Identifier
Mp00029:
Dyck paths
—to binary tree: left tree, up step, right tree, down step⟶
Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
[1,0] => [.,.] => [1] =>
[1,0,1,0] => [[.,.],.] => [1,2] => 1
[1,1,0,0] => [.,[.,.]] => [2,1] => 0
[1,0,1,0,1,0] => [[[.,.],.],.] => [1,2,3] => 11
[1,0,1,1,0,0] => [[.,.],[.,.]] => [3,1,2] => 00
[1,1,0,0,1,0] => [[.,[.,.]],.] => [2,1,3] => 01
[1,1,0,1,0,0] => [.,[[.,.],.]] => [2,3,1] => 00
[1,1,1,0,0,0] => [.,[.,[.,.]]] => [3,2,1] => 00
[1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => [1,2,3,4] => 111
[1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => [4,1,2,3] => 000
[1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => [3,1,2,4] => 001
[1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => [3,4,1,2] => 000
[1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => [4,3,1,2] => 000
[1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => [2,1,3,4] => 011
[1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => [4,2,1,3] => 000
[1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => [2,3,1,4] => 001
[1,1,0,1,0,1,0,0] => [.,[[[.,.],.],.]] => [2,3,4,1] => 000
[1,1,0,1,1,0,0,0] => [.,[[.,.],[.,.]]] => [4,2,3,1] => 000
[1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 001
[1,1,1,0,0,1,0,0] => [.,[[.,[.,.]],.]] => [3,2,4,1] => 000
[1,1,1,0,1,0,0,0] => [.,[.,[[.,.],.]]] => [3,4,2,1] => 000
[1,1,1,1,0,0,0,0] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 000
[1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 1111
[1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 0000
[1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 0001
[1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 0000
[1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 0000
[1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => 0011
[1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 0000
[1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 0001
[1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 0000
[1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0000
[1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => 0001
[1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 0000
[1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 0000
[1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 0000
[1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 0111
[1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 0000
[1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 0001
[1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 0000
[1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 0000
[1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 0011
[1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 0000
[1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 0001
[1,1,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 0000
[1,1,0,1,0,1,1,0,0,0] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => 0000
[1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => 0001
[1,1,0,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => 0000
[1,1,0,1,1,0,1,0,0,0] => [.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => 0000
[1,1,0,1,1,1,0,0,0,0] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => 0000
[1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 0011
[1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 0000
[1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 0001
[1,1,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 0000
[1,1,1,0,0,1,1,0,0,0] => [.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => 0000
[1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 0001
[1,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 0000
[1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 0000
[1,1,1,0,1,1,0,0,0,0] => [.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => 0000
[1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 0001
[1,1,1,1,0,0,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 0000
[1,1,1,1,0,0,1,0,0,0] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 0000
[1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 0000
[1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 0000
[1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 11111
[1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 00000
[1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 00001
[1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 00000
[1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 00000
[1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 00011
[1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 00000
[1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 00001
[1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 00000
[1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 00000
[1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 00001
[1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 00000
[1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 00000
[1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 00000
[1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => 00111
[1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 00000
[1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 00001
[1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 00000
[1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 00000
[1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 00011
[1,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 00000
[1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 00001
[1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 00000
[1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 00000
[1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 00001
[1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 00000
[1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 00000
[1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 00000
[1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => 00011
[1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 00000
[1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 00001
[1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 00000
[1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 00000
[1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 00001
[1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 00000
[1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 00000
[1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 00000
>>> Load all 1655 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 00001
[1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 00000
[1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 00000
[1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 00000
[1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 00000
[1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 01111
[1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 00000
[1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 00001
[1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 00000
[1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 00000
[1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 00011
[1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 00000
[1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 00001
[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 00000
[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 00000
[1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 00001
[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 00000
[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 00000
[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 00000
[1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 00111
[1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 00000
[1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 00001
[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 00000
[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 00000
[1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 00011
[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 00000
[1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 00001
[1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 00000
[1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 00000
[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => 00001
[1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => 00000
[1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 00000
[1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 00000
[1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => 00011
[1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 00000
[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => 00001
[1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => 00000
[1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 00000
[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => 00001
[1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => 00000
[1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 00000
[1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 00000
[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => 00001
[1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => 00000
[1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => 00000
[1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => 00000
[1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => 00000
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 00111
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 00000
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 00001
[1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 00000
[1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 00000
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 00011
[1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 00000
[1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 00001
[1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 00000
[1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 00000
[1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => 00001
[1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => 00000
[1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 00000
[1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 00000
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 00011
[1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 00000
[1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 00001
[1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 00000
[1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 00000
[1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 00001
[1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 00000
[1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 00000
[1,1,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => 00000
[1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => 00001
[1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => 00000
[1,1,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => 00000
[1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => 00000
[1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => 00000
[1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 00011
[1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 00000
[1,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 00001
[1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 00000
[1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 00000
[1,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 00001
[1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 00000
[1,1,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 00000
[1,1,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => 00000
[1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 00001
[1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 00000
[1,1,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 00000
[1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 00000
[1,1,1,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => 00000
[1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 00001
[1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 00000
[1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 00000
[1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 00000
[1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 00000
[1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 00000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => 000000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => 000001
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => 000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => 000000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => 000011
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => 000000
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => 000001
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => 000000
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => 000000
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => 000001
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => 000000
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => 000000
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => 000000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => 000111
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => 000000
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => 000001
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => 000000
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => 000000
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => 000011
