] => [[[[.,.],.],.],.] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [[[.,.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,0] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]]
[1,0,1,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
[1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [[[.,.],.],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]]
[1,0,1,1,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [[.,.],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]]
[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] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [.,[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [.,[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [.,[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [[[.,.],.],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [[.,.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [[[[.,.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [[[[.,.],.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [[.,.],[[[[.,.],.],.],.]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [[[[.,.],.],.],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]]
>>> Load all 1924 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]]
[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] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [.,[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [.,[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [.,[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [.,[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [.,[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [.,[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
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[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
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[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],.]]
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[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [[[.,.],.],[[[[.,.],.],.],.]]
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[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [[[[.,.],.],.],[[[.,.],.],.]]
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[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
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[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
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[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]]
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[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [[.,.],[.,[[.,.],[[.,.],.]]]]
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[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]]
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[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[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] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [.,[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [6,8,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [5,8,7,6,4,3,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [5,7,8,6,4,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [5,6,8,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [4,7,8,6,5,3,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [4,7,6,8,5,3,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [5,4,7,8,6,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [5,6,4,8,7,3,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [5,7,6,4,8,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [4,5,8,7,6,3,2,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [4,6,5,8,7,3,2,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [4,6,7,5,8,3,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [5,4,7,6,8,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [4,5,7,6,8,3,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [4,6,5,7,8,3,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [3,8,7,6,5,4,2,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [3,7,8,6,5,4,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [3,6,8,7,5,4,2,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [3,7,6,8,5,4,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [3,7,6,5,8,4,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [3,5,6,8,7,4,2,1] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [3,5,7,6,8,4,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [3,5,6,7,8,4,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [4,3,7,8,6,5,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [4,3,6,7,8,5,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [5,4,3,8,7,6,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [5,4,3,7,8,6,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [6,5,4,3,8,7,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [5,6,4,3,8,7,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [5,7,6,4,3,8,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [6,5,7,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [4,5,3,7,8,6,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [4,7,6,5,3,8,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [5,4,7,6,3,8,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [4,5,6,3,8,7,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [3,5,4,7,8,6,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [3,6,5,4,8,7,2,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [3,7,6,5,4,8,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [3,5,7,6,4,8,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [3,5,6,7,4,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [4,3,5,7,8,6,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [4,3,7,6,5,8,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
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[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [4,5,3,6,8,7,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [4,5,3,7,6,8,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
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[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [3,4,6,7,5,8,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [3,5,4,7,6,8,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [3,6,5,4,7,8,2,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [3,5,6,4,7,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [4,3,5,6,8,7,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
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[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [4,3,6,5,7,8,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
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[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [3,4,5,7,6,8,2,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [3,4,6,5,7,8,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [3,5,4,6,7,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
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[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [2,7,6,8,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [2,6,7,8,5,4,3,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
