Identifier
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
[1,0] => [1] => [.,.] => [1] => [1]
[1,0,1,0] => [1,2] => [.,[.,.]] => [2,1] => [1,1]
[1,1,0,0] => [2,1] => [[.,.],.] => [1,2] => [2]
[1,0,1,0,1,0] => [1,2,3] => [.,[.,[.,.]]] => [3,2,1] => [1,1,1]
[1,0,1,1,0,0] => [1,3,2] => [.,[[.,.],.]] => [2,3,1] => [2,1]
[1,1,0,0,1,0] => [2,1,3] => [[.,.],[.,.]] => [3,1,2] => [1,2]
[1,1,0,1,0,0] => [2,3,1] => [[.,.],[.,.]] => [3,1,2] => [1,2]
[1,1,1,0,0,0] => [3,2,1] => [[[.,.],.],.] => [1,2,3] => [3]
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,1,1,1]
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [3,4,2,1] => [2,1,1]
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [4,2,3,1] => [1,2,1]
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [.,[[.,.],[.,.]]] => [4,2,3,1] => [1,2,1]
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [.,[[[.,.],.],.]] => [2,3,4,1] => [3,1]
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [4,3,1,2] => [1,1,2]
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [[.,.],[[.,.],.]] => [3,4,1,2] => [2,2]
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [[.,.],[.,[.,.]]] => [4,3,1,2] => [1,1,2]
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => [4,3,1,2] => [1,1,2]
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [[.,.],[[.,.],.]] => [3,4,1,2] => [2,2]
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [[[.,.],.],[.,.]] => [4,1,2,3] => [1,3]
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [[[.,.],.],[.,.]] => [4,1,2,3] => [1,3]
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [[[.,.],[.,.]],.] => [3,1,2,4] => [1,3]
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [[[[.,.],.],.],.] => [1,2,3,4] => [4]
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [2,1,1,1]
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [1,2,1,1]
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [1,2,1,1]
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [3,1,1]
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [1,1,2,1]
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [2,2,1]
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [1,1,2,1]
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [1,1,2,1]
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [2,2,1]
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [1,3,1]
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [1,3,1]
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [1,3,1]
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [4,1]
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [1,1,1,2]
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [2,1,2]
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [1,2,2]
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [1,2,2]
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [3,2]
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [1,1,1,2]
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [2,1,2]
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [1,1,1,2]
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [1,1,1,2]
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [2,1,2]
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [1,2,2]
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [1,2,2]
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [1,2,2]
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [3,2]
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [1,1,3]
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [2,3]
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [1,1,3]
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [1,1,3]
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [2,3]
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [1,1,3]
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [1,1,3]
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [1,1,3]
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [2,3]
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,4]
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,4]
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [1,4]
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [1,4]
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [5]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [1,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [3,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [2,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [1,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [2,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [1,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [4,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [2,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [2,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [1,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [2,1,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [1,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [1,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [2,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [1,1,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [2,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [1,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [2,3,1]
>>> Load all 1765 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [1,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [1,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [5,1]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [2,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [1,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [3,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [1,1,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [1,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [4,2]
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [1,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [3,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [2,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [2,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [1,2,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [3,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [1,1,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [2,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [1,1,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [1,1,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [2,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [1,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [1,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [1,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [4,2]
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [1,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [2,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [1,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [3,3]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [1,1,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [2,1,3]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [1,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [2,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [1,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [1,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [3,3]
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [1,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [2,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [1,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [2,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [2,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [1,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [3,3]
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [1,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [2,4]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [1,1,4]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [2,4]
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [1,1,4]
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [1,1,4]
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [1,1,4]
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [2,4]
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [1,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [2,4]
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,5]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,5]
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [1,5]
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [1,5]
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [1,5]
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [3,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [4,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [3,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [2,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [3,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [2,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [2,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [2,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [1,4,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [5,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [3,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [1,3,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [4,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [3,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [2,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [3,1,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [2,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [1,3,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [4,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [1,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [2,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [3,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [2,1,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [1,2,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [3,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [2,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [2,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [2,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [1,2,3,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [1,2,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [1,2,3,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [1,2,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [3,3,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [1,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [2,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [1,1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [1,1,4,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [2,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [1,1,4,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [1,1,4,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [1,1,4,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [2,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [1,1,4,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [1,1,4,