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => 000000
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => 000001
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => 000000
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => 000000
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => 000001
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => 000000
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => 000000
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => 000000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => 000011
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => 000000
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => 000001
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => 000000
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => 000000
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => 000001
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => 000000
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => 000000
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => 000000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => 000001
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => 000000
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => 000000
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => 000000
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => 000000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => 001111
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => 000000
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => 000001
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => 000000
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => 000000
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => 000011
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => 000000
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => 000001
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => 000000
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => 000000
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => 000001
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => 000000
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => 000000
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => 000000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => 000111
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => 000000
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => 000001
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => 000000
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => 000000
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => 000011
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => 000000
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => 000001
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => 000000
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => 000000
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => 000001
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => 000000
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => 000000
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => 000000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => 000011
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => 000000
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => 000001
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => 000000
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => 000000
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => 000001
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => 000000
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => 000000
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => 000000
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => 000001
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => 000000
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => 000000
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => 000000
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => 000000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => 000111
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => 000000
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => 000001
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => 000000
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => 000000
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => 000011
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => 000000
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => 000001
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => 000000
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => 000000
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => 000001
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => 000000
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => 000000
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => 000000
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => 000011
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => 000000
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => 000001
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => 000000
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => 000000
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => 000001
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => 000000
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => 000000
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => 000000
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => 000001
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => 000000
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => 000000
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => 000000
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => 000000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => 000011
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => 000000
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => 000001
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => 000000
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => 000000
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => 000001
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => 000000
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => 000000
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => 000000
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => 000001
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => 000000
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => 000000
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => 000000
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => 000000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => 000001
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => 000000
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => 000000
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => 000000
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => 000000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => 000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 011111
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => 000000
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => 000001
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => 000000
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => 000000
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => 000011
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => 000000
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => 000001
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => 000000
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => 000000
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => 000001
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => 000000
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => 000000
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => 000000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => 000111
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => 000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => 000001
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => 000000
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => 000000
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => 000011
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => 000000
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => 000001
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => 000000
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => 000000
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => 000001
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => 000000
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => 000000
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => 000000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => 000011
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => 000000
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => 000001
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => 000000
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => 000000
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => 000001
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => 000000
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => 000000
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => 000000
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => 000001
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => 000000
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => 000000
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => 000000
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => 000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 001111
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => 000000
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => 000001
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => 000000
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => 000000
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => 000011
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => 000000
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => 000001
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => 000000
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => 000000
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => 000001
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => 000000
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => 000000
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => 000000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 000111
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => 000000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => 000001
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => 000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => 000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 000011
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => 000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => 000000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => 000001
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => 000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => 000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => 000000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => 000011
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => 000000
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => 000001
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => 000000
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => 000000
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => 000001
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => 000000
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => 000000
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => 000000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => 000001
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => 000000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => 000000
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => 000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => 000000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => 000111
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => 000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => 000001
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => 000000
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => 000000
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => 000011
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => 000000
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => 000001
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => 000000
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => 000000
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => 000001
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => 000000
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => 000000
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => 000000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => 000011
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => 000000
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => 000001
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => 000000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => 000000
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => 000001
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => 000000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => 000000
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => 000000