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[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [2,4,8,7,6,5,3,1] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [2,4,7,8,6,5,3,1] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [2,4,6,7,8,5,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [2,5,4,8,7,6,3,1] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [2,5,4,7,8,6,3,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [2,6,5,4,8,7,3,1] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [2,7,6,5,4,8,3,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [2,5,6,4,8,7,3,1] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [2,5,6,7,4,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [2,4,5,7,8,6,3,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [2,4,6,5,8,7,3,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [2,4,6,7,5,8,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [2,5,4,7,6,8,3,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [2,6,5,4,7,8,3,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [2,5,6,4,7,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [2,4,5,6,8,7,3,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [2,4,6,5,7,8,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [2,5,4,6,7,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [2,4,5,6,7,8,3,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [3,2,7,8,6,5,4,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [3,2,6,8,7,5,4,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [3,2,5,7,8,6,4,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [3,2,6,7,5,8,4,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [3,2,5,7,6,8,4,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [3,2,5,6,7,8,4,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [4,3,2,7,8,6,5,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [4,3,2,6,8,7,5,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [5,4,3,2,8,7,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [5,4,3,2,7,8,6,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [6,5,4,3,2,8,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [5,7,6,4,3,2,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [4,5,3,2,8,7,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [4,6,5,3,2,8,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [4,7,6,5,3,2,8,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [4,6,7,5,3,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [5,4,6,3,2,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [4,5,6,3,2,8,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [4,6,5,7,3,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [3,4,2,7,8,6,5,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [3,5,4,2,7,8,6,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [3,6,5,4,2,8,7,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [3,5,6,4,2,8,7,1] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [3,5,7,6,4,2,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [3,5,6,7,4,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [4,3,5,2,8,7,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [4,3,6,5,2,8,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [4,3,7,6,5,2,8,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
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[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [5,4,3,6,2,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [5,4,3,7,6,2,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [4,6,5,3,7,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [3,4,5,2,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [3,4,7,6,5,2,8,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [3,4,6,7,5,2,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [3,5,4,7,6,2,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [3,6,5,4,7,2,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [3,4,5,6,2,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [3,4,5,7,6,2,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [3,4,6,5,7,2,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [3,5,4,6,7,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [4,3,5,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [2,3,6,7,8,5,4,1] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [2,3,5,8,7,6,4,1] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [2,3,5,7,8,6,4,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [2,3,6,5,8,7,4,1] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [2,3,7,6,5,8,4,1] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [2,3,5,7,6,8,4,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [2,3,5,6,7,8,4,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [2,4,3,8,7,6,5,1] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [2,4,3,6,8,7,5,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [2,4,3,6,7,8,5,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [2,5,4,3,7,8,6,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [2,6,5,4,3,8,7,1] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [2,6,5,7,4,3,8,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [2,5,6,7,4,3,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [2,4,5,3,8,7,6,1] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [2,4,5,3,7,8,6,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [2,4,6,5,3,8,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [2,4,6,7,5,3,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [2,5,4,7,6,3,8,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [2,4,5,6,3,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [2,5,4,6,7,3,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [2,4,5,6,7,3,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [3,2,4,8,7,6,5,1] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [3,2,4,7,8,6,5,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [3,2,5,4,7,8,6,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [3,2,7,6,5,4,8,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [3,2,6,7,5,4,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [3,2,5,7,6,4,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [3,2,5,6,7,4,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [4,3,2,5,8,7,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [4,3,2,5,7,8,6,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [4,3,2,6,5,8,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [4,3,2,6,7,5,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [5,4,3,2,6,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [5,4,3,2,7,6,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [3,4,2,5,8,7,6,1] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [3,4,2,5,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [3,4,2,6,5,8,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [3,4,2,7,6,5,8,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [3,4,2,6,7,5,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [3,5,4,2,7,6,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [3,6,5,4,2,7,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [3,5,6,4,2,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [3,4,5,2,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [3,4,6,5,2,7,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [3,5,4,6,2,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
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[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [2,3,4,6,8,7,5,1] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
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[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [2,3,7,6,5,4,8,1] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
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[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
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[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [2,5,4,3,6,8,7,1] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
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[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [2,4,6,5,3,7,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
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[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [3,2,4,5,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