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [2,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [1,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [1,5,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [1,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [1,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [6,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [3,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [2,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [2,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [1,3,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [4,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [2,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [2,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [2,1,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [1,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [3,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [1,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [1,1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [1,1,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [2,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [1,1,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [2,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [1,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [1,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [1,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [1,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [5,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [3,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [2,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [2,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [1,3,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [4,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [3,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [2,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [3,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [2,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [2,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [2,2,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [1,3,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [4,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,1,1,2,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [2,1,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [3,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [2,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [2,1,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [1,2,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [3,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [2,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [2,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [2,1,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [1,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [1,2,2,2]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [3,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [1,1,3,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [2,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [2,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [1,1,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [1,1,3,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [1,1,3,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [2,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [1,1,3,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [1,1,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [1,1,3,2]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [1,1,3,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [2,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [1,4,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [1,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [1,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [1,4,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [1,4,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [5,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [1,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [2,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [3,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [1,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [2,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [2,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [1,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [4,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [1,1,1,1,3]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [2,1,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [1,2,1,3]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [1,2,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [3,1,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [2,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [2,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [1,2,1,3]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [1,2,1,3]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [1,2,1,3]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [3,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [2,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [2,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [1,1,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [2,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [1,3,3]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [1,3,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [1,3,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [1,3,3]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [4,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [1,1,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [2,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [3,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [2,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [2,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [1,2,1,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [3,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [2,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [2,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [2,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [1,2,1,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [1,2,1,3]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [3,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [1,1,2,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [2,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [2,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [1,1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [1,1,2,3]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [1,1,2,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [2,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [1,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [1,1,2,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [2,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [1,3,3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [1,3,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [1,3,3]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [1,3,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [4,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [1,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [2,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [1,2,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [3,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [1,1,1,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [2,1,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [2,1,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [1,2,4]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [1,2,4]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [1,2,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [3,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [1,1,1,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [2,1,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [2,1,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [1,1,1,4]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [2,1,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [1,2,4]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [1,2,4]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [1,2,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [3,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [1,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [2,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [2,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [1,1,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [2,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [1,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [2,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [1,2,4]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [1,2,4]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [1,2,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [1,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [1,2,4]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [3,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [2,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [1,1,5]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [2,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [1,1,5]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [1,1,5]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [1,1,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [2,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [1,1,5]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [1,1,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [1,1,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [1,1,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [2,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [1,1,5]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [1,1,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [1,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [2,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [1,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [1,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [1,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [1,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [1,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [8,6,7,5,4,3,2,1] => [1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [8,6,7,5,4,3,2,1] => [1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [8,7,5,6,4,3,2,1] => [1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => [2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [8,7,5,6,4,3,2,1] => [1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [8,7,5,6,4,3,2,1] => [1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => [2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [8,5,6,7,4,3,2,1] => [1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [8,5,6,7,4,3,2,1] => [1