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => 000001
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => 000000
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => 000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => 000000
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => 000000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => 000011
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => 000000
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => 000001
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => 000000
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => 000000
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => 000001
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => 000000
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => 000000
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => 000000
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => 000001
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => 000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => 000000
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => 000000
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => 000000
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => 000001
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => 000000
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => 000000
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => 000000
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => 000000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => 000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 001111
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => 000000
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => 000001
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => 000000
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => 000000
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => 000011
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => 000000
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => 000001
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => 000000
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => 000000
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => 000001
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => 000000
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => 000000
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => 000000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => 000111
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => 000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => 000001
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => 000000
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => 000000
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => 000011
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => 000000
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => 000001
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 000000
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => 000000
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => 000001
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => 000000
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => 000000
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => 000000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => 000011
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => 000000
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => 000001
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => 000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => 000000
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => 000001
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => 000000
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => 000000
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => 000000
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => 000001
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => 000000
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => 000000
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => 000000
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => 000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => 000111
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => 000000
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => 000001
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => 000000
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => 000000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => 000011
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => 000000
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => 000001
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 000000
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => 000000
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => 000001
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => 000000
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => 000000
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => 000000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => 000011
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => 000000
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => 000001
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 000000
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => 000000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => 000001
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => 000000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => 000000
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => 000001
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => 000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => 000000
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => 000000
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => 000000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => 000011
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => 000000
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => 000001
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => 000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => 000000
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => 000001
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => 000000
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => 000000
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => 000000
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => 000001
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => 000000
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => 000000
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => 000000
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => 000000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => 000001
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => 000000
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => 000000
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => 000000
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => 000000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => 000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 000111
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => 000000
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => 000001
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => 000000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => 000000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => 000011
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => 000000
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => 000001
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 000000
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => 000000
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => 000001
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => 000000
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => 000000
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => 000000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => 000011
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => 000000
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => 000001
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 000000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => 000000
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => 000001
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => 000000
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => 000000
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => 000000
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => 000001
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => 000000
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => 000000
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => 000000
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => 000000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => 000011
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => 000000
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => 000001
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => 000000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => 000000
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 000001
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => 000000
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => 000000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => 000000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 000001
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => 000000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => 000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => 000000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => 000000
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => 000001
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => 000000
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => 000000
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => 000000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => 000000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => 000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 000011
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => 000000
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 000001
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => 000000
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => 000000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 000001
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => 000000
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => 000000
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => 000000
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 000001
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => 000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => 000000
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => 000000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => 000000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 000001
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => 000000
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => 000000
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => 000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => 000000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => 000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 000001
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => 000000
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => 000000
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => 000000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => 000000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => 000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 1111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => 0000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => 0000001
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => 0000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => 0000000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => 0000011
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => 0000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => 0000001
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => 0000000
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => 0000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => 0000001
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => 0000000
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => 0000000
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => 0000000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => 0000000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => 0000001
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => 0000000
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => 0000000
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => 0000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => 0000001
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => 0000001
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => 0000000
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => 0000001
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => 0000001
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => 0000001
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => 0000000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => 0001111
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => 0000000
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [7,4,1,2,3,5,6,8] => 0000001