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[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [3,2,5,6,4,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [4,3,2,5,6,8,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
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[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
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[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [3,4,2,5,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
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[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [2,3,4,7,6,5,8,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [2,3,4,6,7,5,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [2,3,5,4,7,6,8,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [2,3,6,5,4,7,8,1] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => [2,3,5,6,4,7,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [2,4,3,5,7,6,8,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [2,4,3,6,5,7,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => [2,4,5,3,6,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [3,2,4,5,6,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [3,2,5,4,6,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
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[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [2,3,4,6,5,7,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => [2,4,3,5,6,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,6,5,8,7,4,3,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,5,7,6,8,4,3,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,6,5,7,8,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,4,6,7,8,5,3,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,5,4,7,8,6,3,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,4,5,8,7,6,3,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,4,6,5,8,7,3,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,4,7,6,5,8,3,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,4,6,7,5,8,3,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,6,5,4,7,8,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,5,6,4,7,8,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,5,4,6,7,8,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,4,5,6,7,8,3,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => [.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,3,7,8,6,5,4,2] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,3,6,8,7,5,4,2] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,3,6,7,8,5,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,3,5,8,7,6,4,2] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,3,6,7,5,8,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,3,5,6,8,7,4,2] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,4,3,6,8,7,5,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,4,3,7,6,8,5,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,4,3,6,7,8,5,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,5,4,3,8,7,6,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,6,7,5,4,3,8,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,6,5,7,4,3,8,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,5,6,7,4,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,4,5,3,8,7,6,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,4,5,3,7,8,6,2] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,4,6,5,3,8,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,4,5,6,3,8,7,2] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,4,6,5,7,3,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,3,4,7,6,8,5,2] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,3,4,6,7,8,5,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,3,5,4,8,7,6,2] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,3,6,5,4,8,7,2] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,3,6,5,7,4,8,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,3,5,6,7,4,8,2] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,4,3,5,8,7,6,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,4,3,5,7,8,6,2] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,5,4,3,6,8,7,2] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,4,5,3,6,8,7,2] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,5,4,6,3,7,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,3,4,5,8,7,6,2] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,3,4,7,6,5,8,2] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,3,4,6,7,5,8,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,3,5,4,7,6,8,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,4,3,6,5,7,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,5,4,3,6,7,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,3,4,5,7,6,8,2] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,3,4,6,5,7,8,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [2,1,7,8,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [2,1,6,8,7,5,4,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [2,1,5,8,7,6,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [2,1,6,5,8,7,4,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [2,1,7,6,5,8,4,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [2,1,5,6,8,7,4,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [2,1,5,7,6,8,4,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [2,1,4,7,8,6,5,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [2,1,4,6,7,8,5,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [2,1,5,4,8,7,6,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [2,1,5,4,7,8,6,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [2,1,6,5,4,8,7,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [2,1,7,6,5,4,8,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [2,1,6,7,5,4,8,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [2,1,5,6,4,8,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [2,1,5,7,6,4,8,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [2,1,5,6,7,4,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [2,1,4,5,7,8,6,3] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [2,1,4,7,6,5,8,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [2,1,4,6,7,5,8,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [2,1,5,4,6,8,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [2,1,5,6,4,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [2,1,4,5,6,8,7,3] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [2,1,5,4,6,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [3,2,1,7,8,6,5,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [3,2,1,6,8,7,5,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [3,2,1,7,6,8,5,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [3,2,1,5,7,6,8,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [3,2,1,6,5,7,8,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [5,6,4,3,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [4,5,3,2,1,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [4,6,5,3,2,1,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [4,6,7,5,3,2,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [5,4,6,3,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [5,4,7,6,3,2,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [4,5,7,6,3,2,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [4,6,5,7,3,2,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [3,4,2,1,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [3,5,4,2,1,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [3,5,4,2,1,7,8,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [3,6,5,4,2,1,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [3,5,7,6,4,2,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [3,5,6,7,4,2,