Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ 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 1691 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] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [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] => [[.,[[[[.,.],[.,.]],.],[.,.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [2,8,5,7,4,6,3,1] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.]
[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] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [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] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [2,6,8,3,4,5,7,1] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,7,2,1] => [2,7,6,3,4,8,5,1] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[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] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [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] => [[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [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] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [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] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [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] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [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] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [5,4,2,8,3,6,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,3,6,1] => [6,4,2,5,8,3,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[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] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [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] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => [7,3,5,8,4,2,6,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[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] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [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] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [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] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [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] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [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] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [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] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [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] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [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] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,1,3] => [2,6,1,8,4,5,7,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [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] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [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] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [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] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [6,3,4,5,8,2,1,7] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [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] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,1,6] => [5,4,2,8,3,1,7,6] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [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] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [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] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [5,3,6,2,4,8,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [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] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,1,2,8] => [3,1,4,7,5,6,2,8] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [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] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [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] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [2,5,1,6,4,7,3,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,1,3,8] => [2,7,1,5,6,4,3,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [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] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [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] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [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] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [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] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [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] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [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] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [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] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [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] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [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] => [[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [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] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [4,2,1,3,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[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
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
searching the database
Sorry, this map was not found in the database.