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [7,8,4,1,2,3,5,6] => 0000000
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => 0000000
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => 0000011
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => 0000000
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [7,6,8,4,1,2,3,5] => 0000000
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => 0000000
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],[[.,.],.]],.],.],.] => [4,5,1,2,3,6,7,8] => 0000111
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [7,4,5,1,2,3,6,8] => 0000001
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => 0000000
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [8,4,5,6,1,2,3,7] => 0000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => 0000000
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => 0000000
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => 0000001
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => 0000000
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => 0000000
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => 0000000
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => 0000000
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [6,7,8,4,5,1,2,3] => 0000000
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => 0000000
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => 0000000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [5,4,1,2,3,6,7,8] => 0000111
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => 0000000
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => 0000000
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => 0000001
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,1,2,3] => 0000000
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [8,5,4,6,7,1,2,3] => 0000000
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [8,7,5,4,6,1,2,3] => 0000000
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => 0000001
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => 0000001
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => 0000000
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8] => 0000011
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => 0000000
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => 0000001
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => 0000000
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => 0000000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => 0011111
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => 0000000
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => 0000001
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [7,8,3,1,2,4,5,6] => 0000000
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [6,3,1,2,4,5,7,8] => 0000011
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [6,7,3,1,2,4,5,8] => 0000001
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [6,7,8,3,1,2,4,5] => 0000000
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [8,6,7,3,1,2,4,5] => 0000000
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [7,8,6,3,1,2,4,5] => 0000000
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [8,7,6,3,1,2,4,5] => 0000000
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => 0000111
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8] => 0000001
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => 0000001
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => 0000000
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => 0000000
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => 0000000
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,1,2,4] => 0000000
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,1,2,4] => 0000000
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => 0000000
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,1,2,4] => 0000000
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,1,2,4] => 0000000
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => 0000000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => 0001111
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => 0000000
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [8,6,3,4,1,2,5,7] => 0000000
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [6,7,3,4,1,2,5,8] => 0000001
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => 0000000
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [7,8,6,3,4,1,2,5] => 0000000
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => 0000000
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[[[.,.],.],.]],.],.],.] => [3,4,5,1,2,6,7,8] => 0000111
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [7,8,3,4,5,1,2,6] => 0000000
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [3,4,5,6,1,2,7,8] => 0000011
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => 0000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [3,4,5,6,7,1,2,8] => 0000001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => 0000000
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => 0000000
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [7,3,4,5,6,8,1,2] => 0000000
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => 0000000
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => 0000000
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [6,7,3,4,5,1,2,8] => 0000001
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => 0000000
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => 0000000
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => 0000000
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => 0000000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[[.,.],[.,.]]],.],.],.] => [5,3,4,1,2,6,7,8] => 0000111
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [8,7,5,3,4,1,2,6] => 0000000
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [5,3,4,6,7,8,1,2] => 0000000
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => 0000000
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => 0000011
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => 0000000
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [5,6,3,4,7,1,2,8] => 0000001
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => 0000000
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => 0000000
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => 0000000
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => 0000000
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => 0000000
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [8,6,5,3,4,1,2,7] => 0000000
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [6,5,7,3,4,1,2,8] => 0000001
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => 0000000
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => 0000000
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [7,6,5,3,4,1,2,8] => 0000001
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [7,6,5,3,4,8,1,2] => 0000000
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => 0000000
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => 0000000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [4,3,1,2,5,6,7,8] => 0001111
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [7,4,3,1,2,5,6,8] => 0000001
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [7,8,4,3,1,2,5,6] => 0000000
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [6,4,3,1,2,5,7,8] => 0000011
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => 0000000
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => 0000001
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => 0000000
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => [4,3,5,1,2,6,7,8] => 0000111
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[.,[.,.]],.],.]],.],.] => [4,3,5,6,1,2,7,8] => 0000011
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [8,4,3,5,6,1,2,7] => 0000000
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => [4,3,5,6,7,1,2,8] => 0000001
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => 0000000
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => 0000000
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [8,7,4,3,5,6,1,2] => 0000000
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [6,4,3,5,1,2,7,8] => 0000011
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => 0000000
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => 0000000
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [7,4,5,3,6,8,1,2] => 0000000
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => 0000000
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [8,7,4,5,3,6,1,2] => 0000000
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => [4,5,6,3,7,8,1,2] => 0000000
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => [4,5,6,7,3,1,2,8] => 0000001
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => 0000000
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => 0000000
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => 0000000
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [6,4,5,3,1,2,7,8] => 0000011
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,3,1,2,7] => 0000000
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [6,4,5,3,7,1,2,8] => 0000001
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => 0000000
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => 0000000
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,3,1,2] => 0000000
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => 0000000
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => 0000000
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,3,1,2,8] => 0000001
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => 0000000
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => 0000000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [5,4,3,1,2,6,7,8] => 0000111
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [7,5,4,3,1,2,6,8] => 0000001
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => 0000000
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => 0000011
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [8,5,4,3,6,1,2,7] => 0000000
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => 0000000
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => 0000000
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => 0000011
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => 0000000
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [8,5,4,6,3,7,1,2] => 0000000
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [5,4,6,7,3,1,2,8] => 0000001
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [5,4,6,7,8,3,1,2] => 0000000
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,3,8,1,2] => 0000000
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => 0000011
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [5,6,4,3,7,8,1,2] => 0000000
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => 0000000
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [5,6,7,4,3,8,1,2] => 0000000
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => 0000000
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => 0000001
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [7,5,6,4,3,8,1,2] => 0000000
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,3,1,2] => 0000000
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => 0000000
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => 0000000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [6,5,4,3,1,2,7,8] => 0000011
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => 0000000
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [6,5,4,3,7,1,2,8] => 0000001
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [6,5,4,3,7,8,1,2] => 0000000
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,3,7,1,2] => 0000000
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [6,5,4,7,3,8,1,2] => 0000000
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,3,1,2] => 0000000
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,3,1,2] => 0000000
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,3,1,2] => 0000000
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,3,1,2,8] => 0000001
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,3,1,2] => 0000000
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => 0000000
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => 0000000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => 0000001
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => 0000000
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,3,1,2] => 0000000
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,3,1,2] => 0000000
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,3,1,2] => 0000000
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => 0000000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => 0000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 0111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => 0000000
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => 0000001
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => 0000000
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [8,7,2,1,3,4,5,6] => 0000000
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => 0000000
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [7,8,6,2,1,3,4,5] => 0000000
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => 0000000
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [5,2,1,3,4,6,7,8] => 0000111
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [8,5,2,1,3,4,6,7] => 0000000
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => 0000000
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => 0000000
