Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
[1,0] => [1] => [1] => [.,.]
[1,0,1,0] => [2,1] => [2,1] => [[.,.],.]
[1,1,0,0] => [1,2] => [1,2] => [.,[.,.]]
[1,0,1,0,1,0] => [3,2,1] => [2,3,1] => [[.,.],[.,.]]
[1,0,1,1,0,0] => [2,3,1] => [3,2,1] => [[[.,.],.],.]
[1,1,0,0,1,0] => [3,1,2] => [3,1,2] => [[.,[.,.]],.]
[1,1,0,1,0,0] => [2,1,3] => [2,1,3] => [[.,.],[.,.]]
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [2,3,4,1] => [[.,.],[.,[.,.]]]
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [2,4,3,1] => [[.,.],[[.,.],.]]
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [3,4,2,1] => [[[.,.],.],[.,.]]
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [4,3,2,1] => [[[[.,.],.],.],.]
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [4,2,3,1] => [[[.,.],[.,.]],.]
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [3,1,4,2] => [[.,[.,.]],[.,.]]
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [4,1,3,2] => [[.,[[.,.],.]],.]
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [2,4,1,3] => [[.,.],[[.,.],.]]
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [2,3,1,4] => [[.,.],[.,[.,.]]]
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [4,1,2,3] => [[.,[.,[.,.]]],.]
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [3,1,2,4] => [[.,[.,.]],[.,.]]
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [2,5,3,4,1] => [[.,.],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [3,5,2,4,1] => [[[.,.],.],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [5,3,4,2,1] => [[[[.,.],.],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [4,5,2,3,1] => [[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [5,4,2,3,1] => [[[[.,.],[.,.]],.],.]
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [3,1,5,4,2] => [[.,[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [4,1,5,3,2] => [[.,[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [5,1,4,3,2] => [[.,[[[.,.],.],.]],.]
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [5,1,3,4,2] => [[.,[[.,.],[.,.]]],.]
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [2,4,1,5,3] => [[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [2,5,1,4,3] => [[.,.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [2,3,5,1,4] => [[.,.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [2,4,3,1,5] => [[.,.],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [3,5,2,1,4] => [[[.,.],.],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [3,4,2,1,5] => [[[.,.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [5,1,2,4,3] => [[.,[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [3,1,5,2,4] => [[.,[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [4,1,3,2,5] => [[.,[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [2,5,1,3,4] => [[.,.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [2,4,1,3,5] => [[.,.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [2,3,4,6,5,1] => [[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [2,3,5,6,4,1] => [[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [2,3,6,5,4,1] => [[.,.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [2,3,6,4,5,1] => [[.,.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [2,4,5,3,6,1] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [2,4,6,3,5,1] => [[.,.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [2,5,4,6,3,1] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [2,6,4,5,3,1] => [[.,.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [2,6,5,4,3,1] => [[.,.],[[[[.,.],.],.],.]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [2,5,6,3,4,1] => [[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [2,6,5,3,4,1] => [[.,.],[[[.,[.,.]],.],.]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [2,6,4,3,5,1] => [[.,.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [2,6,3,4,5,1] => [[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [3,4,2,6,5,1] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [3,5,2,6,4,1] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [3,6,2,5,4,1] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [3,6,2,4,5,1] => [[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [4,3,6,2,5,1] => [[[[.,.],.],.],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [5,3,4,6,2,1] => [[[[.,.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [6,3,5,4,2,1] => [[[[.,.],.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [4,5,2,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [4,6,2,3,5,1] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [5,4,2,6,3,1] => [[[[.,.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [6,4,2,5,3,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [6,5,2,4,3,1] => [[[[.,.],[[.,.],.]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [5,3,6,2,4,1] => [[[[.,.],.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [6,3,5,2,4,1] => [[[[.,.],.],[[.,.],.]],.]
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.]
>>> Load all 1731 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [5,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.]
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [6,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [3,1,4,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [3,1,4,6,5,2] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [3,1,5,6,4,2] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [3,1,6,5,4,2] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [3,1,6,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [4,1,5,3,6,2] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => [[.,[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [5,1,4,6,3,2] => [[.,[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [6,1,4,5,3,2] => [[.,[[[.,.],.],[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [6,1,5,4,3,2] => [[.,[[[[.,.],.],.],.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [5,1,6,3,4,2] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [6,1,5,3,4,2] => [[.,[[[.,.],[.,.]],.]],.]
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [6,1,4,3,5,2] => [[.,[[[.,.],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [6,1,3,4,5,2] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [2,4,1,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [2,4,1,6,5,3] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [2,5,1,6,4,3] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [2,6,1,5,4,3] => [[.,.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [2,6,1,4,5,3] => [[.,.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [2,3,5,1,6,4] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [2,3,6,1,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [2,3,4,6,1,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [2,3,5,4,1,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [2,4,6,3,1,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [2,4,5,3,1,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [2,5,4,3,1,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [2,5,3,4,1,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [3,5,2,1,6,4] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [3,6,2,1,5,4] => [[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [3,4,2,6,1,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [3,5,2,4,1,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [4,3,6,2,1,5] => [[[[.,.],.],.],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [5,3,4,2,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [4,6,2,3,1,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [4,5,2,3,1,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [5,4,2,3,1,6] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [4,1,2,5,6,3] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [4,1,2,6,5,3] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => [[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => [[.,[.,[[[.,.],.],.]]],.]
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [3,1,5,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [3,1,6,2,5,4] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [3,1,4,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [3,1,4,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [3,1,5,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => [[.,[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => [[.,[[[.,.],.],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,3,4,2,6] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [2,5,1,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [2,6,1,3,5,4] => [[.,.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [2,4,1,6,3,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [2,4,1,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [2,5,1,4,3,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [2,3,6,1,4,5] => [[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [2,3,5,1,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [2,4,3,1,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [3,6,2,1,4,5] => [[[.,.],.],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [3,5,2,1,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [2,3,4,5,7,6,1] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [2,3,4,6,7,5,1] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [2,3,4,7,6,5,1] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [2,3,4,7,5,6,1] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [2,3,5,6,4,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [2,3,5,7,4,6,1] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [2,3,6,5,7,4,1] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [2,3,7,5,6,4,1] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [2,3,7,6,5,4,1] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [2,3,6,7,4,5,1] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [2,3,7,6,4,5,1] => [[.,.],[.,[[[.,[.,.]],.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [2,3,7,5,4,6,1] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [2,3,7,4,5,6,1] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [2,4,5,3,6,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [2,4,5,3,7,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [2,4,6,3,7,5,1] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [2,4,7,3,6,5,1] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [2,4,7,3,5,6,1] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [2,5,4,6,3,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [2,5,4,7,3,6,1] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [2,6,4,5,7,3,1] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [2,7,4,5,6,3,1] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [2,7,4,6,5,3,1] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [2,6,5,7,4,3,1] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [2,7,5,6,4,3,1] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [2,7,6,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [2,7,6,4,5,3,1] => [[.,.],[[[[.,.],[.,.]],.],.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [2,5,6,3,4,7,1] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [2,5,7,3,4,6,1] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [2,6,5,3,7,4,1] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [2,7,5,3,6,4,1] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [2,7,6,3,5,4,1] => [[.,.],[[[.,[[.,.],.]],.],.]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [2,6,4,7,3,5,1] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [2,7,4,6,3,5,1] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [2,7,4,5,3,6,1] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [2,7,5,4,3,6,1] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [2,6,7,3,4,5,1] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [2,7,6,3,4,5,1] => [[.,.],[[[.,[.,[.,.]]],.],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [2,7,5,3,4,6,1] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [2,7,4,3,5,6,1] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [2,7,3,4,5,6,1] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [3,4,2,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [3,4,2,5,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [3,4,2,6,7,5,1] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [3,4,2,7,6,5,1] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [3,4,2,7,5,6,1] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [3,5,2,6,4,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [3,5,2,7,4,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [3,6,2,5,7,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [3,7,2,5,6,4,1] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [3,7,2,6,5,4,1] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [3,6,2,7,4,5,1] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [3,7,2,6,4,5,1] => [[[.,.],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [3,7,2,5,4,6,1] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [3,7,2,4,5,6,1] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [4,3,5,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [4,3,5,2,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [4,3,6,2,7,5,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [4,3,7,2,6,5,1] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [4,3,7,2,5,6,1] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [5,3,4,6,2,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [5,3,4,7,2,6,1] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [6,3,4,5,7,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [7,3,4,5,6,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [7,3,4,6,5,2,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [6,3,5,7,4,2,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [7,3,5,6,4,2,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [7,3,6,5,4,2,1] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [7,3,6,4,5,2,1] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [5,4,6,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [5,4,7,3,2,6,1] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [6,4,5,3,7,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [7,4,5,3,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [7,4,6,3,5,2,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [7,5,4,6,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [6,5,7,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [7,5,6,3,4,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [4,5,2,3,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [4,5,2,3,7,6,1] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [4,6,2,3,7,5,1] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [4,7,2,3,6,5,1] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [4,7,2,3,5,6,1] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [5,4,2,6,3,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [5,4,2,7,3,6,1] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [6,4,2,5,7,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [7,4,2,5,6,3,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [7,4,2,6,5,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [6,5,2,7,4,3,1] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [7,5,2,6,4,3,1] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [7,6,2,5,4,3,1] => [[[[.,.],[[[.,.],.],.]],.],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [7,6,2,4,5,3,1] => [[[[.,.],[[.,.],[.,.]]