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => [1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [4,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [2,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [6,7,8,4,5,3,2,1] => [3,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [2,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [2,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [7,6,8,4,5,3,2,1] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [6,7,8,4,5,3,2,1] => [3,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [8,7,4,5,6,3,2,1] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [7,8,4,5,6,3,2,1] => [2,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [8,7,4,5,6,3,2,1] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [8,7,4,5,6,3,2,1] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [7,8,4,5,6,3,2,1] => [2,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [8,6,4,5,7,3,2,1] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [8,6,4,5,7,3,2,1] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [6,7,4,5,8,3,2,1] => [2,3,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [8,4,5,6,7,3,2,1] => [1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [8,4,5,6,7,3,2,1] => [1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [5,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [2,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [6,7,8,5,3,4,2,1] => [3,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [7,8,5,6,3,4,2,1] => [2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [7,8,5,6,3,4,2,1] => [2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [8,5,6,7,3,4,2,1] => [1,3,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => [4,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [6,7,8,5,3,4,2,1] => [3,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [2,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [2,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [7,6,8,5,3,4,2,1] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [6,7,8,5,3,4,2,1] => [3,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [7,8,5,6,3,4,2,1] => [2,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [8,6,5,7,3,4,2,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [7,6,5,8,3,4,2,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [8,5,6,7,3,4,2,1] => [1,3,2,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => [4,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [7,8,6,3,4,5,2,1] => [2,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [8,6,7,3,4,5,2,1] => [1,2,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => [3,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [7,8,6,3,4,5,2,1] => [2,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [8,6,7,3,4,5,2,1] => [1,2,3,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [7,6,8,3,4,5,2,1] => [1,2,3,1,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => [3,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [8,7,5,3,4,6,2,1] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [8,7,5,3,4,6,2,1] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [5,6,7,3,4,8,2,1] => [3,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [8,7,3,4,5,6,2,1] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [8,7,3,4,5,6,2,1] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [7,8,3,4,5,6,2,1] => [2,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,7,5,4,6,3,8] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [8,6,3,4,5,7,2,1] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,7,5,4,6,8,3] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [8,6,3,4,5,7,2,1] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [8,3,4,5,6,7,2,1] => [1,5,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [8,3,4,5,6,7,2,1] => [1,5,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [7,3,4,5,6,8,2,1] => [1,5,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [7,3,4,5,6,8,2,1] => [1,5,1,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [6,3,4,5,7,8,2,1] => [1,5,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [6,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [1,1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [2,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [1,1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [1,1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [1,1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,2,3,1] => [1,3,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,2,3,1] => [1,3,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,2,3,1] => [1,3,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => [4,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [1,1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,2,3,1] => [3,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [1,1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,2,3,1] => [2,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [1,1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [1,1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,2,3,1] => [2,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,2,3,1] => [3,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,2,3,1] => [1,1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => [2,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,2,3,1] => [1,1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,2,3,1] => [1,1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => [2,3,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,2,3,1] => [1,1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,2,3,1] => [2,3,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [8,4,5,6,7,2,3,1] => [1,4,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [8,4,5,6,7,2,3,1] => [1,4,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [7,4,5,6,8,2,3,1] => [1,4,2,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [7,4,5,6,8,2,3,1] => [1,4,2,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => [5,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [2,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,2,3,1] => [1,3,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,2,3,1] => [1,3,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => [4,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [2,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [2,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,2,3,1] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,2,3,1] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,2,3,1] => [1,3,1,2,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => [4,1,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,2,3,1] => [2,1,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,2,3,1] => [3,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,2,3,1] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,2,3,1] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [8,6,5,4,7,2,3,1] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [8,6,5,4,7,2,3,1] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,2,3,1] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,2,3,1] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,2,3,1] => [1,2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => [2,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,2,3,1] => [1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => [2,3,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,2,3,1] => [1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,2,3,1] => [2,3,2,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,2,3,1] => [1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,2,3,1] => [2,3,2,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [7,4,5,6,8,2,3,1] => [1,4,2,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [6,4,5,7,8,2,3,1] => [1,4,2,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => [5,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,2,3,4,1] => [1,2,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,2,3,4,1] => [1,2,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => [3,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,2,3,4,1] => [1,1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,2,3,4,1] => [1,1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [7,8,5,6,2,3,4,1] => [2,2,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => [1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => [1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => [4,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,2,3,4,1] => [1,2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,3,5,6,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,2,3,4,1] => [1,2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,2,3,4,1] => [1,2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => [3,1,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,2,3,4,1] => [1,1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,2,3,4,1] => [1,1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,2,3,4,1] => [1,1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [7,8,5,6,2,3,4,1] => [2,2,3,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,2,3,4,1] => [1,1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [6,7,5,8,2,3,4,1] => [2,2,3,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => [4,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,2,3,5,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [8,6,7,4,2,3,5,1] => [1,2,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [6,7,8,4,2,3,5,1] => [3,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [7,8,6,4,2,3,5,1] => [2,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,2,3,5,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,2,3,5,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [7,6,8,4,2,3,5,1] => [1,2,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,2,3,6,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,2,3,6,1] => [2,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,2,3,7,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,2,3,7,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [7,5,6,4,2,3,8,1] => [1,2,1,3,1]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [5,6,7,4,2,3,8,1] => [3,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [7,8,4,5,2,3,6,1] => [2,2,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [8,6,4,5,2,3,7,1] => [1,1,2,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,2,3,8,1] => [1,1,2,3,1]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,2,3,8,1] => [1,1,2,3,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,2,3,8,1] => [1,1,2,3,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => [2,2,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [7,4,5,6,2,3,8,1] => [1,3,3,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [6,4,5,7,2,3,8,1] => [1,3,3,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => [4,3,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => [1,1,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [8,6,7,2,3,4,5,1] => [1,2,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [8,6,7,2,3,4,5,1] => [1,2,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [6,7,8,2,3,4,5,1] => [3,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => [1,1,1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => [1,1,1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => [1,1,1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [7,8,6,2,3,4,5,1] => [2,1,4,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [6,7,8,2,3,4,5,1] => [3,4,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [7,8,5,2,3,4,6,1] => [2,1,4,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [1,1,1,4,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [7,5,6,2,3,4,8,1] => [1,2,4,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [7,5,6,2,3,4,8,1] => [1,2,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [7,8,5,2,3,4,6,1] => [2,1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [7,8,5,2,3,4,6,1] => [2,1,4,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [1,1,1,4,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,8,4,5,6,3,7,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [1,1,1,4,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [1,1,1,4,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [7,5,6,2,3,4,8,1] => [1,2,4,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [7,5,6,2,3,4,8,1] => [1,2,4,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => [5,6,7,2,3,4,8,1] => [3,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [8,7,2,3,4,5,6,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [7,8,2,3,4,5,6,1] => [2,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [7,8,2,3,4,5,6,1] => [2,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [8,6,2,3,4,5,7,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [8,6,2,3,4,5,7,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [7,6,2,3,4,5,8,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [7,6,2,3,4,5,8,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [7,6,2,3,4,5,8,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => [2,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [8,5,2,3,4,6,7,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [7,5,2,3,4,6,8,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [7,5,2,3,4,6,8,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [6,5,2,3,4,7,8,1] => [1,1,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [8,2,3,4,5,6,7,1] => [1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [8,2,3,4,5,6,7,1] => [1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [7,2,3,4,5,6,8,1] => [1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [7,2,3,4,5,6,8,1] => [1,6,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [6,2,3,4,5,7,8,1] => [1,6,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [6,2,3,4,5,7,8,1] => [1,6,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [2,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => [3,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,3,1,2] => [2,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,3,1,2] => [1,3,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => [1,3,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [4,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => [1,2,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => [3,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [7,6,8,4,5,3,1,2] => [1,2,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => [2,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => [2,3,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => [1,1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,3,1,2] => [2,3,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [7,4,5,6,8,3,1,2] => [1,4,1,2]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [7,4,5,6,8,3,1,2] => [1,4,1,2]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => [5,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [2,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => [3,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,4,1,2] => [1,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [1,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [4,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [2,1,1,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => [3,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [2,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [2,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,4,1,2] => [1,2,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => [3,1,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => [1,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,4,1,2] => [1,3,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [1,3,2,2]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [1,3,2,2]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [4,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => [2,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => [1,2,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [6,7,8,3,4,5,1,2] => [3,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => [2,1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => [2,1,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => [1,2,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [7,6,8,3,4,5,1,2] => [1,2,3,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [6,7,8,3,4,5,1,2] => [3,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => [2,1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [8,7,5,3,4,6,1,2] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => [2,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [7,6,5,3,4,8,1,2] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [6,7,5,3,4,8,1,2] => [2,1,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [8,5,6,3,4,7,1,2] => [1,2,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => [1,2,3,2]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => [1,2,3,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [5,6,7,3,4,8,1,2] => [3,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [2,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [2,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [6,7,3,4,5,8,1,2] => [2,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [8,6,3,4,5,7,1,2] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [6,7,3,4,5,8,1,2] => [2,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [1,5,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [1,5,2]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [7,3,4,5,6,8,1,2] => [1,5,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [7,3,4,5,6,8,1,2] => [1,5,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => [1,5,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [6,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [2,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,3,1,2] => [2,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,3,1,2] => [1,3,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [4,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => [1,2,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => [1,2,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => [2,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => [2,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [7,4,5,6,8,3,1,2] => [1,4,1,2]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => [5,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => [3,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,3,1,2] => [2,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,3,1,2] => [2,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,3,1,2] => [1,3,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,3,1,2] => [1,3,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => [1,3,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [4,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => [3,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,3,1,2] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => [3,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,3,1,2] => [2,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,3,1,2] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,3,1,2] => [2,2,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,3,1,2] => [1,3,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,3,1,2] => [1,3,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => [1,3,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => [1,3,1,1,2]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [4,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [2,1,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => [1,2,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => [3,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => [1,2,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [7,6,8,4,5,3,1,2] => [1,2,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => [3,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,3,1,2] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,3,1,2] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,3,1,2] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,3,1,2] => [1,2,2,1,2]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,3,1,2] => [1,2,2,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => [2,3,1,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,3,1,2] => [2,3,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [7,4,5,6,8,3,1,2] => [1,4,1,2]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => [5,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,1,1,1,2,2]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => [3,1,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,4,1,2] => [1,3,2,2]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [4,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [2,1,1,2,2]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => [3,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [2,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [2,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,4,1,2] => [1,2,1,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,4,1,2] => [1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => [1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,8,5,7,6,1] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,4,1,2] => [1,3,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [1,3,2,2]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [4,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,3,5,1,2] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [6,7,8,4,3,5,1,2] => [3,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,3,5,1,2] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,3,5,1,2] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [7,8,6,4,3,5,1,2] => [2,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [8,6,7,4,3,5,1,2] => [1,2,1,2,2]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [7,6,8,4,3,5,1,2] => [1,2,1,2,2]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [6,7,8,4,3,5,1,2] => [3,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,3,6,1,2] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