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [5,6,2,1,3,4,7,8] => 0000011
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => 0000000
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => 0000001
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => 0000000
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [7,5,6,8,2,1,3,4] => 0000000
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => 0000000
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,1,3,4] => 0000000
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => 0000000
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,1,3,4] => 0000000
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [6,7,5,2,1,3,4,8] => 0000001
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [6,7,5,8,2,1,3,4] => 0000000
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => 0000000
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [7,6,5,2,1,3,4,8] => 0000001
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,1,3,4] => 0000000
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => 0000000
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => 0000000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [4,2,1,3,5,6,7,8] => 0001111
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => 0000000
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [8,7,4,2,1,3,5,6] => 0000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [6,4,2,1,3,5,7,8] => 0000011
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => 0000000
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => 0000000
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [7,6,4,2,1,3,5,8] => 0000001
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => 0000000
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [4,5,2,1,3,6,7,8] => 0000111
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [7,4,5,2,1,3,6,8] => 0000001
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [4,5,6,2,1,3,7,8] => 0000011
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [4,5,6,7,2,1,3,8] => 0000001
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => 0000000
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,2,1,3] => 0000000
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,2,1,3,8] => 0000001
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,2,1,3] => 0000000
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,2,1,3] => 0000000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [5,4,2,1,3,6,7,8] => 0000111
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [8,5,4,2,1,3,6,7] => 0000000
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => 0000000
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [5,4,6,2,1,3,7,8] => 0000011
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,2,1,3] => 0000000
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => 0000011
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,2,1,3,7] => 0000000
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,2,1,3] => 0000000
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => 0000000
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,2,1,3] => 0000000
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,2,1,3] => 0000000
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [8,7,5,6,4,2,1,3] => 0000000
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [6,5,4,2,1,3,7,8] => 0000011
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => 0000000
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => 0000001
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,2,1,3] => 0000000
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,2,1,3] => 0000000
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,2,1,3] => 0000000
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [8,6,7,5,4,2,1,3] => 0000000
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => 0000001
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,2,1,3] => 0000000
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,2,1,3] => 0000000
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => 0000000
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,2,1,3] => 0000000
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => 0000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => 0011111
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => 0000000
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[[.,.],.]],.],.],[.,.]],.] => [7,2,3,1,4,5,6,8] => 0000001
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [7,8,2,3,1,4,5,6] => 0000000
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[[.,.],.]],.],[.,.]],.],.] => [6,2,3,1,4,5,7,8] => 0000011
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [6,7,2,3,1,4,5,8] => 0000001
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [6,7,8,2,3,1,4,5] => 0000000
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [7,6,8,2,3,1,4,5] => 0000000
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [7,8,6,2,3,1,4,5] => 0000000
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [8,7,6,2,3,1,4,5] => 0000000
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => [5,2,3,1,4,6,7,8] => 0000111
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [7,5,2,3,1,4,6,8] => 0000001
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [8,5,6,2,3,1,4,7] => 0000000
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => [5,6,7,8,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [8,5,6,7,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [7,8,5,6,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => 0000000
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [6,5,7,8,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [6,7,5,8,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [6,7,8,5,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [7,6,5,2,3,1,4,8] => 0000001
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,3,1,4] => 0000000
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,3,1,4] => 0000000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => 0001111
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => 0000000
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[[.,.],.],.]],.],[.,.]],.] => [7,2,3,4,1,5,6,8] => 0000001
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[[.,.],.],.]],.],[[.,.],.]] => [7,8,2,3,4,1,5,6] => 0000000
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [8,7,2,3,4,1,5,6] => 0000000
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [8,6,2,3,4,1,5,7] => 0000000
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[[.,.],.]],.] => [6,7,2,3,4,1,5,8] => 0000001
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [6,7,8,2,3,4,1,5] => 0000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [7,6,2,3,4,1,5,8] => 0000001
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [7,6,8,2,3,4,1,5] => 0000000
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [8,7,6,2,3,4,1,5] => 0000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 0000111
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[[.,.],.],.],.]],.],[.,.]] => [8,2,3,4,5,1,6,7] => 0000000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[[.,.],.],.],.]],[.,.]],.] => [7,2,3,4,5,1,6,8] => 0000001
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[[.,.],.],.],.]],[[.,.],.]] => [7,8,2,3,4,5,1,6] => 0000000
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [8,7,2,3,4,5,1,6] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 0000011
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [8,2,3,4,5,6,1,7] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 0000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [8,2,3,4,5,6,7,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[[.,.],.],.],.],[.,.]]],.] => [7,2,3,4,5,6,1,8] => 0000001
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [7,2,3,4,5,6,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [7,8,2,3,4,5,6,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [8,7,2,3,4,5,6,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[[.,.],.],.],[.,.]]],.],.] => [6,2,3,4,5,1,7,8] => 0000011
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[[.,.],.],.],[.,.]],.]],.] => [6,2,3,4,5,7,1,8] => 0000001
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [6,2,3,4,5,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[[.,.],.],.],[[.,.],.]]],.] => [6,7,2,3,4,5,1,8] => 0000001
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [6,7,8,2,3,4,5,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [8,6,7,2,3,4,5,1] => 0000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [7,6,2,3,4,5,1,8] => 0000001
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [7,6,2,3,4,5,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [7,6,8,2,3,4,5,1] => 0000000
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [7,8,6,2,3,4,5,1] => 0000000
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => 0000000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],.],[.,.]]],.],.],.] => [5,2,3,4,1,6,7,8] => 0000111
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [7,5,2,3,4,1,6,8] => 0000001
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [7,8,5,2,3,4,1,6] => 0000000
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],.],[.,.]],.]],.],.] => [5,2,3,4,6,1,7,8] => 0000011
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],.],[.,.]],.],.]],.] => [5,2,3,4,6,7,1,8] => 0000001
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[[.,.],.]]],.],.] => [5,6,2,3,4,1,7,8] => 0000011
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => 0000001
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => [5,6,7,2,3,4,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => 0000000
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => 0000000
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [7,5,6,2,3,4,1,8] => 0000001
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [7,5,6,2,3,4,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,2,3,4,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [6,5,2,3,4,1,7,8] => 0000011
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [8,6,5,2,3,4,1,7] => 0000000
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [6,5,2,3,4,7,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => 0000001
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [6,5,7,8,2,3,4,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [8,6,5,7,2,3,4,1] => 0000000
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [6,7,5,2,3,4,1,8] => 0000001
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [6,7,5,8,2,3,4,1] => 0000000
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => 0000000
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,2,3,4,1] => 0000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => 0000001
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => 0000000
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,2,3,4,1] => 0000000
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,2,3,4,1] => 0000000
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => 0000000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,.],[.,.]]],.],.],.],.] => [4,2,3,1,5,6,7,8] => 0001111
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [8,4,2,3,1,5,6,7] => 0000000
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [7,8,4,2,3,1,5,6] => 0000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [8,6,4,2,3,1,5,7] => 0000000
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [6,7,8,4,2,3,1,5] => 0000000
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [7,6,4,2,3,1,5,8] => 0000001
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [7,6,8,4,2,3,1,5] => 0000000
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,2,3,1,5] => 0000000
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],[.,.]],.]],.],.],.] => [4,2,3,5,1,6,7,8] => 0000111
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],[.,.]],.],.]],.],.] => [4,2,3,5,6,1,7,8] => 0000011
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],[.,.]],.],.],.]],.] => [4,2,3,5,6,7,1,8] => 0000001
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [8,6,4,2,3,5,1,7] => 0000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [8,6,4,2,3,5,7,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [6,7,4,2,3,5,1,8] => 0000001
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [6,7,8,4,2,3,5,1] => 0000000
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [7,6,4,2,3,5,1,8] => 0000001
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [7,6,4,2,3,5,8,1] => 0000000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[[.,.],.]]],.],.],.] => [4,5,2,3,1,6,7,8] => 0000111
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [7,8,4,5,2,3,1,6] => 0000000
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [8,7,4,5,2,3,1,6] => 0000000
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [8,4,5,2,3,6,1,7] => 0000000
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => [4,5,2,3,6,7,8,1] => 0000000
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [8,4,5,2,3,6,7,1] => 0000000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [7,4,5,2,3,6,1,8] => 0000001
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [7,4,5,2,3,6,8,1] => 0000000
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [8,4,5,6,2,3,1,7] => 0000000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[[.,.],.],.],.]]],.] => [4,5,6,7,2,3,1,8] => 0000001
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => 0000000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => 0000000
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [6,4,5,2,3,7,8,1] => 0000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [6,7,4,5,2,3,1,8] => 0000001