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [5,3,6,2,4,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [5,3,7,2,4,6,1] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [6,3,5,2,7,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [7,3,5,2,6,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [7,3,6,2,5,4,1] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [6,3,4,7,2,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [7,3,4,6,2,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [7,3,4,5,2,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [7,3,5,4,2,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [6,4,7,3,2,5,1] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [7,4,6,3,2,5,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [7,4,5,3,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [5,6,2,3,4,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [5,7,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [6,5,2,3,7,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [7,5,2,3,6,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [7,6,2,3,5,4,1] => [[[[.,.],[.,[[.,.],.]]],.],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [6,4,2,7,3,5,1] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [7,4,2,6,3,5,1] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [7,4,2,5,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [7,5,2,4,3,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [6,3,7,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [7,3,6,2,4,5,1] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [7,3,5,2,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [7,3,4,2,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [6,7,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [7,6,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [7,5,2,3,4,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [7,4,2,3,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [3,1,4,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [3,1,4,5,7,6,2] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [3,1,4,6,7,5,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [3,1,4,7,6,5,2] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [3,1,4,7,5,6,2] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [3,1,5,6,4,7,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [3,1,5,7,4,6,2] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [3,1,6,5,7,4,2] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [3,1,7,5,6,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [3,1,7,6,5,4,2] => [[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [3,1,6,7,4,5,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [3,1,7,6,4,5,2] => [[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [3,1,7,5,4,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [3,1,7,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [4,1,5,3,6,7,2] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [4,1,5,3,7,6,2] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [4,1,6,3,7,5,2] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [4,1,7,3,6,5,2] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [4,1,7,3,5,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [5,1,4,6,3,7,2] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [5,1,4,7,3,6,2] => [[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [6,1,4,5,7,3,2] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [7,1,4,5,6,3,2] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [7,1,4,6,5,3,2] => [[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [6,1,5,7,4,3,2] => [[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [7,1,5,6,4,3,2] => [[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [7,1,6,5,4,3,2] => [[.,[[[[[.,.],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [7,1,6,4,5,3,2] => [[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [5,1,6,3,4,7,2] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [5,1,7,3,4,6,2] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [6,1,5,3,7,4,2] => [[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [7,1,5,3,6,4,2] => [[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [7,1,6,3,5,4,2] => [[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [6,1,4,7,3,5,2] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [7,1,4,6,3,5,2] => [[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [7,1,4,5,3,6,2] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [7,1,5,4,3,6,2] => [[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [6,1,7,3,4,5,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [7,1,6,3,4,5,2] => [[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [7,1,5,3,4,6,2] => [[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [7,1,4,3,5,6,2] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [7,1,3,4,5,6,2] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [2,4,1,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [2,4,1,5,7,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [2,4,1,6,7,5,3] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [2,4,1,7,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [2,4,1,7,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [2,5,1,6,4,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [2,5,1,7,4,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [2,6,1,5,7,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [2,7,1,5,6,4,3] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [2,7,1,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [2,6,1,7,4,5,3] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [2,7,1,6,4,5,3] => [[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [2,7,1,5,4,6,3] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [2,7,1,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [2,3,5,1,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [2,3,5,1,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [2,3,6,1,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [2,3,7,1,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [2,3,7,1,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [2,3,4,6,1,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [2,3,4,7,1,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [2,3,4,5,7,1,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [2,3,4,6,5,1,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [2,3,5,7,4,1,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [2,3,5,6,4,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [2,3,6,5,4,1,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [2,3,6,4,5,1,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [2,4,6,3,1,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [2,4,7,3,1,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [2,4,5,3,7,1,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [2,4,5,3,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [2,4,6,3,5,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [2,5,4,7,3,1,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [2,5,4,6,3,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [2,6,4,5,3,1,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [2,6,5,4,3,1,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [2,5,7,3,4,1,6] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [2,5,6,3,4,1,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [2,6,5,3,4,1,7] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [2,6,4,3,5,1,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [2,6,3,4,5,1,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [3,5,2,1,6,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [3,5,2,1,7,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [3,6,2,1,7,5,4] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [3,7,2,1,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [3,7,2,1,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [3,4,2,6,1,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [3,4,2,7,1,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [3,4,2,5,7,1,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [3,4,2,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [3,4,2,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [3,5,2,7,4,1,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [3,5,2,6,4,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [3,6,2,5,4,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [3,6,2,4,5,1,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [4,3,6,2,1,7,5] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [4,3,7,2,1,6,5] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [4,3,5,2,7,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [4,3,5,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [4,3,6,2,5,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [5,3,4,7,2,1,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [5,3,4,6,2,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [6,3,4,5,2,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [6,3,5,4,2,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [5,4,7,3,2,1,6] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [5,4,6,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [6,4,5,3,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [4,6,2,3,1,7,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [4,7,2,3,1,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [4,5,2,3,7,1,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [4,5,2,3,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [4,6,2,3,5,1,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [5,4,2,7,3,1,6] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [5,4,2,6,3,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [6,4,2,5,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [6,5,2,4,3,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [5,3,7,2,4,1,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [5,3,6,2,4,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [6,3,5,2,4,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [6,3,4,2,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [5,7,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [5,6,2,3,4,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [6,5,2,3,4,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [6,4,2,3,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [4,1,2,5,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [4,1,2,5,7,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [4,1,2,6,7,5,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [4,1,2,7,6,5,3] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [4,1,2,7,5,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [5,1,2,6,4,7,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [5,1,2,7,4,6,3] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [6,1,2,5,7,4,3] => [[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [7,1,2,5,6,4,3] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [7,1,2,6,5,4,3] => [[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [6,1,2,7,4,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [7,1,2,6,4,5,3] => [[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [7,1,2,5,4,6,3] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [7,1,2,4,5,6,3] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [3,1,5,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [3,1,5,2,7,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [3,1,6,2,7,5,4] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [3,1,7,2,6,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [3,1,7,2,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [3,1,4,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [3,1,4,7,2,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [3,1,4,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [3,1,4,