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [4,3,5,2,1,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [4,3,6,5,2,1,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [4,3,7,6,5,2,1,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [5,4,3,6,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [5,4,3,7,6,2,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [4,5,3,6,2,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [3,4,5,2,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [3,4,6,5,2,1,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [3,5,4,7,6,2,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [3,6,5,4,7,2,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [3,5,6,4,7,2,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [4,3,5,6,2,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [4,3,6,5,7,2,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [3,4,5,6,2,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [2,3,1,7,8,6,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [2,3,1,6,8,7,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [2,3,1,7,6,8,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [2,3,1,6,7,8,5,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [2,3,1,5,7,8,6,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [2,3,1,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [2,3,1,7,6,5,8,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [2,3,1,6,7,5,8,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [2,3,1,5,7,6,8,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => [2,3,1,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [2,4,3,1,7,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [2,4,3,1,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [2,5,4,3,1,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [2,5,4,3,1,7,8,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [2,6,5,4,3,1,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [2,6,7,5,4,3,1,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [2,5,6,4,3,1,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [2,5,7,6,4,3,1,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [2,5,6,7,4,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [2,4,5,3,1,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [2,4,5,3,1,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [2,4,6,5,3,1,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [2,5,4,7,6,3,1,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [2,5,6,4,7,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [2,5,4,6,7,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[.,[[.,.],[[[[.,.],.],.],.]]],.] => [2,4,5,6,7,3,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [3,2,4,1,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [3,2,5,4,1,7,8,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [3,2,6,5,4,1,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [3,2,6,7,5,4,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [3,2,5,6,4,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [3,2,5,7,6,4,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [3,2,6,5,7,4,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [3,2,5,6,7,4,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [4,3,2,5,1,7,8,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [4,3,2,6,5,1,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [4,3,2,6,7,5,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [5,4,3,2,6,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [4,5,3,2,6,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [4,5,3,2,7,6,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [3,4,2,5,1,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [3,4,2,6,5,1,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [3,4,2,7,6,5,1,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [3,4,2,6,7,5,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [3,5,4,2,6,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [3,5,4,2,7,6,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [3,6,5,4,2,7,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [3,5,6,4,2,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [4,3,5,2,7,6,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [3,4,5,2,6,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [3,4,5,2,7,6,1,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [3,4,6,5,2,7,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [2,3,4,1,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [2,3,4,1,6,8,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [2,3,5,4,1,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [2,3,6,5,4,1,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [2,3,7,6,5,4,1,8] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [2,3,6,7,5,4,1,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [2,3,5,6,4,1,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [2,3,5,7,6,4,1,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [2,3,6,5,7,4,1,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[.,[[[.,.],.],[[[.,.],.],.]]],.] => [2,3,5,6,7,4,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [2,4,3,5,1,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [2,4,3,5,1,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [2,5,4,3,6,1,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [2,4,5,3,6,1,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [2,5,4,6,3,7,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[.,[[[.,.],[[[.,.],.],.]],.]],.] => [2,4,5,6,3,7,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [3,2,4,5,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [3,2,4,6,7,5,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [3,2,6,5,4,7,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [4,3,2,5,6,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [4,3,2,5,7,6,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [4,3,2,6,5,7,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [3,4,2,5,6,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [3,4,2,5,7,6,1,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [3,4,2,6,5,7,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [3,5,4,2,6,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [2,3,4,5,1,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [2,3,4,7,6,5,1,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[.,[[[[.,.],.],.],[[.,.],.]]],.] => [2,3,4,6,7,5,1,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[.,[[[[.,.],.],[[.,.],.]],.]],.] => [2,3,5,6,4,7,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [2,4,3,5,6,1,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [2,4,3,6,5,7,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [2,5,4,3,6,7,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[.,[[[[[.,.],.],[.,.]],.],.]],.] => [2,3,5,4,6,7,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[.,[[[[[.,.],[.,.]],.],.],.]],.] => [2,4,3,5,6,7,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => [.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,2,7,6,8,5,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,2,5,8,7,6,4,3] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,2,6,5,8,7,4,3] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,2,5,6,8,7,4,3] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,2,5,7,6,8,4,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,2,6,5,7,8,4,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,2,5,6,7,8,4,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,2,4,7,8,6,5,3] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,2,4,6,8,7,5,3] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,2,5,4,8,7,6,3] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,2,5,4,7,8,6,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,2,6,5,4,8,7,3] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,2,7,6,5,4,8,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,2,5,7,6,4,8,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,2,4,5,8,7,6,3] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,2,4,5,7,8,6,3] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,2,4,6,5,8,7,3] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,2,4,7,6,5,8,3] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,2,5,4,6,8,7,3] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,2,5,4,7,6,8,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,2,6,5,4,7,8,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,2,5,6,4,7,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,2,4,5,6,8,7,3] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,3,2,7,6,8,5,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,3,2,6,7,8,5,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,3,2,5,8,7,6,4] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,3,2,5,7,8,6,4] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,3,2,6,5,8,7,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,3,2,7,6,5,8,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,3,2,6,7,5,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,3,2,5,6,8,7,4] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,3,2,6,5,7,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,3,2,5,6,7,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,4,3,2,6,8,7,5] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,5,4,3,2,7,8,6] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,6,5,7,4,3,2,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,5,6,7,4,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,4,5,3,2,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,4,5,3,2,7,8,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,4,7,6,5,3,2,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,4,6,7,5,3,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,5,4,6,3,2,8,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,5,6,4,7,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,4,6,5,7,3,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,5,4,6,7,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,3,4,2,7,8,6,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,3,4,2,6,8,7,5] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,3,4,2,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,3,5,4,2,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,3,6,5,4,2,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,3,6,7,5,4,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,3,5,7,6,4,2,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,3,6,5,7,4,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,3,5,6,7,4,2,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,5,4,6,3,7,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,4,5,6,3,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,3,4,5,2,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,3,4,5,2,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,3,5,4,7,6,2,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,3,6,5,4,7,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,4,3,5,7,6,2,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,4,3,6,5,7,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,5,4,3,6,7,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,4,5,3,6,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,3,4,5,6,2,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,3,4,5,7,6,2,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,3,4,6,5,7,2,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,4,3,5,6,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,3,4,5,6,7,2,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [2,1,3,7,8,6,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [2,1,3,6,8,7,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [2,1,3,6,7,8,5,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [2,1,3,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [2,1,3,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [2,1,7,6,5,4,3,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [2,1,6,7,5,4,3,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [2,1,5,6,7,4,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [2,1,4,5,3,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [2,1,5,4,6,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [2,1,4,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [3,2,1,4,7,8,6,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [3,2,1,4,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [3,2,1,4,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [3,2,1,4,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [3,2,1,6,5,4,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [3,2,1,5,7,6,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [3,2,1,6,5,7,4,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [4,5,3,2,1,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [4,5,3,2,1,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => [3,5,4,2,1,6,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [3,5,4,2,1,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [3,6,5,4,2,1,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [4,3,5,2,1,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [4,3,6,5,2,1,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [3,4,5,2,1,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [3,4,5,2,1,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [2,3,1,4,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [2,3,1,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [2,3,1,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [2,3,1,6,7,5,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [2,3,1,6,5,7,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [2,4,3,1,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [2,5,4,3,1,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [2,5,4,3,1,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [2,4,5,3,1,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [2,4,5,3,1,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [2,4,6,5,3,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [[[.,[[.,.],[[[.,.],.],.]]],.],.] => [2,4,5,6,3,1,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [3,2,5,4,1,6,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [3,2,5,4,1,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [4,3,2,6,5,1,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [3,4,2,5,1,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [3,5,4,2,6,1,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [2,3,4,1,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [[[.,[[[.,.],.],.]],.],[[.,.],.]] => [2,3,4,1,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [[[.,[[[.,.],.],.]],[[.,.],.]],.] => [2,3,4,1,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [2,3,5,4,1,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [2,3,5,4,1,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [2,3,6,5,4,1,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [[[.,[[[.,.],.],[[.,.],.]]],.],.] => [2,3,5,6,4,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [2,4,3,5,1,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [2,4,3,6,5,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,[[[[.,.],.],.],.]],.],[.,.]] => [2,3,4,5,1,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [[[.,[[[[.,.],.],.],.]],[.,.]],.] => [2,3,4,5,1,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,2,4,3,7,8,6,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,2,5,4,3,7,8,6] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,2,6,7,5,4,3,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,2,5,7,6,4,3,8] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,2,5,6,7,4,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,2,4,5,3,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,2,4,6,7,5,3,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,2,5,6,4,7,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,2,4,5,6,3,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,2,4,6,5,7,3,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,2,5,4,6,7,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,2,4,5,6,7,3,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,3,2,4,6,8,7,5] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,3,2,4,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,3,2,7,6,5,4,8] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,3,2,6,7,5,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,3,2,5,6,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,3,2,5,7,6,4,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,3,2,6,5,7,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,3,2,5,6,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,4,3,2,5,7,8,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,4,3,2,6,7,5,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,5,6,4,3,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,4,5,3,2,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,4,5,3,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,4,6,5,3,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,5,4,6,3,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,4,5,6,3,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,3,4,2,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,3,5,4,2,6,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,4,3,5,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,4,3,6,5,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,5,4,3,6,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,4,5,3,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,4,3,5,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [2,1,3,4,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [2,1,3,5,4,7,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [2,1,3,6,7,5,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [2,1,4,3,5,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [2,1,4,3,6,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [2,1,5,4,3,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [2,1,5,6,4,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [2,1,4,6,5,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [3,2,1,4,5,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [3,2,1,5,6,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [3,5,4,2,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [2,3,1,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [2,3,1,6,5,4,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [[[[.,[[.,.],.]],[[.,.],.]],.],.] => [2,3,1,5,6,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [2,4,3,1,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [2,5,4,3,1,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [3,2,5,4,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => [2,3,4,1,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [[[[.,[[[.,.],.],.]],.],[.,.]],.] => [2,3,4,1,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [[[[.,[[[.,.],.],.]],[.,.]],.],.] => [2,3,4,1,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [[[[.,[[[.,.],.],[.,.]]],.],.],.] => [2,3,5,4,1,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,2,3,5,4,7,8,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,2,3,5,7,6,4,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,2,3,6,5,7,4,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,2,4,3,5,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,2,4,3,6,7,5,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,2,4,5,3,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,2,4,6,5,3,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,3,2,4,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,3,2,4,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,3,2,5,6,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,4,5,3,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,3,4,2,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,3,4,2,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,4,3,5,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [2,1,3,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [3,2,1,5,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [2,3,1,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => [2,3,1,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,3,2,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [2,3,1,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [2,4,3,5,6,7,8,9,1] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,10,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [2,3,4,5,6,7,1,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => [5,4,3,2,6,7,8,9,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,9,8,1] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [2,1,3,4,5,6,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]] => [5,4,3,2,6,7,8,9,10,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,4,3,5,6,7,8,9,2] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,6,8,7,10,9] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,7,9,10,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,10,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,8,10,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.] => [6,5,8,7,4,3,2,1,9] => [[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => [7,6,5,8,4,3,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.] => [6,7,5,8,4,3,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.] => [6,5,7,8,4,3,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.] => [6,5,4,7,8,3,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.] => [6,5,4,3,7,8,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [2,8,7,6,5,4,3,1,9] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => [6,5,4,3,2,7,8,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [2,3,4,5,6,8,7,1,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,8,7,6,5,4,3,2,9] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,3,4,5,6,7,8,2,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [2,1,8,7,6,5,4,3,9] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [5,4,3,2,1,8,7,6,9] => [[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [6,5,4,3,2,1,8,7,9] => [[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.] => [5,6,4,3,2,7,1,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [2,3,4,5,7,6,1,8,9] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.] => [5,6,4,3,2,1,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [2,3,4,6,5,1,7,8,9] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [[[[[.,[[.,[[.,.],.]],.]],.],.],.],.] => [3,4,2,5,1,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [2,3,5,4,1,6,7,8,9] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [1,3,4,5,2,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [2,1,4,5,3,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [3,2,1,5,4,6,7,8,9] => [[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [2,3,1,5,4,6,7,8,9] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [2,4,3,1,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [1,2,4,5,3,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [1,3,2,5,4,6,7,8,9] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,4,3,2,5,6,7,8,9] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,3,4,2,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [2,1,3,4,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [2,1,4,3,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,8,7,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,7,6,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,6,5,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,2,3,5,4,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [6,8,7,9,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [5,8,7,6,9,4,3,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [4,8,7,6,5,9,3,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [3,8,7,6,5,4,9,2,1] => [[[.,.