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => 0000000
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,2,3,1] => 0000000
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,2,3,1] => 0000000
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => 0000000
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => 0000001
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [7,6,8,4,5,2,3,1] => 0000000
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => 0000000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [5,4,2,3,1,6,7,8] => 0000111
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [7,5,4,2,3,1,6,8] => 0000001
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [5,4,2,3,6,7,1,8] => 0000001
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [5,4,2,3,6,7,8,1] => 0000000
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,2,3,6,1] => 0000000
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [5,4,6,2,3,7,8,1] => 0000000
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [5,4,6,7,2,3,1,8] => 0000001
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [5,4,6,7,2,3,8,1] => 0000000
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [7,5,4,6,2,3,1,8] => 0000001
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,2,3,8,1] => 0000000
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [5,6,4,2,3,7,8,1] => 0000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [5,6,4,7,2,3,1,8] => 0000001
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [5,6,7,4,2,3,1,8] => 0000001
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => 0000000
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,2,3,1] => 0000000
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,2,3,1,8] => 0000001
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => 0000000
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,2,3,1,7] => 0000000
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [6,5,4,2,3,7,8,1] => 0000000
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,2,3,7,1] => 0000000
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [6,5,4,7,2,3,1,8] => 0000001
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [6,5,4,7,2,3,8,1] => 0000000
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,2,3,8,1] => 0000000
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => 0000001
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [6,7,5,4,2,3,8,1] => 0000000
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,2,3,1] => 0000000
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => 0000000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,2,3,1,8] => 0000001
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => 0000000
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,2,3,1] => 0000000
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,2,3,1] => 0000000
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => 0000000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => 0000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 0011111
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => 0000000
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [7,3,2,1,4,5,6,8] => 0000001
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => 0000000
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => 0000000
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [8,6,3,2,1,4,5,7] => 0000000
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [6,7,3,2,1,4,5,8] => 0000001
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [6,7,8,3,2,1,4,5] => 0000000
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [7,6,3,2,1,4,5,8] => 0000001
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [7,6,8,3,2,1,4,5] => 0000000
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [7,8,6,3,2,1,4,5] => 0000000
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => 0000000
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [5,3,2,1,4,6,7,8] => 0000111
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [7,5,3,2,1,4,6,8] => 0000001
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [7,8,5,3,2,1,4,6] => 0000000
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [8,7,5,3,2,1,4,6] => 0000000
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => 0000011
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [6,5,3,2,1,4,7,8] => 0000011
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [8,6,5,3,2,1,4,7] => 0000000
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [7,6,5,3,2,1,4,8] => 0000001
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,2,1,4] => 0000000
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => 0000000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => 0001111
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [7,8,3,2,4,1,5,6] => 0000000
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [8,7,3,2,4,1,5,6] => 0000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [8,6,3,2,4,1,5,7] => 0000000
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [6,7,3,2,4,1,5,8] => 0000001
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [6,7,8,3,2,4,1,5] => 0000000
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [8,6,7,3,2,4,1,5] => 0000000
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [7,6,3,2,4,1,5,8] => 0000001
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => 0000000
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => 0000111
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => 0000011
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [8,3,2,4,5,6,1,7] => 0000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => 0000001
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 0000000
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [8,3,2,4,5,6,7,1] => 0000000
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => 0000000
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [6,3,2,4,5,7,1,8] => 0000001
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [6,7,3,2,4,5,1,8] => 0000001
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [6,7,3,2,4,5,8,1] => 0000000
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [6,7,8,3,2,4,5,1] => 0000000
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [8,6,7,3,2,4,5,1] => 0000000
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [7,6,3,2,4,5,1,8] => 0000001
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [8,7,6,3,2,4,5,1] => 0000000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [5,3,2,4,1,6,7,8] => 0000111
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [7,5,3,2,4,1,6,8] => 0000001
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [8,7,5,3,2,4,1,6] => 0000000
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [5,3,2,4,6,1,7,8] => 0000011
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [8,5,3,2,4,6,1,7] => 0000000
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [5,3,2,4,6,7,8,1] => 0000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [7,5,3,2,4,6,1,8] => 0000001
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [7,5,3,2,4,6,8,1] => 0000000
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => 0000001
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => 0000000
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,2,4,1] => 0000000
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [6,5,3,2,4,7,8,1] => 0000000
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [8,6,5,3,2,4,7,1] => 0000000
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => 0000001
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [6,5,7,3,2,4,8,1] => 0000000
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => 0000000
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [6,7,5,3,2,4,8,1] => 0000000
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,2,4,1] => 0000000
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,2,4,1] => 0000000
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [7,6,5,3,2,4,1,8] => 0000001
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => 0000000
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,2,4,1] => 0000000
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,2,4,1] => 0000000
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,2,4,1] => 0000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => 0001111
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [7,8,3,4,2,1,5,6] => 0000000
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [8,7,3,4,2,1,5,6] => 0000000
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [6,3,4,2,1,5,7,8] => 0000011
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [8,6,3,4,2,1,5,7] => 0000000
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [6,7,3,4,2,1,5,8] => 0000001
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [6,7,8,3,4,2,1,5] => 0000000
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [7,6,3,4,2,1,5,8] => 0000001
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => 0000000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => 0000111
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [7,8,3,4,2,5,1,6] => 0000000
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => 0000011
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [8,3,4,2,5,6,1,7] => 0000000
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => 0000001
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 0000000
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [8,3,4,2,5,6,7,1] => 0000000
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [6,7,3,4,2,5,1,8] => 0000001
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [6,7,8,3,4,2,5,1] => 0000000
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [7,8,6,3,4,2,5,1] => 0000000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => 0000111
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [8,3,4,5,2,1,6,7] => 0000000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [7,3,4,5,2,1,6,8] => 0000001
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [7,8,3,4,5,2,1,6] => 0000000
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [8,7,3,4,5,2,1,6] => 0000000
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => 0000011
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => 0000011
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [8,3,4,5,6,2,1,7] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => 0000001
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [8,3,4,5,6,2,7,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => 0000001
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [8,3,4,5,6,7,2,1] => 0000000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [7,3,4,5,6,2,1,8] => 0000001
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [7,3,4,5,6,2,8,1] => 0000000
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [8,7,3,4,5,6,2,1] => 0000000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [6,3,4,5,2,7,1,8] => 0000001
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [6,3,4,5,2,7,8,1] => 0000000
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [8,6,3,4,5,2,7,1] => 0000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [6,3,4,5,7,2,8,1] => 0000000
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => 0000000
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [8,6,7,3,4,5,2,1] => 0000000
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => 0000001
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [7,6,3,4,5,2,8,1] => 0000000
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => 0000000
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [7,6,8,3,4,5,2,1] => 0000000
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [7,8,6,3,4,5,2,1] => 0000000
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1] => 0000000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [5,3,4,2,1,6,7,8] => 0000111
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [5,3,4,2,6,7,8,1] => 0000000
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [8,5,3,4,2,6,7,1] => 0000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [7,5,3,4,2,6,1,8] => 0000001
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [5,3,4,6,7,8,2,1] => 0000000
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [8,5,3,4,6,7,2,1] => 0000000
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [7,8,5,3,4,6,2,1] => 0000000
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [8,7,5,3,4,6,2,1] => 0000000
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [5,6,3,4,2,1,7,8] => 0000011
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [8,5,6,3,4,2,1,7] => 0000000
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [5,6,3,4,2,7,1,8] => 0000001
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [5,6,3,4,7,2,8,1] => 0000000
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [5,6,7,3,4,2,1,8] => 0000001
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => 0000000
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [8,5,6,7,3,4,2,1] => 0000000
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => 0000001
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [7,8,5,6,3,4,2,1] => 0000000
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => 0000000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [6,5,3,4,2,1,7,8] => 0000011
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [8,6,5,3,4,2,1,7] => 0000000
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [6,5,3,4,7,2,8,1] => 0000000
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [6,5,7,8,3,4,2,1] => 0000000
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [6,7,5,3,4,2,1,8] => 0000001
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [6,7,5,8,3,4,2,1] => 0000000
