Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Images
[1,0] => [1] => [.,.] => [1,0]
[1,0,1,0] => [1,2] => [.,[.,.]] => [1,0,1,0]
[1,1,0,0] => [2,1] => [[.,.],.] => [1,1,0,0]
[1,0,1,0,1,0] => [1,2,3] => [.,[.,[.,.]]] => [1,0,1,0,1,0]
[1,0,1,1,0,0] => [1,3,2] => [.,[[.,.],.]] => [1,0,1,1,0,0]
[1,1,0,0,1,0] => [2,1,3] => [[.,.],[.,.]] => [1,1,0,0,1,0]
[1,1,0,1,0,0] => [2,3,1] => [[.,.],[.,.]] => [1,1,0,0,1,0]
[1,1,1,0,0,0] => [3,2,1] => [[[.,.],.],.] => [1,1,1,0,0,0]
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [[[[.,.],.],.],.] => [1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0]
>>> Load all 1857 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,6,7,5,3,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,7,8,6,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,4,7,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,4,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,7,6,4,3] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,5,4,3,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,5,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,5,8,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,6,8,5,2] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,7,4,2] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,5,7,4,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,7,5,4,2] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,3,5,6,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,6,8,7,5,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,5,3,2,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,3,2,7,8,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,3,6,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,3,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,3,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,5,6,3,8,7,2] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,5,3,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,5,3,8,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,5,7,3,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,5,7,3,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,5,8,7,3,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,5,3,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,4,6,3,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,4,6,3,2,8,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,4,6,7,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,4,7,8,6,3,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,4,3,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,4,3,2,8,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,5,6,4,7,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,4,7,8,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,4,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,5,7,4,3,2,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,5,4,3,8,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,5,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,7,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,4,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,7,4,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,5,4,3,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,7,5,4,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,5,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,7,8,6,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,4,1,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,4,8,7,1] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,6,4,1,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,7,6,4,1] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,5,7,4,1,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,5,4,1,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,6,7,8,5,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,3,1,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,3,6,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,3,8,7,6,1] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,3,7,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,5,8,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,4,3,1,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,4,3,7,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,4,7,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,5,6,7,4,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,7,6,4,3,1] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,5,4,3,1,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,7,8,6,5,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,5,7,6,4,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,5,7,6,8,4,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,6,5,7,4,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,6,7,5,8,4,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,2,5,7,6,1,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,2,6,5,8,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,4,2,7,6,5,1,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,2,7,6,5,8,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,2,7,8,6,5,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,2,1,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,5,2,1,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,5,2,7,6,1,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,2,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,2,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,6,2,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,5,2,7,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,5,2,7,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,5,7,8,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,5,8,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,5,4,2,6,1,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,4,2,6,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,4,2,7,6,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,4,6,2,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,4,6,7,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,4,7,6,2,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,4,2,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,4,7,2,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,4,7,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,4,2,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,5,4,2,7,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,5,4,2,7,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,5,4,2,8,7,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,5,4,7,2,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,5,4,7,8,2,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,5,4,8,7,2,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,3,2,5,7,8,6,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,6,7,5,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,6,7,5,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,3,5,6,8,7,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,3,6,5,2,1,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,3,6,5,7,2,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,6,7,5,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,3,2,1,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,5,3,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,3,2,6,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,3,2,8,7,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,5,7,3,2,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,5,3,2,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,4,3,6,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,4,3,6,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,4,3,6,8,7,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,4,3,7,6,2,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,4,3,7,6,2,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,4,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,4,3,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,5,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,7,9,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [8,7,9,6,5,4,3,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,6,5,8,4,3,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,8,10,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [8,7,6,9,5,4,3,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [6,7,5,8,4,3,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,6,5,4,3,8,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [6,5,7,8,4,3,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [8,7,6,5,4,9,3,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [7,6,8,9,5,4,3,2,1,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [8,7,6,5,4,3,9,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [6,5,4,3,7,8,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,2,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,6,3,7,8,9,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,8,3,9,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,6,8,5,4,3,2,9,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [7,6,8,5,9,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,6,8,9,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,10,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,2,7,8,9,10,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,10,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,10,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,9,2,10,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,9,8,7,6] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,9,8,7,6,5] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,10,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,10,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [8,7,9,10,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,2,1,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,7,2,1,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,6,2,1,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,9,7,6,5,4,3,2,10,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,5,7,9,10,8,6,4,2] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [5,6,4,3,2,7,1,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,10,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,10,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,4,6,3,7,2,8,1,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,5,3,6,2,7,1,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,12,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
Map
to 312-avoiding permutation
Description
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
searching the database
Sorry, this map was not found in the database.