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [3,1,4,6,5,2,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [3,1,5,7,4,2,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [3,1,5,6,4,2,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [3,1,6,5,4,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [3,1,6,4,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [4,1,6,3,2,7,5] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [4,1,7,3,2,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [4,1,5,3,7,2,6] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [4,1,5,3,6,2,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [4,1,6,3,5,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [5,1,4,7,3,2,6] => [[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [5,1,4,6,3,2,7] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [6,1,4,5,3,2,7] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [6,1,5,4,3,2,7] => [[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [5,1,7,3,4,2,6] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [5,1,6,3,4,2,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [6,1,5,3,4,2,7] => [[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [6,1,4,3,5,2,7] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [6,1,3,4,5,2,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [2,5,1,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [2,5,1,3,7,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [2,6,1,3,7,5,4] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [2,7,1,3,6,5,4] => [[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [2,7,1,3,5,6,4] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [2,4,1,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [2,4,1,7,3,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [2,4,1,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [2,4,1,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [2,4,1,6,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [2,5,1,7,4,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [2,5,1,6,4,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [2,6,1,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [2,6,1,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [2,3,6,1,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [2,3,7,1,4,6,5] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [2,3,5,1,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [2,3,5,1,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [2,3,6,1,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [2,3,4,7,1,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [2,3,4,6,1,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [2,3,5,4,1,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [2,4,7,3,1,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [2,4,6,3,1,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [2,4,5,3,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [2,5,4,3,1,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [2,5,3,4,1,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [3,6,2,1,4,7,5] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [3,7,2,1,4,6,5] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [3,5,2,1,7,4,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [3,5,2,1,6,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [3,6,2,1,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [3,4,2,7,1,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [3,4,2,6,1,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [3,4,2,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [3,5,2,4,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [4,3,7,2,1,5,6] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [4,3,6,2,1,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [4,3,5,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [5,3,4,2,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [4,7,2,3,1,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [4,6,2,3,1,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [4,5,2,3,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [5,4,2,3,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [5,1,2,3,6,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [5,1,2,3,7,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [6,1,2,3,7,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [7,1,2,3,6,5,4] => [[.,[.,[.,[[[.,.],.],.]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [4,1,2,6,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [4,1,2,7,3,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [4,1,2,5,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [4,1,2,5,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [4,1,2,6,5,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [5,1,2,7,4,3,6] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [5,1,2,6,4,3,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [6,1,2,5,4,3,7] => [[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [3,1,6,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [3,1,7,2,4,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [3,1,5,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [3,1,5,2,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [3,1,6,2,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [3,1,4,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [3,1,4,6,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [3,1,4,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [3,1,5,4,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [4,1,7,3,2,5,6] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [4,1,6,3,2,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [4,1,5,3,2,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [5,1,4,3,2,6,7] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [5,1,3,4,2,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [2,6,1,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [2,7,1,3,4,6,5] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [2,5,1,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [2,5,1,3,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [2,6,1,3,5,4,7] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [2,4,1,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [2,4,1,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [2,4,1,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [2,5,1,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [2,3,7,1,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [2,3,6,1,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [2,3,5,1,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [2,4,3,1,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [3,7,2,1,4,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [3,6,2,1,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [3,5,2,1,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [3,4,2,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [6,1,2,3,4,7,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => [[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [5,1,2,3,7,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [5,1,2,3,6,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [4,1,2,7,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [4,1,2,6,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [4,1,2,5,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [3,1,7,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [3,1,6,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [3,1,5,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [3,1,4,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [2,7,1,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [2,6,1,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [2,5,1,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [2,4,1,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [2,3,4,5,6,8,7,1] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [2,3,4,5,7,8,6,1] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [2,3,4,5,8,7,6,1] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [2,3,4,5,8,6,7,1] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [2,3,4,6,7,5,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [2,3,4,6,8,5,7,1] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [2,3,4,7,6,8,5,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [2,3,4,8,6,7,5,1] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [2,3,4,8,7,6,5,1] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [2,3,4,7,8,5,6,1] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [2,3,4,8,7,5,6,1] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [2,3,4,8,6,5,7,1] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [2,3,4,8,5,6,7,1] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [2,3,5,6,4,7,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [2,3,5,6,4,8,7,1] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [2,3,5,7,4,8,6,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,2,1] => [2,3,5,8,4,6,7,1] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,3,2,1] => [2,3,6,5,8,4,7,1] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [2,3,7,5,6,8,4,1] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [2,3,8,5,6,7,4,1] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [2,3,8,5,7,6,4,1] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [2,3,8,6,7,5,4,1] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [2,3,8,7,6,5,4,1] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [2,3,6,7,4,5,8,1] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,2,1] => [2,3,6,8,4,5,7,1] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,2,1] => [2,3,7,5,8,4,6,1] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [2,3,8,5,6,4,7,1] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [2,3,8,6,5,4,7,1] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [2,3,8,7,4,5,6,1] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [2,3,8,6,4,5,7,1] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [2,3,8,5,4,6,7,1] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [2,3,8,4,5,6,7,1] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [2,4,5,3,6,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [2,4,5,3,6,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [2,4,5,3,7,8,6,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [2,4,5,3,8,7,6,1] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,2,1] => [2,4,5,3,8,6,7,1] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [2,4,6,3,7,5,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [2,4,6,3,8,5,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => [2,4,8,3,7,6,5,1] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [2,4,7,3,8,5,6,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,2,1] => [2,4,8,3,7,5,6,1] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [2,4,8,3,6,5,7,1] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [2,4,8,3,5,6,7,1] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [2,5,4,8,3,7,6,1] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [2,5,4,8,3,6,7,1] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [2,6,4,5,7,3,8,1] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [2,6,4,5,8,3,7,1] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [2,7,4,5,6,8,3,1] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [2,8,4,5,6,7,3,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,7,2,1] => [2,7,4,6,8,5,3,1] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [2,8,4,7,6,5,3,1] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => [2,6,5,7,4,3,8,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [2,8,7,5,6,4,3,1] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,2,1] => [2,8,7,6,5,4,3,1] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [2,8,7,6,4,5,3,1] => [[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [2,8,7,5,4,6,3,1] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [2,8,7,4,5,6,3,1] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [2,5,6,3,4,7,8,1] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [2,5,6,3,4,8,7,1] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [2,5,7,3,4,8,6,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [2,5,8,3,4,6,7,1] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => [2,6,5,3,7,4,8,1] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [2,6,5,3,8,4,7,1] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,7,2,1] => [2,7,6,3,8,5,4,1] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [2,6,4,7,3,5,8,1] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,2,1] => [2,6,4,8,3,5,7,1] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [2,7,4,6,3,8,5,1] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [2,7,4,5,8,3,6,1] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [2,8,4,5,7,3,6,1] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [2,8,4,5,6,3,7,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,2,1] => [2,8,4,6,5,3,7,1] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => [2,8,5,3,6,4,7,1] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [2,7,4,8,3,5,6,1] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,6,8,2,1] => [2,8,4,7,3,5,6,1] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [2,8,4,5,3,6,7,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,2,1] => [2,8,5,4,3,6,7,1] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [2,7,8,3,4,5,6,1] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [2,8,7,3,4,5,6,1] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [2,8,6,3,4,5,7,1] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [2,8,5,3,4,6,7,1] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [2,8,4,3,5,6,7,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [2,8,3,4,5,6,7,1] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [3,4,2,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [3,4,2,5,6,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [3,4,2,5,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [3,4,2,5,8,7,6,1] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [3,4,2,6,7,5,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,3,1] => [3,4,2,6,8,5,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [3,4,2,8,6,7,5,1] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [3,4,2,8,7,6,5,1] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [3,4,2,8,5,6,7,1] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [3,5,2,6,4,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,2,3,1] => [3,5,2,6,4,8,7,1] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [3,5,2,7,4,8,6,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [3,5,2,8,4,7,6,1] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [3,5,2,8,4,6,7,1] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [3,6,2,5,7,4,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [3,7,2,6,8,5,4,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [3,8,2,6,7,5,4,1] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [3,8,2,7,6,5,4,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [3,6,2,8,4,5,7,1] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,3,1] => [3,8,2,5,7,4,6,1] => [[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [3,7,2,8,4,5,6,1] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,3,1] => [3,8,2,5,4,6,7,1] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [3,8,2,4,5,6,7,1] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [4,3,5,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [4,3,5,2,8,7,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [4,3,5,2,8,6,7,1] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [4,3,6,2,7,5,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,4,1] => [4,3,6,2,8,5,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [4,3,7,2,6,8,5,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [4,3,8,2,6,7,5,1] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [4,3,8,2,7,6,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [4,3,7,2,8,5,6,1] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,4,1] => [4,3,8,2,7,5,6,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,4,1] => [4,3,8,2,6,5,7,1] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [4,3,8,2,5,6,7,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => [5,3,4,6,2,8,7,1] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [5,3,4,8,2,7,6,1] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => [5,3,4,8,2,6,7,1] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [6,3,4,5,7,2,8,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [6,3,4,5,8,2,7,1] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [7,3,4,5,6,8,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [8,3,4,5,6,7,2,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [8,3,4,5,7,6,2,1] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [8,3,4,7,6,5,2,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [8,3,5,6,4,7,2,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,8,1] => [8,3,6,5,7,4,2,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => [8,3,7,5,6,4,2,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,8,1] => [8,3,7,6,5,4,2,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,8,1] => [8,3,7,5,4,6,2,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [8,3,7,4,5,6,2,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [5,4,6,3,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [5,4,6,3,2,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [5,4,7,3,2,8,6,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [5,4,8,3,2,7,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [5,4,8,3,2,6,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [6,4,5,3,7,2,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [6,4,5,3,8,2,7,1] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [7,4,6,3,8,5,2,1] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [8,4,6,3,7,5,2,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [8,4,7,3,6,5,2,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,8,1] => [8,4,7,3,5,6,2,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [6,5,4,7,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => [6,5,4,8,3,2,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [7,5,4,6,3,8,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [8,5,4,6,3,7,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,8,1] => [8,5,4,7,3,6,2,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => [7,6,4,5,8,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [8,6,4,5,7,3,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,8,1] => [8,7,4,6,5,3,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [8,6,5,7,4,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [8,7,5,6,4,3,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,6,1] => [6,5,8,3,4,2,7,1] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [8,6,5,3,7,4,2,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [8,7,5,3,6,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => [8,7,6,3,5,4,2,1] => [[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [8,7,4,6,3,5,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => [8,7,4,5,3,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => [7,6,8,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [8,6,7,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [8,7,6,3,4,5,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,2,8,1] => [8,7,5,3,4,6,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => [8,7,4,3,5,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [4,5,2,3,6,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [4,5,2,3,8,6,7,1] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [4,6,2,3,7,5,8,1] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [4,7,2,3,8,5,6,1] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => [4,8,2,3,6,5,7,1] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [4,8,2,3,5,6,7,1] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,5,1] => [5,4,2,6,3,7,8,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,3,5,1] => [5,4,2,6,3,8,7,1] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [5,4,2,8,3,6,7,1] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [8,4,2,5,6,7,3,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => [8,4,2,5,7,6,3,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => [7,4,2,6,8,5,3,1] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [8,4,2,6,7,5,3,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [8,5,2,7,4,6,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,2,3,7,1] => [7,6,2,5,8,4,3,1] => [[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => [8,6,2,5,7,4,3,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [8,7,2,5,6,4,3,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => [8,6,2,7,4,5,3,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [8,7,2,6,4,5,3,1] => [[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [8,7,2,4,5,6,3,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [5,3,6,2,4,7,8,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [5,3,6,2,4,8,7,1] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [5,3,7,2,4,8,6,1] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [5,3,8,2,4,6,7,1] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,4,8,1] => [8,3,6,2,7,5,4,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => [8,3,7,2,6,5,4,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [6,3,4,8,2,5,7,1] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [8,3,4,7,2,6,5,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [7,3,4,5,8,2,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [8,3,4,5,6,2,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,8,1] => [8,3,5,7,4,2,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => [8,3,6,5,4,2,7,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [8,3,6,4,5,2,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,6,1] => [6,4,7,3,2,5,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [7,4,5,3,8,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,8,1] => [8,4,5,3,7,2,6,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => [8,4,5,3,6,2,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,8,1] => [8,4,6,3,5,2,7,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,7,1] => [7,5,4,8,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,7,8,1] => [8,5,4,6,3,2,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => [8,6,4,5,3,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,8,1] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [7,5,8,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,6,8,1] => [8,5,7,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [8,5,6,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,8,1] => [8,6,5,3,4,2,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [8,6,3,4,5,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [5,7,2,3,4,8,6,1] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => [5,8,2,3,4,7,6,1] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [5,8,2,3,4,6,7,1] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,6,1] => [6,5,2,3,8,4,7,1] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [8,5,2,3,6,7,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => [8,6,2,3,7,5,4,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [8,4,2,6,3,7,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => [7,4,2,5,8,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [8,4,2,5,7,3,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => [8,4,2,5,6,3,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => [8,4,2,6,5,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,8,1] => [8,6,2,5,4,3,7,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [8,6,2,4,5,3,7,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [6,3,8,2,4,5,7,1] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [8,3,6,2,4,7,5,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [8,3,5,2,7,4,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [8,3,4,7,2,5,6,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [8,3,4,5,2,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [8,3,5,4,2,6,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [7,4,8,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7,3,4,2,5,6,8,1] => [8,4,7,3,2,5,6,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [8,4,5,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [8,5,3,4,2,6,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [6,7,2,3,4,5,8,1] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [7,6,2,3,4,8,5,1] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,7,1] => [7,5,2,3,8,4,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => [8,5,2,3,7,4,6,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,8,1] => [8,4,2,7,3,5,6,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [8,4,2,5,3,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [7,3,8,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [8,3,7,2,4,5,6,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,8,1] => [8,3,6,2,4,5,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [8,3,4,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [7,8,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [8,7,2,3,4,5,6,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => [8,6,2,3,4,5,7,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [8,4,2,3,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [3,1,4,5,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [3,1,4,5,6,8,7,2] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [3,1,4,5,7,8,6,2] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [3,1,4,5,8,6,7,2] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [3,1,4,6,7,5,8,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [3,1,4,6,8,5,7,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [3,1,4,7,6,8,5,2] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [3,1,4,8,7,6,5,2] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [3,1,4,8,6,5,7,2] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [3,1,4,8,5,6,7,2] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [3,1,5,6,4,7,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [3,1,5,6,4,8,7,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [3,1,5,7,4,8,6,2] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [3,1,6,5,7,4,8,2] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [3,1,8,6,7,5,4,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [3,1,8,7,6,5,4,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [3,1,6,8,4,5,7,2] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => [3,1,7,6,4,8,5,2] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [3,1,8,6,4,7,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,1,2] => [3,1,8,5,7,4,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [3,1,8,5,4,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [3,1,8,4,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [4,1,5,3,6,7,8,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [4,1,5,3,6,8,7,2] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [4,1,5,3,8,7,6,2] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [4,1,5,3,8,6,7,2] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [4,1,6,3,7,5,8,2] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [4,1,6,3,8,5,7,2] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [4,1,7,3,6,8,5,2] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [4,1,8,3,6,7,5,2] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [4,1,7,3,8,5,6,2] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [4,1,8,3,7,5,6,2] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [4,1,8,3,6,5,7,2] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [4,1,8,3,5,6,7,2] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,1,2] => [5,1,4,8,3,7,6,2] => [[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [6,1,4,5,8,3,7,2] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [7,1,4,5,6,8,3,2] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [8,1,4,5,6,7,3,2] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,1,2] => [8,1,4,5,7,6,3,2] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => [8,1,4,7,6,5,3,2] => [[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,1,2] => [8,1,5,6,4,7,3,2] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [8,1,5,7,4,6,3,2] => [[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => [7,1,6,5,8,4,3,2] => [[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => [8,1,7,5,6,4,3,2] => [[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [8,1,7,6,5,4,3,2] => [[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,1,2] => [8,1,6,7,4,5,3,2] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,1,2] => [8,1,7,6,4,5,3,2] => [[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [5,1,6,3,4,7,8,2] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [5,1,7,3,4,8,6,2] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,1,2] => [5,1,8,3,4,6,7,2] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [6,1,5,3,8,4,7,2] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,1,2] => [8,1,6,3,7,5,4,2] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,8,1,2] => [8,1,7,3,6,5,4,2] => [[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,1,2] => [8,1,7,3,5,6,4,2] => [[.,[[[.,.],[[.,.],[.,.]]],.]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [6,1,4,8,3,5,7,2] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,1,2] => [7,1,4,6,3,8,5,2] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => [8,1,4,6,3,7,5,2] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,8,1,2] => [8,1,4,7,3,6,5,2] => [[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => [8,1,4,5,7,3,6,2] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [8,1,4,5,6,3,7,2] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [8,1,4,6,5,3,7,2] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [6,1,8,3,4,5,7,2] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => [7,1,5,3,8,4,6,2] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [8,1,5,3,7,4,6,2] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,1,2] => [8,1,5,3,6,4,7,2] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [8,1,6,3,5,4,7,2] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [7,1,4,8,3,5,6,2] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [8,1,4,6,3,5,7,2] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [8,1,4,5,3,6,7,2] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [8,1,5,4,3,6,7,2] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [7,1,8,3,4,5,6,2] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [8,1,7,3,4,5,6,2] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [8,1,6,3,4,5,7,2] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [8,1,4,3,5,6,7,2] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [8,1,3,4,5,6,7,2] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [2,4,1,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [2,4,1,5,8,7,6,3] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [2,4,1,6,7,5,8,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [2,4,1,6,8,5,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,1,3] => [2,4,1,7,6,8,5,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [2,4,1,8,6,7,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [2,4,1,8,7,6,5,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [2,4,1,8,5,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,1,3] => [2,5,1,8,4,7,6,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,1,3] => [2,5,1,8,4,6,7,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,1,3] => [2,6,1,5,7,4,8,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,2,1,3] => [2,6,1,5,8,4,7,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,1,3] => [2,7,1,5,6,8,4,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [2,8,1,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [2,8,1,7,5,6,4,3] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,1,3] => [2,6,1,8,4,5,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,1,3] => [2,8,1,7,4,6,5,3] => [[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,2,1,3] => [2,8,1,5,6,4,7,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [2,8,1,5,4,6,7,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [2,8,1,4,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [2,3,5,1,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [2,3,6,1,7,5,8,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [2,3,6,1,8,5,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [2,3,7,1,6,8,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [2,3,8,1,6,7,5,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [2,3,8,1,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [2,3,7,1,8,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [2,3,8,1,6,5,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [2,3,8,1,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [2,3,4,6,1,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [2,3,4,6,1,8,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [2,3,4,8,1,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [2,3,4,8,1,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [2,3,4,5,7,1,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [2,3,4,5,8,1,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [2,3,4,5,6,8,1,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [2,3,4,5,7,6,1,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [2,3,4,6,8,5,1,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [2,3,4,6,7,5,1,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [2,3,4,7,6,5,1,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [2,3,4,7,5,6,1,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [2,3,5,6,4,7,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,1,7] => [2,3,6,5,8,4,1,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [2,3,6,5,7,4,1,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [2,3,7,5,6,4,1,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [2,3,7,6,5,4,1,8] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [2,3,6,8,4,5,1,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [2,3,7,5,4,6,1,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [2,4,5,3,7,1,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [2,4,5,3,6,8,1,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [2,4,6,3,8,5,1,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [2,4,6,3,7,5,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [2,4,7,3,5,6,1,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,1,6] => [2,5,4,7,3,1,8,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,1,6] => [2,5,4,8,3,1,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [2,5,4,6,3,7,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [2,5,4,7,3,6,1,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,1,7] => [2,6,4,5,8,3,1,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [2,6,4,5,7,3,1,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [2,7,4,5,6,3,1,8] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [2,7,4,6,5,3,1,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [2,7,6,5,4,3,1,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [2,5,6,3,4,7,1,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,1,8] => [2,7,5,3,6,4,1,8] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,1,8] => [2,7,6,3,5,4,1,8] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,6,2,1,8] => [2,6,4,7,3,5,1,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => [2,6,7,3,4,5,1,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,1,8] => [2,7,6,3,4,5,1,8] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [2,7,3,4,5,6,1,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [3,5,2,1,6,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [3,5,2,1,6,8,7,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [3,5,2,1,7,8,6,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [3,5,2,1,8,7,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [3,6,2,1,7,5,8,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [3,8,2,1,6,7,5,4] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [3,8,2,1,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [3,8,2,1,7,5,6,4] => [[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [3,8,2,1,5,6,7,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => [3,4,2,8,1,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [3,4,2,8,1,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [3,4,2,5,6,8,1,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [3,4,2,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [3,4,2,5,7,6,1,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [3,4,2,6,7,5,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [3,4,2,7,5,6,1,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [3,5,2,7,4,1,8,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,1,7] => [3,5,2,6,4,8,1,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [3,5,2,6,4,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [3,5,2,7,4,6,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [3,7,2,5,6,4,1,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [3,7,2,6,5,4,1,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [3,6,2,8,4,5,1,7] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => [3,7,2,5,4,6,1,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [4,3,7,2,1,8,6,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [4,3,8,2,1,6,7,5] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [4,3,5,2,7,1,8,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,4,1,6] => [4,3,5,2,8,1,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [4,3,5,2,6,8,1,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,4,1,8] => [4,3,6,2,7,5,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [4,3,7,2,6,5,1,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [4,3,7,2,5,6,1,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,1,7] => [5,3,4,6,2,8,1,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [5,3,4,6,2,7,1,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [5,3,4,7,2,6,1,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [6,3,4,5,8,2,1,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [7,3,4,5,6,2,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,1,7] => [6,3,5,8,4,2,1,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => [7,3,6,5,4,2,1,8] => [[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [5,4,8,3,2,1,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,1,7] => [6,4,5,3,8,2,1,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [7,4,6,3,5,2,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [6,5,4,8,3,2,1,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [6,5,4,7,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,7,1,8] => [7,5,4,6,3,2,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [7,6,4,5,3,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,1,7] => [6,5,8,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,6,1,8] => [6,5,7,3,4,2,1,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [7,5,6,3,4,2,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [7,6,5,3,4,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [4,5,2,3,8,1,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [4,5,2,3,6,7,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [4,5,2,3,7,6,1,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [4,6,2,3,7,5,1,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [4,7,2,3,6,5,1,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [4,7,2,3,5,6,1,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,3,5,1,6] => [5,4,2,7,3,1,8,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,1,6] => [5,4,2,8,3,1,7,6] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [5,4,2,6,3,7,1,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [5,4,2,7,3,6,1,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,1,8] => [6,4,2,5,7,3,1,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,1,8] => [7,4,2,5,6,3,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [6,5,2,8,4,3,1,7] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,1,8] => [7,5,2,6,4,3,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => [7,6,2,5,4,3,1,8] => [[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,1,8] => [7,6,2,4,5,3,1,8] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,1,6] => [5,3,8,2,4,1,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [5,3,6,2,4,8,1,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [5,3,6,2,4,7,1,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [5,3,7,2,4,6,1,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [6,3,5,2,7,4,1,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [7,3,5,2,6,4,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