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => 0000000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [7,6,5,3,4,2,1,8] => 0000001
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => 0000000
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [7,6,5,8,3,4,2,1] => 0000000
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [7,6,8,5,3,4,2,1] => 0000000
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => 0000000
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => 0000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 0001111
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => 0000000
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8] => 0000001
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => 0000000
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [8,7,4,3,2,1,5,6] => 0000000
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8] => 0000011
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => 0000000
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [6,7,4,3,2,1,5,8] => 0000001
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [6,7,8,4,3,2,1,5] => 0000000
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [8,6,7,4,3,2,1,5] => 0000000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => 0000001
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [7,6,8,4,3,2,1,5] => 0000000
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [7,8,6,4,3,2,1,5] => 0000000
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => 0000000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => 0000111
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [7,8,4,3,2,5,1,6] => 0000000
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [8,7,4,3,2,5,1,6] => 0000000
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => 0000011
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => 0000001
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 0000000
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [8,4,3,2,5,6,7,1] => 0000000
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [7,4,3,2,5,6,8,1] => 0000000
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [7,8,4,3,2,5,6,1] => 0000000
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [8,7,4,3,2,5,6,1] => 0000000
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [6,4,3,2,5,1,7,8] => 0000011
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [8,6,4,3,2,5,7,1] => 0000000
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [6,7,4,3,2,5,1,8] => 0000001
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [6,7,4,3,2,5,8,1] => 0000000
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [7,6,4,3,2,5,1,8] => 0000001
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [7,6,8,4,3,2,5,1] => 0000000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => 0000111
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [8,4,3,5,2,1,6,7] => 0000000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [7,4,3,5,2,1,6,8] => 0000001
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [8,4,3,5,2,6,1,7] => 0000000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [7,4,3,5,2,6,1,8] => 0000001
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [7,4,3,5,2,6,8,1] => 0000000
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [7,8,4,3,5,2,6,1] => 0000000
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [8,7,4,3,5,2,6,1] => 0000000
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [8,4,3,5,6,2,1,7] => 0000000
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => 0000000
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => 0000000
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [8,4,3,5,6,7,2,1] => 0000000
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [8,7,4,3,5,6,2,1] => 0000000
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [8,6,4,3,5,2,7,1] => 0000000
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [6,4,3,5,7,2,8,1] => 0000000
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [8,6,4,3,5,7,2,1] => 0000000
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [6,7,4,3,5,2,1,8] => 0000001
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => 0000001
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [7,6,4,3,5,2,8,1] => 0000000
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => 0000000
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [7,6,8,4,3,5,2,1] => 0000000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => 0000111
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [8,4,5,3,2,1,6,7] => 0000000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [7,4,5,3,2,1,6,8] => 0000001
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [7,8,4,5,3,2,1,6] => 0000000
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [8,7,4,5,3,2,1,6] => 0000000
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => 0000011
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [8,4,5,3,2,6,7,1] => 0000000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [7,4,5,3,2,6,1,8] => 0000001
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [8,4,5,3,6,2,1,7] => 0000000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => 0000001
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [8,4,5,3,6,2,7,1] => 0000000
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [8,7,4,5,3,6,2,1] => 0000000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => 0000011
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => 0000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => 0000001
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => 0000000
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => 0000000
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => 0000000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => 0000001
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => 0000000
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [8,7,4,5,6,3,2,1] => 0000000
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [8,6,4,5,3,2,1,7] => 0000000
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [8,6,4,5,3,2,7,1] => 0000000
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [6,4,5,3,7,2,8,1] => 0000000
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [6,4,5,7,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [6,7,4,5,3,2,1,8] => 0000001
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [6,7,4,5,3,2,8,1] => 0000000
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [6,7,4,5,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => 0000000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => 0000001
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [7,6,4,5,3,2,8,1] => 0000000
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => 0000000
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => 0000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 0000111
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [8,5,4,3,2,1,6,7] => 0000000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [7,5,4,3,2,1,6,8] => 0000001
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => 0000000
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [8,7,5,4,3,2,1,6] => 0000000
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => 0000011
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [8,5,4,3,2,6,1,7] => 0000000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => 0000001
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => 0000000
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [8,5,4,3,2,6,7,1] => 0000000
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [7,5,4,3,2,6,1,8] => 0000001
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [7,5,4,3,2,6,8,1] => 0000000
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [7,8,5,4,3,2,6,1] => 0000000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => 0000011
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => 0000001
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => 0000000
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [8,5,4,3,6,2,7,1] => 0000000
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => 0000001
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => 0000000
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => 0000000
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [8,5,4,3,6,7,2,1] => 0000000
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => 0000001
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [7,5,4,3,6,2,8,1] => 0000000
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [7,5,4,3,6,8,2,1] => 0000000
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [7,8,5,4,3,6,2,1] => 0000000
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => 0000000
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => 0000011
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => 0000001
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => 0000000
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [8,5,4,6,3,2,7,1] => 0000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => 0000001
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 0000000
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => 0000001
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => 0000000
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => 0000000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [7,5,4,6,3,2,1,8] => 0000001
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [7,5,4,6,3,8,2,1] => 0000000
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => 0000000
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [8,7,5,4,6,3,2,1] => 0000000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => 0000011
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [8,5,6,4,3,2,1,7] => 0000000
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => 0000001
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [8,5,6,4,3,2,7,1] => 0000000
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => 0000001
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => 0000001
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => 0000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 0000001
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => 0000000
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => 0000000
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => 0000000
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [8,5,6,7,4,3,2,1] => 0000000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [7,5,6,4,3,2,1,8] => 0000001
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [7,5,6,4,3,8,2,1] => 0000000
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [7,5,6,4,8,3,2,1] => 0000000
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => 0000000
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => 0000000
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [8,7,5,6,4,3,2,1] => 0000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 0000011
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => 0000000
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => 0000001
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => 0000000
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [8,6,5,4,3,2,7,1] => 0000000
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => 0000001
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 0000000
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => 0000000
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [8,6,5,4,3,7,2,1] => 0000000
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 0000001
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => 0000000
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => 0000000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 0000001
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 0000000
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 0000000
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => 0000000
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [8,6,5,7,4,3,2,1] => 0000000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 0000001
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => 0000000
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => 0000000
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => 0000000
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => 0000000
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => 0000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 0000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 0000000
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => 0000000
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 0000000
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => 0000000
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 0000000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => 0000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 0000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 00000001
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => 00000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 000000001
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 00000001
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2] => 00000000
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => 000000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 0000000001
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 000000001
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 00000001
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => [8,6,7,5,4,3,2,1,9] => 00000001
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,3,1,2] => 00000000
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => 00000000