,3,6,1,2] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => [2,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,3,7,1,2] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [6,7,5,4,3,8,1,2] => [2,1,1,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,6,3,5,4,8,7,1] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,3,8,1,2] => [1,1,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => [2,2,2,2]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,8,3,7,5,6,4,1] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [6,4,5,7,3,8,1,2] => [1,3,2,2]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => [4,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => [1,1,1,3,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => [2,1,3,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => [1,2,3,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => [1,2,3,2]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [6,7,8,3,4,5,1,2] => [3,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => [2,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => [1,1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => [1,1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => [2,1,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => [1,2,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [7,6,8,3,4,5,1,2] => [1,2,3,2]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [6,7,8,3,4,5,1,2] => [3,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => [2,1,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => [2,1,3,2]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [7,6,5,3,4,8,1,2] => [1,1,1,3,2]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [6,7,5,3,4,8,1,2] => [2,1,3,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [8,5,6,3,4,7,1,2] => [1,2,3,2]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => [1,2,3,2]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => [1,2,3,2]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [5,6,7,3,4,8,1,2] => [3,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [8,7,5,3,4,6,1,2] => [1,1,1,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [7,6,5,3,4,8,1,2] => [1,1,1,3,2]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [7,6,5,3,4,8,1,2] => [1,1,1,3,2]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [7,6,5,3,4,8,1,2] => [1,1,1,3,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [8,5,6,3,4,7,1,2] => [1,2,3,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [8,5,6,3,4,7,1,2] => [1,2,3,2]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => [1,2,3,2]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [5,6,7,3,4,8,1,2] => [3,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [2,4,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [8,7,3,4,5,6,1,2] => [1,1,4,2]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [2,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [8,6,3,4,5,7,1,2] => [1,1,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => [1,1,4,2]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [6,7,3,4,5,8,1,2] => [2,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [8,6,3,4,5,7,1,2] => [1,1,4,2]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => [1,1,4,2]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [6,7,3,4,5,8,1,2] => [2,4,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [8,5,3,4,6,7,1,2] => [1,1,4,2]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [6,5,3,4,7,8,1,2] => [1,1,4,2]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => [2,4,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [1,5,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [1,5,2]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => [1,5,2]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => [1,5,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [6,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => [2,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => [3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,1,2,3] => [2,2,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [1,3,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [1,3,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,1,2,3] => [1,3,1,3]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => [4,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [1,1,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [1,2,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [1,1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [1,1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [7,8,6,4,5,1,2,3] => [2,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [1,2,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [1,2,2,3]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [6,7,8,4,5,1,2,3] => [3,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [2,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [2,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,1,2,3] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => [2,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => [1,4,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => [1,4,3]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,1,2,3] => [1,4,3]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,1,2,3] => [1,4,3]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => [5,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => [2,1,1,1,3]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => [3,1,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,1,2,3] => [2,2,1,3]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,1,2,3] => [2,2,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [1,3,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [1,3,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,1,2,3] => [1,3,1,3]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => [4,1,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => [3,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => [2,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,1,2,3] => [1,2,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,1,2,3] => [2,2,1,3]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,1,2,3] => [1,1,2,1,3]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,1,2,3] => [1,1,2,1,3]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [1,3,1,3]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,1,2,3] => [1,3,1,3]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => [4,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [1,1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [7,8,6,4,5,1,2,3] => [2,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [1,2,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [1,2,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [6,7,8,4,5,1,2,3] => [3,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [7,8,6,4,5,1,2,3] => [2,1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [1,1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [7,8,6,4,5,1,2,3] => [2,1,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [1,2,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [1,2,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,6,4,5,1,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [8,7,5,4,6,1,2,3] => [1,1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [7,8,5,4,6,1,2,3] => [2,1,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,1,2,3] => [1,1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,1,2,3] => [1,1,1,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [8,5,6,4,7,1,2,3] => [1,2,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [8,5,6,4,7,1,2,3] => [1,2,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [7,5,6,4,8,1,2,3] => [1,2,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [2,3,3]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [1,1,3,3]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [2,3,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => [1,1,3,3]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,1,2,3] => [1,1,3,3]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => [2,3,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => [1,1,3,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => [1,1,3,3]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,1,2,3] => [1,1,3,3]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => [2,3,3]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => [1,4,3]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => [1,4,3]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,8,6,5,7,4,1] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,1,2,3] => [1,4,3]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [6,4,5,7,8,1,2,3] => [1,4,3]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => [5,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,1,2,4] => [1,2,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,1,2,4] => [1,2,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,2,3,1,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,1,2,4] => [3,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,1,2,4] => [1,1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => [2,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,1,2,4] => [1,1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => [2,2,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,1,2,4] => [1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,1,2,4] => [1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => [1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => [4,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,1,2,4] => [2,1,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,1,2,4] => [3,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,1,2,4] => [2,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,1,2,4] => [2,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,2,3,5,8,7,6,1] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,1,2,4] => [3,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => [2,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,3,7,5,6,1,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,1,2,4] => [1,1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,1,2,4] => [1,1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,1,2,4] => [1,1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => [2,2,1,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,1,2,4] => [1,3,1,3]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => [4,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [7,8,6,4,3,1,2,5] => [2,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [8,6,7,4,3,1,2,5] => [1,2,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => [3,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [7,8,6,4,3,1,2,5] => [2,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [8,6,7,4,3,1,2,5] => [1,2,1,1,3]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [7,6,8,4,3,1,2,5] => [1,2,1,1,3]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => [3,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [7,8,5,4,3,1,2,6] => [2,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [7,8,5,4,3,1,2,6] => [2,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,3,1,2,8] => [2,1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,3,1,2,7] => [1,1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,3,1,2,8] => [1,1,2,1,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,3,1,2,7] => [1,1,2,1,3]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,3,1,2,8] => [1,1,2,1,3]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [7,4,5,6,3,1,2,8] => [1,3,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => [1,1,1,2,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [7,8,6,3,4,1,2,5] => [2,1,2,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [8,6,7,3,4,1,2,5] => [1,2,2,3]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => [3,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => [1,1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [7,8,6,3,4,1,2,5] => [2,1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [5,2,4,3,6,7,1,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => [1,1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [8,6,7,3,4,1,2,5] => [1,2,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [8,6,7,3,4,1,2,5] => [1,2,2,3]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,2,4,3,8,7,6,1] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => [3,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [7,8,5,3,4,1,2,6] => [2,1,2,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [1,2,2,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [1,2,2,3]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [7,5,6,3,4,1,2,8] => [1,2,2,3]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [7,5,6,3,4,1,2,8] => [1,2,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,2,4,5,3,1,7,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [8,7,5,3,4,1,2,6] => [1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [8,6,5,3,4,1,2,7] => [1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [8,6,5,3,4,1,2,7] => [1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [6,7,5,3,4,1,2,8] => [2,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [7,6,5,3,4,1,2,8] => [1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [6,7,5,3,4,1,2,8] => [2,1,2,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [1,2,2,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [1,2,2,3]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [5,6,7,3,4,1,2,8] => [3,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [8,7,3,4,5,1,2,6] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [7,8,3,4,5,1,2,6] => [2,3,3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [8,7,3,4,5,1,2,6] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,2,5,4,3,7,8,1] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [8,7,3,4,5,1,2,6] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [8,6,3,4,5,1,2,7] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [6,7,3,4,5,1,2,8] => [2,3,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [8,6,3,4,5,1,2,7] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8,2,5,4,7,6,3,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [6,7,3,4,5,1,2,8] => [2,3,3]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [8,5,3,4,6,1,2,7] => [1,1,3,3]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [8,5,3,4,6,1,2,7] => [1,1,3,3]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [7,5,3,4,6,1,2,8] => [1,1,3,3]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [7,5,3,4,6,1,2,8] => [1,1,3,3]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [6,5,3,4,7,1,2,8] => [1,1,3,3]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [5,6,3,4,7,1,2,8] => [2,3,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,6,5,4,3,8,1] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => [1,4,3]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [7,3,4,5,6,1,2,8] => [1,4,3]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [7,3,4,5,6,1,2,8] => [1,4,3]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [6,3,4,5,7,1,2,8] => [1,4,3]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [6,3,4,5,7,1,2,8] => [1,4,3]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [3,4,5,6,7,1,2,8] => [5,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [2,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [1,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [1,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => [3,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [1,1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [2,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [1,1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [1,1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [2,2,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => [1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [1,1,1,1,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [1,2,1,4]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => [3,1,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [1,1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [2,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [1,1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [1,1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [2,1,1,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [1,2,1,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [1,2,1,4]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => [3,1,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [1,1,2,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [2,2,4]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [1,1,2,4]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [1,1,2,4]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [2,2,4]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => [1,1,2,4]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => [1,1,2,4]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => [2,2,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [1,3,4]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => [1,3,4]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [4,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [1,1,1,1,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => [2,1,1,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,1,2,3,5] => [1,2,1,4]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => [3,1,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [1,1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => [2,1,1,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [1,1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,1,2,3,5] => [1,2,1,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => [1,1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => [1,1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [1,1,1,1,4]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,1,2,3,8] => [1,2,1,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => [2,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,3,2,5,4,8,7,1] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => [2,2,4]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [6,7,4,5,1,2,3,8] => [2,2,4]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8,3,2,5,6,4,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,1,2,3,8] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,1,2,3,8] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [6,7,4,5,1,2,3,8] => [2,2,4]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => [1,3,4]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [6,4,5,7,1,2,3,8] => [1,3,4]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => [4,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => [2,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,1,2,3,5] => [1,2,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => [3,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => [2,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,1,2,3,5] => [1,2,1,4]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,1,2,3,5] => [1,2,1,4]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [7,6,8,4,1,2,3,5] => [1,2,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => [2,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,2,6,5,1,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,1,2,3,7] => [1,2,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,1,2,3,7] => [1,2,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,1,2,3,8] => [1,2,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,3,4,5,2,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => [2,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => [2,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [6,7,5,4,1,2,3,8] => [2,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [6,7,5,4,1,2,3,8] => [2,1,1,4]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => [3,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => [2,2,4]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => [1,1,2,4]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => [1,1,2,4]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => [2,2,4]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [1,1,2,4]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,1,2,3,8] => [1,1,2,4]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [6,7,4,5,1,2,3,8] => [2,2,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [1,1,2,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [1,1,2,4]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,1,2,3,8] => [1,1,2,4]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [6,7,4,5,1,2,3,8] => [2,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [8,5,4,6,1,2,3,7] => [1,1,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [8,5,4,6,1,2,3,7] => [1,1,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,1,2,3,8] => [1,1,2,4]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [6,5,4,7,1,2,3,8] => [1,1,2,4]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => [2,2,4]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [8,4,5,6,1,2,3,7] => [1,3,4]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [8,4,5,6,1,2,3,7] => [1,3,4]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => [1,3,4]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => [1,3,4]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [6,4,5,7,1,2,3,8] => [1,3,4]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [6,4,5,7,1,2,3,8] => [1,3,4]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => [4,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [1,1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [2,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [1,2,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [1,2,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => [3,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [1,1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [2,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [1,1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [1,1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [2,1,5]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [1,2,5]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [1,2,5]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => [1,2,5]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => [3,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => [1,1,1,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [2,1,5]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,4,3,2,5,8,7,1] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [2,1,5]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [1,1,1,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => [1,2,5]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => [1,2,5]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => [3,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [2,1,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => [1,1,1,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => [1,1,1,5]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => [2,1,5]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [1,1,1,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [1,1,1,5]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => [2,1,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => [1,2,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => [1,2,5]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => [1,2,5]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => [3,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => [1,1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [7,8,4,1,2,3,5,6] => [2,1,5]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,3,4,2,7,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => [1,1,1,5]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [8,6,4,1,2,3,5,7] => [1,1,1,5]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [7,6,4,1,2,3,5,8] => [1,1,1,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [8,6,4,1,2,3,5,7] => [1,1,1,5]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [7,6,4,1,2,3,5,8] => [1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [8,5,4,1,2,3,6,7] => [1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [8,5,4,1,2,3,6,7] => [1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [7,5,4,1,2,3,6,8] => [1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8] => [1,1,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [8,4,5,1,2,3,6,7] => [1,2,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [8,4,5,1,2,3,6,7] => [1,2,5]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8,6,3,5,4,7,2,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [7,4,5,1,2,3,6,8] => [1,2,5]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [6,4,5,1,2,3,7,8] => [1,2,5]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [6,4,5,1,2,3,7,8] => [1,2,5]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => [3,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [2,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [2,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => [2,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => [1,1,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => [1,1,6]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => [1,1,6]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => [1,1,6]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => [2,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => [1,1,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => [1,1,6]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [1,1,6]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [1,1,6]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [6,5,1,2,3,4,7,8] => [1,1,6]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [5,6,1,2,3,4,7,8] => [2,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => [1,1,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => [1,1,6]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [1,1,6]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [6,5,1,2,3,4,7,8] => [1,1,6]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [6,5,1,2,3,4,7,8] => [1,1,6]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [5,6,1,2,3,4,7,8] => [2,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => [1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => [1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => [1,7]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => [1,7]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => [1,7]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => [1,7]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => [1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [8]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => [1,8]
[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] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [8,1]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => [1,9]
[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] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [9,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => [1,10]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [10,1]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => [1,1,7]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [9,3,4,5,6,7,8,1,2] => [1,6,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => [2,7]
[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] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => [7,2]
[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] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,2,3,1] => [6,2,1]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => [1,1,7]
[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] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [9,2,3,4,5,6,7,8,1] => [1,7,1]
[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] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => [7,1,1]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => [1,1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => [2,8]
[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] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => [8,2]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => [4,5,6,7,8,9,10,2,3,1] => [7,2,1]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => [1,1,8]
[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] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [10,2,3,4,5,6,7,8,9,1] => [1,8,1]
[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] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => [8,1,1]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2] => [2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,9,7,8,1] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,3,1,2] => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,3,1,2] => [6,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,9,3,4,5,6,7,8,1] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,3,9,1,2] => [1,1,1,1,1,2,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [9,3,4,5,6,7,8,1,2] => [1,6,2]
[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] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => [7,2]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,3]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,1,2,3] => [6,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [9,7,6,5,4,3,1,2,8] => [1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,3]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,2,8,7,6,5,4,3,1] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [3,4,5,6,7,8,1,2,9] => [6,3]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,3,2,4,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9,3,4,2,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9,3,4,5,2,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,3,4,5,6,7,8,2,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,4]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,5]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4,3,2,9,8,7,6,1] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => [4,5]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => [1,1,1,6]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => [1,1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,6,5,4,3,2,9,8,1] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => [2,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [9,7,1,2,3,4,5,6,8] => [1,1,7]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => [1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => [1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [9,7,6,5,4,3,8,2,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => [1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [9,8,6,5,4,3,7,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => [1,8]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [9,8,6,5,4,7,3,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => [1,8]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9,8,7,5,4,6,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [6,1,2,3,4,5,7,8,9] => [1,8]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,8,7,5,6,4,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [6,1,2,3,4,5,7,8,9] => [1,8]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [9]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1]
[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] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [2,1,1,1,1,1,1,1]
[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] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [9,7,8,6,5,4,3,2,1] => [1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [9,8,7,5,6,4,3,2,1] => [1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,4,5,3,2,1] => [1,1,1,1,2,1,1,1]
[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] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,2,1]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [2,1,1,1,1,1,1,1,1]
[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] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [10,8,9,7,6,5,4,3,2,1] => [1,2,1,1,1,1,1,1,1]
[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] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [9,6,7,8,5,4,3,2,1] => [1,3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [10,9,8,6,7,5,4,3,2,1] => [1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,5,6,4,3,2,1] => [1,1,1,1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,2,1]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,2]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => [2,1,1,1,1,1,1,1,1,1]
[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] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => [3,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => [11,9,10,8,7,6,5,4,3,2,1] => [1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,9,7,8,6] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [8,6,7,9,5,4,3,2,1] => [1,3,1,1,1,1,1]
[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] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => [4,1,1,1,1,1]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,9,6,7,8,5] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [8,7,5,6,9,4,3,2,1] => [1,1,3,1,1,1,1]