,7,1,8] => [7,3,6,2,5,4,1,8] => [[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,1,8] => [7,3,5,4,2,6,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,1,8] => [7,4,5,3,2,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,1,8] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,1,8] => [6,5,2,3,7,4,1,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,7,1,8] => [7,6,2,3,5,4,1,8] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,1,7] => [6,4,2,8,3,5,1,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [6,4,2,7,3,5,1,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [7,4,2,6,3,5,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => [7,4,2,5,3,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [6,3,8,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,1,8] => [7,3,5,2,4,6,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [6,7,2,3,4,5,1,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => [7,6,2,3,4,5,1,8] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [7,4,2,3,5,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [4,1,2,5,6,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [4,1,2,5,6,8,7,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [4,1,2,5,8,6,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [4,1,2,6,8,5,7,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [4,1,2,8,7,6,5,3] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [4,1,2,7,8,5,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [4,1,2,8,7,5,6,3] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [4,1,2,8,5,6,7,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,1,2,3] => [5,1,2,6,4,8,7,3] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [6,1,2,5,8,4,7,3] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [8,1,2,5,6,7,4,3] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,1,2,3] => [7,1,2,6,8,5,4,3] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,1,2,3] => [8,1,2,6,7,5,4,3] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [8,1,2,7,6,5,4,3] => [[.,[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [6,1,2,7,4,5,8,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [6,1,2,8,4,5,7,3] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,1,2,3] => [8,1,2,6,4,7,5,3] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [8,1,2,7,4,6,5,3] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => [7,1,2,5,8,4,6,3] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [8,1,2,5,7,4,6,3] => [[.,[.,[[[.,.],.],[[.,.],.]]]],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [7,1,2,8,4,5,6,3] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,1,2,3] => [8,1,2,7,4,5,6,3] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,1,2,3] => [8,1,2,6,4,5,7,3] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [8,1,2,4,5,6,7,3] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [3,1,5,2,6,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => [3,1,5,2,8,7,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,1,2,4] => [3,1,5,2,8,6,7,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [3,1,6,2,7,5,8,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [3,1,6,2,8,5,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [3,1,8,2,6,7,5,4] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [3,1,8,2,7,6,5,4] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,1,2,4] => [3,1,7,2,8,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [3,1,8,2,7,5,6,4] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => [3,1,8,2,6,5,7,4] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [3,1,8,2,5,6,7,4] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [3,1,4,6,2,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,1,2,5] => [3,1,4,6,2,8,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [3,1,4,8,2,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [3,1,4,5,7,2,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [3,1,4,5,6,8,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [3,1,4,5,6,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [3,1,4,5,7,6,2,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,1,2,8] => [3,1,4,7,5,6,2,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [3,1,7,4,5,6,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [4,1,6,3,2,7,8,5] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [4,1,7,3,2,8,6,5] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,1,2,5] => [4,1,8,3,2,7,6,5] => [[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [4,1,8,3,2,6,7,5] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [4,1,5,3,7,2,8,6] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,1,2,6] => [4,1,5,3,8,2,7,6] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [4,1,5,3,6,8,2,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [4,1,6,3,8,5,2,7] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,1,2,8] => [4,1,6,3,7,5,2,8] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [4,1,7,3,6,5,2,8] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,1,2,6] => [5,1,4,7,3,2,8,6] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,1,2,6] => [5,1,4,8,3,2,7,6] => [[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,1,2,8] => [5,1,4,7,3,6,2,8] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [6,1,4,5,8,3,2,7] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,1,2,8] => [7,1,4,6,5,3,2,8] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,1,2,8] => [6,1,5,7,4,3,2,8] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => [7,1,5,6,4,3,2,8] => [[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,1,2,8] => [7,1,6,5,4,3,2,8] => [[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [5,1,7,3,4,2,8,6] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [5,1,8,3,4,2,7,6] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [5,1,6,3,4,8,2,7] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,1,2,8] => [7,1,5,3,6,4,2,8] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [7,1,6,3,5,4,2,8] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [6,1,8,3,4,5,2,7] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [7,1,3,4,5,6,2,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [2,5,1,3,6,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [2,5,1,3,6,8,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,1,3,4] => [2,5,1,3,7,8,6,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [2,5,1,3,8,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [2,6,1,3,8,5,7,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [2,7,1,3,6,8,5,4] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [2,8,1,3,6,7,5,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [2,8,1,3,7,6,5,4] => [[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [2,8,1,3,7,5,6,4] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [2,8,1,3,6,5,7,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [2,8,1,3,5,6,7,4] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [2,4,1,6,3,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [2,4,1,7,3,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,1,3,6] => [2,4,1,5,7,3,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [2,4,1,5,8,3,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [2,4,1,5,6,8,3,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [2,4,1,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [2,4,1,6,8,5,3,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,1,3,8] => [2,4,1,7,5,6,3,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,1,3,6] => [2,5,1,8,4,3,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,1,3,7] => [2,5,1,6,4,8,3,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [2,5,1,6,4,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [2,6,1,5,7,4,3,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,1,3,8] => [2,7,1,5,6,4,3,8] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [2,6,1,8,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [2,3,6,1,4,7,8,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [2,3,6,1,4,8,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [2,3,7,1,4,8,6,5] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [2,3,8,1,4,6,7,5] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [2,3,5,1,7,4,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [2,3,5,1,8,4,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [2,3,5,1,6,8,4,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,1,4,8] => [2,3,5,1,7,6,4,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [2,3,6,1,8,5,4,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,1,4,8] => [2,3,6,1,7,5,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,1,4,8] => [2,3,7,1,5,6,4,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [2,3,4,7,1,5,8,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [2,3,4,8,1,5,7,6] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [2,3,4,6,1,8,5,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [2,3,4,6,1,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [2,3,4,7,1,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [2,3,4,5,8,1,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [2,3,4,5,7,1,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [2,3,4,6,5,1,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,2,1,7,8] => [2,3,5,6,4,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => [2,3,6,5,4,1,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [2,3,6,4,5,1,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [2,4,7,3,1,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [2,4,8,3,1,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [2,4,6,3,1,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => [2,5,4,8,3,1,6,7] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => [2,6,4,5,3,1,7,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [2,5,8,3,4,1,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [2,5,7,3,4,1,6,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,1,7,8] => [2,6,5,3,4,1,7,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [2,6,3,4,5,1,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [3,6,2,1,4,7,8,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => [3,6,2,1,4,8,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [3,7,2,1,4,8,6,5] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [3,8,2,1,4,6,7,5] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,3,1,4,6] => [3,5,2,1,7,4,8,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [3,5,2,1,6,8,4,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [3,6,2,1,8,5,4,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [3,6,2,1,7,5,4,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [3,7,2,1,5,6,4,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [3,4,2,6,1,7,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,1,7,8] => [3,4,2,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,1,6,8] => [3,5,2,7,4,1,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [3,6,2,5,4,1,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => [4,3,7,2,1,5,8,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [4,3,8,2,1,5,7,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [4,3,6,2,1,8,5,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => [4,3,7,2,1,6,5,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,1,6,7] => [4,3,5,2,8,1,6,7] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [4,3,5,2,7,1,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,1,7,8] => [4,3,5,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [4,3,6,2,5,1,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,1,6,8] => [5,3,4,7,2,1,6,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [6,3,4,5,2,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,5,1,7,8] => [5,4,6,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [4,8,2,3,1,5,7,6] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [4,6,2,3,1,7,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [4,5,2,3,8,1,6,7] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [4,5,2,3,7,1,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [5,4,2,8,3,1,6,7] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [5,4,2,7,3,1,6,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,1,7,8] => [5,4,2,6,3,1,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,1,7,8] => [6,4,2,5,3,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,1,6,7] => [5,3,8,2,4,1,6,7] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,1,6,8] => [5,3,7,2,4,1,6,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,1,7,8] => [5,3,6,2,4,1,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => [6,3,5,2,4,1,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [5,8,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [5,7,2,3,4,1,6,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [5,6,2,3,4,1,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [6,5,2,3,4,1,7,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [5,1,2,3,6,8,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [5,1,2,3,7,8,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [5,1,2,3,8,7,6,4] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [5,1,2,3,8,6,7,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [6,1,2,3,7,5,8,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [6,1,2,3,8,5,7,4] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [7,1,2,3,6,8,5,4] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [8,1,2,3,6,7,5,4] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [8,1,2,3,7,6,5,4] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [7,1,2,3,8,5,6,4] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [8,1,2,3,7,5,6,4] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [8,1,2,3,6,5,7,4] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [4,1,2,6,3,7,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => [4,1,2,6,3,8,7,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,1,2,3,5] => [4,1,2,7,3,8,6,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [4,1,2,8,3,6,7,5] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [4,1,2,5,7,3,8,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [4,1,2,5,8,3,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [4,1,2,5,6,8,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [4,1,2,5,6,7,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,1,2,3,8] => [4,1,2,5,7,6,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [4,1,2,6,8,5,3,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,1,2,3,8] => [4,1,2,6,7,5,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [4,1,2,7,5,6,3,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [5,1,2,8,4,3,7,6] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [5,1,2,6,4,8,3,7] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [7,1,2,6,5,4,3,8] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,1,2,3,8] => [7,1,2,6,4,5,3,8] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [7,1,2,5,4,6,3,8] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [7,1,2,4,5,6,3,8] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [3,1,6,2,4,7,8,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [3,1,6,2,4,8,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [3,1,8,2,4,7,6,5] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [3,1,5,2,7,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [3,1,5,2,8,4,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,1,2,4,7] => [3,1,5,2,6,8,4,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [3,1,7,2,5,6,4,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,1,2,5,6] => [3,1,4,7,2,5,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [3,1,4,8,2,5,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [3,1,4,6,2,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,1,2,6,7] => [3,1,4,5,8,2,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [3,1,4,6,5,2,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => [3,1,5,6,4,2,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [3,1,6,5,4,2,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [4,1,7,3,2,5,8,6] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,1,2,5,8] => [4,1,6,3,2,7,5,8] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => [4,1,7,3,2,6,5,8] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [4,1,5,3,8,2,6,7] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [4,1,6,3,5,2,7,8] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,1,2,6,7] => [5,1,4,8,3,2,6,7] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [6,1,4,5,3,2,7,8] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,1,2,7,8] => [5,1,6,3,4,2,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [6,1,3,4,5,2,7,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [2,6,1,3,4,7,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [2,7,1,3,4,8,6,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [2,8,1,3,4,6,7,5] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [2,5,1,3,7,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [2,5,1,3,8,4,7,6] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [2,5,1,3,6,8,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => [2,5,1,3,7,6,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [2,6,1,3,8,5,4,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [2,6,1,3,7,5,4,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [2,7,1,3,5,6,4,8] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [2,4,1,7,3,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [2,4,1,8,3,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [2,4,1,6,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [2,4,1,6,3,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [2,4,1,5,8,3,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [2,4,1,5,6,3,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [2,4,1,6,5,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => [2,5,1,7,4,3,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => [2,5,1,6,4,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [2,6,1,5,4,3,7,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [2,6,1,4,5,3,7,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [2,3,7,1,4,5,8,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [2,3,8,1,4,5,7,6] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [2,3,6,1,4,8,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [2,3,6,1,4,7,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [2,3,5,1,8,4,6,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [2,3,6,1,5,4,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [2,3,4,8,1,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [2,3,4,7,1,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [2,3,4,6,1,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [2,3,5,4,1,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [2,4,8,3,1,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [2,4,5,3,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [2,5,4,3,1,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [2,5,3,4,1,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [3,7,2,1,4,5,8,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [3,8,2,1,4,5,7,6] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,1,4,5,7] => [3,6,2,1,4,8,5,7] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => [3,6,2,1,4,7,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [3,5,2,1,7,4,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,1,4,7,8] => [3,5,2,1,6,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,1,4,7,8] => [3,6,2,1,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [3,4,2,8,1,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,1,5,6,8] => [3,4,2,7,1,5,6,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [3,4,2,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [3,5,2,4,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,1,5,6,7] => [4,3,8,2,1,5,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,1,5,6,8] => [4,3,7,2,1,5,6,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [4,3,5,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [5,3,4,2,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [4,8,2,3,1,5,6,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,1,5,7,8] => [4,6,2,3,1,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [4,5,2,3,1,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [5,4,2,3,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [6,1,2,3,4,7,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [6,1,2,3,4,8,7,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [7,1,2,3,4,8,6,5] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [8,1,2,3,4,7,6,5] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [8,1,2,3,4,6,7,5] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [5,1,2,3,7,4,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [5,1,2,3,8,4,7,6] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [5,1,2,3,6,8,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [5,1,2,3,6,7,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [5,1,2,3,7,6,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [6,1,2,3,8,5,4,7] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [6,1,2,3,7,5,4,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [7,1,2,3,6,5,4,8] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [7,1,2,3,5,6,4,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [4,1,2,7,3,5,8,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [4,1,2,6,3,8,5,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [7,6,4,1,2,3,5,8] => [4,1,2,6,3,7,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [4,1,2,5,8,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,5,4,1,2,3,6,8] => [4,1,2,5,7,3,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [4,1,2,5,6,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,6,4,1,2,3,7,8] => [4,1,2,6,5,3,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [3,1,8,2,4,5,7,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [7,6,3,1,2,4,5,8] => [3,1,6,2,4,7,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [3,1,5,2,8,4,6,7] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [3,1,5,2,7,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,6,3,1,2,4,7,8] => [3,1,6,2,5,4,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [8,4,3,1,2,5,6,7] => [3,1,4,8,2,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [3,1,4,5,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [4,1,8,3,2,5,6,7] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [4,1,7,3,2,5,6,8] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,4,1,2,5,7,8] => [4,1,6,3,2,5,7,8] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [5,1,4,3,2,6,7,8] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [5,1,3,4,2,6,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [2,7,1,3,4,5,8,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [2,8,1,3,4,5,7,6] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [2,5,1,3,8,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1,3,4,7,8] => [2,5,1,3,6,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [2,6,1,3,5,4,7,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [2,4,1,8,3,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [2,4,1,6,3,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [2,4,1,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [2,5,1,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [2,3,8,1,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [2,3,7,1,4,5,6,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,4,5,7,8] => [2,3,6,1,4,5,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [2,3,5,1,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [2,4,3,1,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [3,8,2,1,4,5,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [3,5,2,1,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [3,4,2,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,8,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [8,1,2,3,4,5,7,6] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [6,1,2,3,4,8,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [6,1,2,3,4,7,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [7,1,2,3,4,6,5,8] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [5,1,2,3,8,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,2,3,4,7,8] => [5,1,2,3,6,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,6,1,2,3,4,7,8] => [6,1,2,3,5,4,7,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [4,1,2,8,3,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [4,1,2,7,3,5,6,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [4,1,2,5,3,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [5,1,2,4,3,6,7,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [3,1,8,2,4,5,6,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [3,1,7,2,4,5,6,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [3,1,6,2,4,5,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [3,1,4,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [4,1,3,2,5,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [2,8,1,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [2,7,1,3,4,5,6,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,3,4,5,7,8] => [2,6,1,3,4,5,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [2,5,1,3,4,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [2,4,1,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [10,1,2,3,4,5,6,7,8,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => [2,9,1,3,4,5,6,7,8] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [9,3,2,4,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => [2,10,1,3,4,5,6,7,8,9] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => [3,1,9,2,4,5,6,7,8] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => [9,4,3,2,5,6,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [10,3,2,4,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [12,1,2,3,4,5,6,7,8,9,10,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,1,3,4,5,6,7,8,9,10] => [2,11,1,3,4,5,6,7,8,9,10] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,1,4,5,6,7,8] => [2,3,9,1,4,5,6,7,8] => [[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => [9,3,4,2,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [12,2,1,3,4,5,6,7,8,9,10,11] => [2,12,1,3,4,5,6,7,8,9,10,11] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [10,4,1,2,3,5,6,7,8,9] => [4,1,2,10,3,5,6,7,8,9] => [[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,2,1,4,5,6,7,8,9] => [2,3,10,1,4,5,6,7,8,9] => [[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [9,6,1,2,3,4,5,7,8] => [6,1,2,3,4,9,5,7,8] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [9,4,3,1,2,5,6,7,8] => [3,1,4,9,2,5,6,7,8] => [[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,9,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [9,4,3,2,1,5,6,7,8] => [2,3,4,9,1,5,6,7,8] => [[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [9,1,2,3,4,5,6,8,7] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [9,8,2,3,4,5,6,7,1] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,7,8,9,1] => [9,3,4,5,2,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [9,1,3,4,5,6,7,8,2] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [10,4,3,2,1,5,6,7,8,9] => [2,3,4,10,1,5,6,7,8,9] => [[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,9,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => [8,9,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [2,9,3,4,5,6,7,8,1] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [10,1,2,3,4,5,6,7,9,8] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,1,3,4,5,6,7] => [2,8,1,3,4,5,6,9,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [10,9,2,3,4,5,6,7,8,1] => [[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,2,1] => [2,9,4,3,5,6,7,8,1] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [10,1,3,4,5,6,7,8,9,2] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,10,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [2,10,3,4,5,6,7,8,9,1] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[] => [] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [2,3,4,5,6,8,7,1,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1,9] => [2,3,4,8,5,6,7,1,9] => [[.,.],[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => [2,3,5,6,4,7,8,1,9] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => [2,3,6,5,7,4,8,1,9] => [[.,.],[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1,9] => [2,8,3,4,5,6,7,1,9] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [3,1,4,5,6,7,8,2,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1,7,9] => [2,3,4,5,6,8,1,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,1,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,4,3,2,1,8,9] => [2,3,4,5,7,6,1,8,9] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [7,5,4,3,2,1,6,8,9] => [2,3,4,5,7,1,6,8,9] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9] => [2,3,4,6,5,1,7,8,9] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,2,6,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2,1,3,5,7,9] => [2,4,1,6,3,8,5,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [7,6,4,2,1,3,5,8,9] => [2,4,1,6,3,7,5,8,9] => [[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1,5,7,8,9] => [2,3,4,6,1,5,7,8,9] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,5,3,2,1,6,7,8,9] => [2,3,5,4,1,6,7,8,9] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1,3,6,7,8,9] => [2,4,1,5,3,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1,4,6,7,8,9] => [2,3,5,1,4,6,7,8,9] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,1,5,6,7,8,9] => [3,4,2,1,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6,9] => [7,1,2,3,4,5,8,6,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => [8,1,2,3,4,5,7,6,9] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1,2,3,6,7,8,9] => [4,1,2,5,3,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => [3,1,4,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => [2,8,1,3,4,5,6,7,9] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [4,2,1,3,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [7,1,2,3,4,5,6,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => [2,3,4,5,6,7,9,8,1] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [2,3,4,5,6,9,8,7,1] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => [2,3,4,5,9,7,8,6,1] => [[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => [2,3,4,9,6,7,8,5,1] => [[.,.],[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => [2,3,9,5,6,7,8,4,1] => [[.,.],[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => [2,9,4,5,6,7,8,3,1] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [9,3,4,5,6,7,8,2,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,10,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [2,3,4,5,6,9,7,8,1] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => [2,3,4,5,6,7,10,9,8,1] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [2,3,4,5,6,10,8,9,7,1] => [[.,.],[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [2,3,4,5,10,7,8,9,6,1] => [[.,.],[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [2,3,4,10,6,7,8,9,5,1] => [[.,.],[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [2,3,10,5,6,7,8,9,4,1] => [[.,.],[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [2,10,4,5,6,7,8,9,3,1] => [[.,.],[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [10,3,4,5,6,7,8,9,2,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,1,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,11,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [2,3,4,5,6,7,10,8,9,1] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [7,6,8,9,5,4,3,2,1] => [2,3,4,5,9,7,6,8,1] => [[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [2,3,4,5,9,6,7,8,1] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [11,3,4,5,6,7,8,9,10,2,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,9,10,1,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [2,3,4,5,6,10,7,8,9,1] => [[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [2,3,4,9,6,5,7,8,1] => [[.,.],[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [2,3,4,9,5,6,7,8,1] => [[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [2,3,4,5,10,6,7,8,9,1] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => [2,3,9,5,4,6,7,8,1] => [[.,.],[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [2,3,9,4,5,6,7,8,1] => [[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [2,3,4,10,5,6,7,8,9,1] => [[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,2,1] => [2,3,4,5,6,8,9,7,1] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,9,6,7,5,4,3,2,1] => [2,3,4,5,7,9,6,8,1] => [[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,4,3,2,1] => [2,3,4,6,7,5,8,9,1] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,4,3,2,1] => [2,3,4,6,9,5,7,8,1] => [[.,.],[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,3,2,1] => [2,3,5,6,4,7,8,9,1] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,5,3,2,1] => [2,3,5,9,4,6,7,8,1] => [[.,.],[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,2,1] => [2,4,9,3,5,6,7,8,1] => [[.,.],[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,3,1] => [3,4,2,5,6,7,8,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [3,9,2,4,5,6,7,8,1] => [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,4,1] => [4,5,2,3,6,7,8,9,1] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => [3,1,4,5,6,7,8,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => [4,1,2,5,6,7,8,9,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,9,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [6,1,2,3,4,7,8,9,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,8,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [9,1,2,3,4,5,7,8,6] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [2,3,10,4,5,6,7,8,9,1] => [[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,3,1] => [3,5,2,7,4,9,6,10,8,1] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => [3,1,4,5,6,7,8,9,10,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => [4,1,2,5,6,7,8,9,10,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,9,10,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => [6,1,2,3,4,7,8,9,10,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [10,1,2,3,4,6,7,8,9,5] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,8,9,10,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,9,10,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,1,3] => [2,4,1,5,6,7,8,9,3] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,1,4] => [2,3,5,1,6,7,8,9,4] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,1,5] => [2,3,4,6,1,7,8,9,5] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,3,2,1,6] => [2,3,4,5,7,1,8,9,6] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,2,1,7] => [2,3,4,5,6,8,1,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,9,1,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,1,3] => [2,4,1,5,6,7,8,9,10,3] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,1,4] => [2,3,5,1,6,7,8,9,10,4] => [[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,1,5] => [2,3,4,6,1,7,8,9,10,5] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,4,3,2,1,6] => [2,3,4,5,7,1,8,9,10,6] => [[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,4,3,2,1,7] => [2,3,4,5,6,8,1,9,10,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,9,1,10,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,10,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,1,2] => [3,1,4,5,6,7,8,9,10,11,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,9,8,1,10] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9,10] => [2,4,3,1,5,6,7,8,9,10] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9,10] => [3,1,4,2,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [3,1,2,4,5,6,7,8,9,10,11] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,1,7,8] => [2,3,4,5,6,9,1,7,8] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [9,8,5,4,3,2,1,6,7] => [2,3,4,5,8,1,6,9,7] => [[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,1,3,4] => [2,5,1,3,6,7,8,9,4] => [[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [9,8,6,1,2,3,4,5,7] => [6,1,2,3,4,8,5,9,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [10,8,7,6,9,5,4,3,2,1] => [2,3,4,5,9,7,8,10,6,1] => [[.,.],[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,1,2,8] => [3,1,4,5,6,7,9,2,8] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,9,1] => [9,3,4,5,6,8,7,2,1] => [[[[.,.],.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,9,1,2,3,4,5,6] => [9,1,2,3,4,5,8,7,6] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => [2,3,4,6,7,5,8,9,1,10] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [2,3,4,5,6,7,8,1,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [6,5,7,4,8,3,9,2,10,1] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [7,6,8,4,3,5,9,2,10,1] => [10,9,4,8,3,7,6,5,2,1] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7,6,8,5,9,4,10,2,1,3] => [2,10,1,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [10,8,6,4,2,1,3,5,7,9] => [2,4,1,6,3,8,5,10,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [11,1,3,4,5,6,7,8,9,10,2] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,10,1,8,9] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,5,4,3,2,1,6,7,8] => [2,3,4,5,9,1,6,7,8] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [10,5,4,3,2,1,6,7,8,9] => [2,3,4,5,10,1,6,7,8,9] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [10,6,5,4,3,2,1,7,8,9] => [2,3,4,5,6,10,1,7,8,9] => [[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,2,1,3,4,5,6] => [2,7,1,3,4,5,8,9,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,9,2,1] => [2,9,4,5,6,7,8,10,3,1] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => [11,10,2,3,4,5,6,7,8,9,1] => [[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,11,1,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,8,1] => [8,3,4,5,6,7,9,2,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [9,1,2,3,4,5,6,8,7,10] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,2,1,3,4] => [2,5,1,3,6,7,8,9,10,4] => [[.,.],[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [11,10,1,2,3,4,5,6,7,8,9] => [10,1,2,3,4,5,6,7,8,11,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [9,8,4,1,2,3,5,6,7] => [4,1,2,8,3,5,6,9,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,1,2,9] => [3,1,4,5,6,7,8,10,2,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,8,2,1] => [2,8,4,5,6,7,9,3,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [10,9,2,1,3,4,5,6,7,8] => [2,9,1,3,4,5,6,7,10,8] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [5,4,2,1,3,6,7,8,9,10] => [2,4,1,5,3,6,7,8,9,10] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => [7,1,9,3,4,5,6,2,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,10,1] => [10,3,4,5,6,7,9,8,2,1] => [[[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [6,7,5,8,4,9,3,10,1,2] => [10,1,9,8,7,6,5,4,3,2] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,1,4] => [3,9,2,1,5,6,7,8,4] => [[[.,.],.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,1,2,7,8] => [3,1,4,5,6,9,2,7,8] => [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,3,1,2,4,6,8,10] => [3,1,5,2,7,4,9,6,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => [3,1,2,4,5,6,7,8,9,10,11,12] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [7,5,6,4,8,3,9,2,10,1] => [10,9,8,6,7,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [9,8,10,1,2,3,4,5,6,7] => [10,1,2,3,4,5,6,9,8,7] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1,10] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [6,7,5,8,4,9,3,10,2,11,1,12] => [11,10,9,8,7,6,5,4,3,2,1,12] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,2,1,3,9] => [2,4,1,5,6,7,8,10,3,9] => [[.,.],[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [12,10,11,8,9,6,7,4,5,2,3,1] => [3,5,2,7,4,9,6,11,8,12,10,1] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => [3,1,5,2,7,4,9,6,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [9,8,6,4,2,1,3,5,7] => [2,4,1,6,3,8,5,9,7] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [6,4,5,7,3,8,2,9,1] => [9,8,7,6,4,5,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [6,4,5,7,3,8,2,9,1,10] => [9,8,7,6,4,5,3,2,1,10] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [12,11,10,9,8,7,6,5,4,3,1,2] => [3,1,4,5,6,7,8,9,10,11,12,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [10,5,6,4,7,3,8,2,9,1] => [9,8,7,6,10,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [12,10,9,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,9,10,12,1,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [9,8,6,4,2,1,3,5,7,10] => [2,4,1,6,3,8,5,9,7,10] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
searching the database
Sorry, this map was not found in the database.