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [9,10,8,7,6,5,4,3,1,2] => 000000000
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2] => 0000000000
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => 00000001
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [9,8,10,7,6,5,4,3,1,2] => 000000000
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => 000000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => 00000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [9,7,6,5,4,3,2,1,8] => 00000000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,3,9,1,2] => 00000000
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,2,1,3] => 00000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 00000011
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9] => 00000001
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [9,6,7,5,4,3,2,1,8] => 00000000
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] => [8,9,7,6,5,4,2,1,3] => 00000000
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [10,8,7,6,5,4,3,2,1,9] => 000000000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => 00000011
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,2,1,3] => 000000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 000000011
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [9,8,7,6,5,4,3,1,2,10] => 000000001
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [9,2,3,4,5,6,7,8,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => [8,2,3,4,5,6,7,9,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [8,9,2,3,4,5,6,7,1] => 00000000
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => 00000000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,2,3,1] => 00000000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,2,3,9,1] => 00000000
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,2,3,1] => 00000000
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,2,3,1] => 00000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 00000000
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 00000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => 00000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => 00000000
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [8,7,6,5,3,4,9,2,1] => 00000000
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,3,4,2,1] => 00000000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => 00000000
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [8,7,6,4,5,9,3,2,1] => 00000000
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,4,5,3,2,1] => 00000000
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => 00000000
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [8,7,5,6,9,4,3,2,1] => 00000000
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [9,8,7,5,6,4,3,2,1] => 00000000
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => 00000000
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [8,6,7,9,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [8,9,6,7,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [9,7,6,5,4,3,2,8,1] => 00000000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => 00000000
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 11111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => 00000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => 00000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [5,6,7,8,9,1,2,3,4] => 00000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,1,2,3] => 00000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [8,7,9,1,2,3,4,5,6] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => 000000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [7,6,8,9,1,2,3,4,5] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => 000000000
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [6,5,7,8,9,1,2,3,4] => 00000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => 000000000
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [5,4,6,7,8,9,1,2,3] => 00000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [5,6,7,8,9,10,1,2,3,4] => 000000000
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [4,3,5,6,7,8,9,1,2] => 00000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [4,5,6,7,8,9,10,1,2,3] => 000000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => 1111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => 0000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => 00000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => 000000000
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => 000000000
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,3,1,2] => 00000000
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => 00000000
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => 00000001
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => 00000011
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [9,7,1,2,3,4,5,6,8] => 00000000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [6,1,2,3,4,5,7,8,9] => 00000111
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [9,8,6,1,2,3,4,5,7] => 00000000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [5,1,2,3,4,6,7,8,9] => 00001111
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [9,8,7,5,1,2,3,4,6] => 00000000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9] => 00011111
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,1,2,3,5] => 00000000
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,1,2,3,9] => 00000001
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9] => 00111111
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => 00000000
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [5,3,1,2,4,6,7,8,9] => 00001111
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,1,2,4] => 00000000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [4,3,1,2,5,6,7,8,9] => 00011111
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] => [5,4,3,1,2,6,7,8,9] => 00001111
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => [6,5,4,3,1,2,7,8,9] => 00000111
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [9,7,6,5,4,3,1,2,8] => 00000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 01111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => 00000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [8,2,1,3,4,5,6,7,9] => 00000001
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,2,1,3,9] => 00000001
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 00111111
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,2,1,4] => 00000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 00011111
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,3,2,1,5] => 00000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 00001111
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [8,7,5,4,3,2,1,6,9] => 00000001
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [9,8,7,5,4,3,2,1,6] => 00000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 00000111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [8,6,5,4,3,2,1,7,9] => 00000001
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [9,8,6,5,4,3,2,1,7] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => 000000001
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [8,1,2,3,4,5,6,7,9,10] => 000000011
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [7,1,2,3,4,5,6,8,9,10] => 000000111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [6,1,2,3,4,5,7,8,9,10] => 000001111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [5,1,2,3,4,6,7,8,9,10] => 000011111
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => 000000000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9,10] => 000111111
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9,10] => 001111111
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [10,8,7,6,5,4,3,1,2,9] => 000000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 011111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => 000000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [10,8,6,4,2,1,3,5,7,9] => 000000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 001111111
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,3,2,1,4] => 000000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 000111111
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,4,3,2,1,5] => 000000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 000011111
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [10,9,8,7,5,4,3,2,1,6] => 000000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 000001111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [10,9,8,6,5,4,3,2,1,7] => 000000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 000000111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [9,7,6,5,4,3,2,1,8,10] => 000000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [10,9,7,6,5,4,3,2,1,8] => 000000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 000000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => 00111111
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[[.,.],.],.],.]],.],.],.],.] => [2,3,4,5,1,6,7,8,9] => 00001111
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 00000011
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 00000001
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [4,2,3,1,5,6,7,8,9] => 00011111
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [5,2,3,4,1,6,7,8,9] => 00001111
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [6,2,3,4,5,1,7,8,9] => 00000111
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [7,2,3,4,5,6,1,8,9] => 00000011
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [8,2,3,4,5,6,7,1,9] => 00000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 000000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 0111111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [8,9,2,1,3,4,5,6,7] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [10,2,3,4,5,6,7,8,9,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => 0000000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [9,2,3,1,4,5,6,7,8] => 00000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => 000000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]] => [10,9,8,7,6,5,4,3,2,11,1] => 0000000000
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.] => [6,5,4,3,2,7,1,8,9] => 00000011
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.] => [5,4,3,2,6,1,7,8,9] => 00000111
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.] => [4,3,2,5,1,6,7,8,9] => 00001111
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,[.,.]],.]],.],.],.],.],.] => [3,2,4,1,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => 000000000
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [10,9,8,6,7,5,4,3,2,1] => 000000000
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,5,6,4,3,2,1] => 000000000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => [4,5,6,7,8,9,10,2,3,1] => 000000000
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => 0000000000
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,2,3,1,4] => 00000000
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,3,4,2,1,5] => 00000000
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => [9,8,7,4,5,3,2,1,6] => 00000000
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => [9,8,5,6,4,3,2,1,7] => 00000000
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [4,5,2,1,3,6,7,8,9] => 00001111
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]] => [6,2,3,4,5,7,8,9,10,1] => 000000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => 00000001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [9,3,4,5,6,7,8,1,2] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [9,2,3,4,5,6,7,1,8] => 00000000
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,2,1,3] => 00000000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => 000000000
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]] => [8,9,7,6,4,3,2,1,5] => 00000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [8,9,6,5,4,3,2,1,7] => 00000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => 000000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => 000000000
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => 000000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => [9,10,6,7,4,5,2,3,1,8] => 000000000
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => 00000000000
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => 000000000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => 00001111
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[[[.,.],.],.],.],.]],.],[.,.]] => [9,2,3,4,5,6,1,7,8] => 00000000
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => 000000000
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => 000000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [3,4,5,6,7,8,1,2,9] => 00000001
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [12,10,8,6,4,2,1,3,5,7,9,11] => 00000000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [9,10,7,6,5,4,3,2,1,8] => 000000000
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,4,3,2,1,5] => 000000000
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [10,8,9,6,7,4,5,2,3,1] => 000000000
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [9,8,10,6,7,4,5,2,3,1] => 000000000
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]] => [8,9,6,7,4,5,2,3,10,1] => 000000000
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ 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.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ 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.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
searching the database
Sorry, this map was not found in the database.