[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] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => [4,1,1,1,1,1,1]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,4]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,9,5,6,7,8,4] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [8,7,6,4,5,9,3,2,1] => [1,1,1,3,1,1,1]
[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] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => [5,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,9,4,5,6,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [8,7,6,5,3,4,9,2,1] => [1,1,1,1,3,1,1]
[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] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [5,1,1,1,1,1]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => [1,1,1,1,1,5]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9,3,4,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,2,3,9,1] => [1,1,1,1,1,3,1]
[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] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => [6,1,1,1]
[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] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => [6,1,1,1,1]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => [1,1,1,1,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [10,8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,1,3]
[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] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [9,7,8,6,5,4,3,2,1] => [1,2,1,1,1,1,1,1]
[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] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [8,9,6,7,5,4,3,2,1] => [2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [9,8,7,5,6,4,3,2,1] => [1,1,1,2,1,1,1,1]
[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] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [7,8,9,5,6,4,3,2,1] => [3,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,4,5,3,2,1] => [1,1,1,1,2,1,1,1]
[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] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [6,7,8,9,4,5,3,2,1] => [4,2,1,1,1]
[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] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [5,6,7,8,9,3,4,2,1] => [5,2,1,1]
[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] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,2,1]
[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] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,2,3,1] => [6,2,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [8,9,2,3,4,5,6,7,1] => [2,6,1]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2] => [2,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => [1,2,1,1,1,1,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [9,3,4,5,6,7,8,1,2] => [1,6,2]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,3]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,1,2,3] => [6,3]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [5,6,7,8,9,1,2,3,4] => [5,4]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => [4,5]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => [1,1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => [3,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [10,8,9,7,6,5,4,3,2,1] => [1,2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [10,9,8,6,7,5,4,3,2,1] => [1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,5,6,4,3,2,1] => [1,1,1,1,2,1,1,1,1]
[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] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => [7,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,2,1]
[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] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [10,8,9,6,7,4,5,2,3,1] => [1,2,2,2,2,1]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,10,9,8,7,6,5,4] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => [4,5,6,7,8,9,10,2,3,1] => [7,2,1]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [9,10,8,7,6,5,4,3,1,2] => [2,1,1,1,1,1,1,2]
[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] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,3]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [4,5,6,7,8,9,10,1,2,3] => [7,3]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [5,6,7,8,9,10,1,2,3,4] => [6,4]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => [1,1,1,1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => [5,5]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => [1,1,1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => [4,6]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => [1,1,1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => [3,7]
[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] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [10]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => [1,2,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,2]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [9,10,8,7,6,5,4,3,1,2] => [2,1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [10,9,8,6,5,7,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [7,1,2,3,4,5,6,8,9,10] => [1,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => [1,2,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2] => [2,1,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [9,7,6,5,4,3,1,2,8] => [1,1,1,1,1,1,3]
[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] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => [8,2]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => [1,9]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => [1,10]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => [1,1,1,6]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,5]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,4]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,3]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,9,8,7,5,6,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [6,1,2,3,4,5,7,8,9,10] => [1,9]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,3,1,2] => [6,1,2]
[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] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [10,9,8,6,7,5,4,3,2,1] => [1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [10,9,8,6,7,5,4,3,2,1] => [1,1,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2] => [2,1,1,1,1,1,2]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2] => [2,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [10,8,7,6,5,4,3,2,9,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => [1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [10,8,7,6,5,4,3,9,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => [1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [10,9,7,6,5,4,3,8,2,1] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [8,1,2,3,4,5,6,7,9,10] => [1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [10,9,7,6,5,4,8,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [8,1,2,3,4,5,6,7,9,10] => [1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [10,9,8,6,5,4,7,3,2,1] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [7,1,2,3,4,5,6,8,9,10] => [1,9]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => [1,2,1,1,1,1,2]
[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] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2]
[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] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [9,8,7,6,5,4,3,1,2,10] => [1,1,1,1,1,1,1,3]
[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] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => [11]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [10,8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,1,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,2]
[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] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [5,6,7,8,9,3,4,2,1] => [5,2,1,1]
[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] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [6,7,8,9,4,5,3,2,1] => [4,2,1,1,1]
[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] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [7,8,9,5,6,4,3,2,1] => [3,2,1,1,1,1]
[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] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [8,9,6,7,5,4,3,2,1] => [2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [10,11,1,2,3,4,5,6,7,8,9] => [2,9]
[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] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => [11,9,10,8,7,6,5,4,3,2,1] => [1,2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,2]
[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] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,7,6,5,4,3,2,10,9,1] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => [2,8]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [4,5,6,7,8,9,10,1,2,3] => [7,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [9,10,8,7,6,5,4,3,1,2] => [2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => [1,2,1,1,1,1,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,2,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,6,5,4,3,9,8,2] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [8,9,2,3,4,5,6,7,1] => [2,6,1]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => [1,1,8]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => [1,1,1,7]
[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] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [10,8,9,6,7,4,5,2,3,1] => [1,2,2,2,2,1]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,3]
[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] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,2,1]
[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] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[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] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2]
[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] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2]
[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] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,10,9,7] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,10,9,7] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,7,10,12,11,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,5,8,10,9,7,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5,10,12,11,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,7,10,12,11,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,10,9,7,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,7,10,12,11,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5,8,10,9,7,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5,10,12,11,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,12,11,1] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
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 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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