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [2,8,7,6,5,4,3,9,1] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,9,8,7,6,5,4,3,2,10] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => [7,6,5,4,3,2,8,9,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]] => [8,7,6,5,4,3,2,9,10,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [7,6,5,4,3,2,1,9,8,10] => [[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]] => [7,6,5,4,3,2,8,9,10,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [7,9,8,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [4,9,8,7,6,5,3,2,1] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [3,9,8,7,6,5,4,2,1] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [3,5,6,7,8,9,4,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [2,8,9,7,6,5,4,3,1] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [2,4,5,6,7,8,9,3,1] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [2,3,9,8,7,6,5,4,1] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [2,3,4,5,6,8,9,7,1] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [1,3,4,5,6,7,9,8,2] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,9,8,7,6,5,4,3] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,3] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,9,8,7,6,5,4] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,5,6,7,8,9,4] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,9,8,7,6,5] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,6,7,8,9,5] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,9,8,7,6] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,7,8,9,6] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [6,10,9,8,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,9,10,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,3,5,7,9,10,8,6,4,2] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,2,10,9,8,7,6,5,4,3] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,10,3] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,3,10,9,8,7,6,5,4] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,3,5,6,7,8,9,10,4] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,4,10,9,8,7,6,5] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,4,6,7,8,9,10,5] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,5,10,9,8,7,6] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,5,7,8,9,10,6] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,6,10,9,8,7] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,6,8,9,10,7] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [2,1,9,8,7,6,5,4,3] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [3,2,1,9,8,7,6,5,4] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [4,3,2,1,9,8,7,6,5] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [5,4,3,2,1,9,8,7,6] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [6,5,4,3,2,1,9,8,7] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [7,6,5,4,3,2,1,9,8] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [2,3,1,9,8,7,6,5,4] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [3,2,1,10,9,8,7,6,5,4] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]] => [3,4,2,1,9,8,7,6,5] => [[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => [4,5,3,2,1,9,8,7,6] => [[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [5,4,3,2,1,10,9,8,7,6] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => [5,6,4,3,2,1,9,8,7] => [[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [6,7,5,4,3,2,1,9,8] => [[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [7,6,5,4,3,2,1,10,9,8] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => [5,6,4,3,2,1,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.] => [6,7,5,4,3,2,1,8,9,10,11] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.] => [6,7,5,4,3,2,1,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,8,7,9,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [1,9,8,10,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [2,8,7,9,6,5,4,3,1] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] => [2,1,8,9,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,9,8,10] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,8,10,9,11] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,4,6,5,9,8,7] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,3,5,4,9,8,7,6] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,2,4,3,9,8,7,6,5] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,3,2,9,8,7,6,5,4] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => [8,7,6,5,4,3,2,9,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [2,1,4,5,6,7,8,9,3] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,[.,.]],.],[[[[[.,.],.],.],.],.]] => [2,1,3,5,6,7,8,9,4] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]] => [4,3,2,1,8,9,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]] => [6,5,4,3,2,7,8,9,10,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,7,6,5,4,3,2,9,8] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [6,5,4,3,2,1,8,9,7] => [[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]] => [5,4,3,2,1,7,8,9,6] => [[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]] => [4,3,2,1,6,7,8,9,5] => [[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.] => [7,6,8,9,5,4,3,2,1,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.] => [7,6,5,8,9,4,3,2,1,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.] => [7,6,5,4,8,9,3,2,1,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.] => [7,6,5,4,3,8,9,2,1,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.] => [7,6,5,4,3,2,8,9,1,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [1,4,5,6,7,8,3,9,2] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[[.,.],.],[[[.,[[[.,.],.],.]],.],.]] => [1,2,5,6,7,4,8,9,3] => [.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [1,2,3,6,5,7,8,9,4] => [.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,5,8,7,9,6] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,6,8,7,9,10] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,4,7,6,8,9,5] => [.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,5,7,6,8,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,2,3,4,6,5,7,8,9,10] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [1,2,5,4,6,7,8,9,3] => [.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,2,3,5,4,6,7,8,9,10] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9,10] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,10,1] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,11,10,12,1] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]] => [5,4,3,2,1,8,9,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [7,6,5,4,3,2,9,8,1] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [7,6,5,4,3,2,1,9,10,8] => [[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [8,7,6,5,4,3,2,10,9,1] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [1,6,7,5,8,4,9,3,10,2] => [.,[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,10,9,1] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,10,9,12,11,1] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,9,8,1,10] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,9,8,11,10,1,12] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
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.
searching the database
Sorry, this map was not found in the database.