Identifier
Mp00024:
Dyck paths
—to 321-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] => [2,1,3] => [2,1,3] => [[.,.],[.,.]]
[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] => [1,3,2] => [1,3,2] => [.,[[.,.],.]]
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [2,1,4,3] => [[.,.],[[.,.],.]]
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [4,2,1,3] => [[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [4,2,3,1] => [[[.,.],[.,.]],.]
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [3,4,1,2] => [[.,[.,.]],[.,.]]
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [4,1,3,2] => [[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [3,1,2,4] => [[.,.],[.,[.,.]]]
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [1,4,3,2] => [.,[[[.,.],.],.]]
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [4,1,2,3] => [[.,.],[.,[.,.]]]
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,2,3] => [.,[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
[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] => [2,1,4,3,5] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => [4,2,1,3,5] => [[[.,.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [5,2,1,4,3] => [[[.,.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [2,1,5,3,4] => [[.,.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => [5,2,1,3,4] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [5,2,3,1,4] => [[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
[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] => [3,1,4,2,5] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => [4,1,3,2,5] => [[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => [3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]]
[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] => [3,1,5,2,4] => [3,5,1,2,4] => [[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => [5,1,3,2,4] => [[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => [3,1,2,5,4] => [[.,.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,5,3,2,4] => [.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => [4,5,2,1,3] => [[[.,[.,.]],.],[.,.]]
[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] => [4,1,2,5,3] => [4,1,5,2,3] => [[.,.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
[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] => [1,5,2,3,4] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
[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] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [4,2,1,3,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [2,1,6,4,3,5] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [4,2,6,1,3,5] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [6,2,1,4,3,5] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [5,2,1,4,3,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => [4,2,6,1,5,3] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => [5,2,6,4,1,3] => [[[.,.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => [6,2,1,4,5,3] => [[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [5,2,1,6,3,4] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [2,1,6,3,5,4] => [[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [5,2,6,3,1,4] => [[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [2,1,5,3,4,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [5,2,3,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => [5,2,3,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => [6,2,3,1,5,4] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [2,1,3,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => [3,2,1,6,4,5] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => [6,2,3,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => [[[.,.],[.,[.,.]]],[.,.]]
>>> Load all 1914 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[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] => [3,1,4,2,6,5] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [4,1,3,2,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [3,6,1,4,2,5] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [4,6,3,1,2,5] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [3,5,1,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [5,1,3,4,2,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => [3,6,1,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => [4,6,3,1,5,2] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]]
[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] => [3,1,5,2,6,4] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [5,1,3,6,2,4] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [3,6,1,2,5,4] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [5,6,3,2,1,4] => [[[[.,[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => [3,5,1,2,4,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => [3,1,2,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => [3,1,2,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => [1,6,3,2,5,4] => [.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => [3,6,1,2,4,5] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => [3,1,2,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => [1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => [3,1,2,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => [1,6,3,4,2,5] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [5,1,6,4,2,3] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [4,6,2,1,5,3] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [5,6,2,4,1,3] => [[[.,[.,.]],[.,.]],[.,.]]
[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] => [4,1,5,2,3,6] => [4,5,2,1,3,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => [4,1,5,2,3,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => [4,1,6,2,5,3] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => [1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => [1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => [1,6,2,4,5,3] => [.,[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => [4,6,2,1,3,5] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => [4,1,6,2,3,5] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => [1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => [5,6,2,3,1,4] => [[[.,[.,.]],[.,.]],[.,.]]
[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] => [5,1,2,6,3,4] => [5,1,6,3,2,4] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => [1,5,6,3,2,4] => [.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => [5,1,2,6,3,4] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
[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] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
[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] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7] => [4,2,1,3,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7] => [2,1,6,4,3,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7] => [4,2,6,1,3,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7] => [6,2,1,4,3,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,7,5] => [4,2,1,3,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,1,6,4,7,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5] => [4,2,6,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5] => [6,2,1,4,7,3,5] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,7,3,5] => [2,1,7,4,3,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,7,3,5] => [4,2,7,1,3,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,7,3,5] => [6,2,7,4,3,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5] => [7,2,1,4,3,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,7,5,6] => [4,2,1,3,7,5,6] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6] => [2,1,7,4,3,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,7,3,5,6] => [4,2,7,1,3,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,7,1,3,5,6] => [7,2,1,4,3,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,3,5,7,6] => [4,2,1,3,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6] => [4,2,5,1,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6] => [5,2,1,4,3,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,3,6] => [2,1,7,4,5,3,6] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,6] => [4,2,7,1,5,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6] => [5,2,7,4,1,3,6] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [7,2,1,4,5,3,6] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7] => [4,2,1,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7] => [4,2,5,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7] => [5,2,1,4,3,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7] => [4,2,6,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7] => [5,2,6,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7] => [6,2,1,4,5,3,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3] => [4,2,7,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3] => [5,2,7,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3] => [6,2,7,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3] => [7,2,1,4,5,6,3] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7] => [5,2,1,6,3,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7] => [2,1,6,3,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7] => [5,2,6,3,1,4,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,7] => [6,2,1,3,5,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,1,5,7,3,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,7,4] => [5,2,1,7,3,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,1,6,7,5,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4] => [5,2,6,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4] => [6,2,1,7,5,3,4] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4] => [2,1,7,3,5,6,4] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4] => [5,2,7,3,1,6,4] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4] => [6,2,7,3,5,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,5,6,7,1,3,4] => [7,2,1,3,5,6,4] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6] => [5,2,1,7,3,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6] => [2,1,7,3,5,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,5,1,7,3,4,6] => [5,2,7,3,1,4,6] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,5,7,1,3,4,6] => [7,2,1,3,5,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => [2,1,5,3,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [5,2,1,3,4,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6] => [5,2,3,1,4,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6] => [2,1,3,7,5,4,6] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6] => [3,2,1,7,5,4,6] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,1,7,4,6] => [5,2,3,7,1,4,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [7,2,3,1,5,4,6] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [2,1,5,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7] => [5,2,1,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7] => [5,2,3,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7] => [5,2,3,6,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7] => [6,2,3,1,5,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4] => [5,2,3,7,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4] => [6,2,3,7,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4] => [7,2,3,1,5,6,4] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5] => [2,1,6,7,4,3,5] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,7,4,5] => [6,2,1,7,4,3,5] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,6,7,3,4,5] => [2,1,7,3,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5] => [6,2,7,3,4,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5] => [7,2,1,3,4,6,5] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => [2,1,6,3,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5] => [6,2,1,3,7,4,5] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5] => [3,2,1,6,7,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5] => [6,2,3,1,7,4,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,6,7,4,5] => [2,1,3,7,4,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5] => [3,2,1,7,4,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,7,4,5] => [6,2,3,7,4,1,5] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5] => [7,2,3,1,4,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => [2,1,6,3,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7] => [6,2,1,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7] => [2,1,3,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7] => [3,2,1,6,4,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7] => [6,2,3,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5] => [6,2,3,4,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5] => [7,2,3,4,1,6,5] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => [2,1,7,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6] => [7,2,1,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => [2,1,3,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,7,4,5,6] => [3,2,1,7,4,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6] => [7,2,3,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => [2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6] => [3,2,1,4,7,5,6] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6] => [4,2,3,1,7,5,6] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[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] => [3,1,4,2,6,5,7] => [3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7] => [4,1,3,2,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7] => [3,6,1,4,2,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,7] => [4,6,3,1,2,5,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,7] => [6,1,3,4,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [3,4,1,2,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5] => [4,1,3,2,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [3,6,1,4,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5] => [4,6,3,1,7,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5] => [6,1,3,4,7,2,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,7,2,5] => [3,7,1,4,2,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5] => [4,7,3,1,2,6,5] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,4,6,1,7,2,5] => [6,7,3,4,2,1,5] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5] => [7,1,3,4,2,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6] => [3,4,1,2,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6] => [4,1,3,2,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6] => [3,7,1,4,2,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,1,7,2,5,6] => [4,7,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,4,7,1,2,5,6] => [7,1,3,4,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6] => [3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6] => [4,1,3,2,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6] => [3,5,1,4,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6] => [4,5,3,1,2,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,7,6] => [5,1,3,4,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6] => [3,7,1,4,5,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6] => [4,7,3,1,5,2,6] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6] => [5,7,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [7,1,3,4,5,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7] => [3,5,1,4,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7] => [4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7] => [5,1,3,4,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7] => [3,6,1,4,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7] => [4,6,3,1,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7] => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7] => [6,1,3,4,5,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2] => [3,7,1,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2] => [4,7,3,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2] => [5,7,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[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] => [3,1,5,2,6,4,7] => [3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,7] => [5,1,3,6,2,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7] => [3,6,1,2,5,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7] => [5,6,3,2,1,4,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7] => [6,1,3,2,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [3,5,1,7,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4] => [5,1,3,7,2,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [3,6,1,7,5,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4] => [5,6,3,7,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4] => [6,1,3,7,5,2,4] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4] => [3,7,1,2,5,6,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4] => [5,7,3,2,1,6,4] => [[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4] => [6,7,3,2,5,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4] => [7,1,3,2,5,6,4] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => [3,5,1,7,2,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6] => [5,1,3,7,2,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6] => [3,7,1,2,5,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6] => [5,7,3,2,1,4,6] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6] => [7,1,3,2,5,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6] => [3,5,1,2,4,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [5,1,3,2,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6] => [3,1,2,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => [1,5,3,2,4,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6] => [3,1,2,7,5,4,6] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => [1,3,2,7,5,4,6] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => [1,5,3,7,2,4,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [1,7,3,2,5,4,6] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [3,5,1,2,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7] => [5,1,3,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,7] => [3,1,2,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => [1,5,3,2,4,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7] => [3,1,2,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => [1,5,3,6,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => [1,6,3,2,5,4,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4] => [3,1,2,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => [1,5,3,7,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => [1,6,3,7,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => [1,7,3,2,5,6,4] => [.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => [3,6,1,7,4,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,7,4,5] => [6,1,3,7,4,2,5] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5] => [3,7,1,2,4,6,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,6,1,7,2,4,5] => [6,7,3,2,4,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5] => [7,1,3,2,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => [3,6,1,2,7,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5] => [6,1,3,2,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [3,1,2,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => [1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => [1,6,3,2,7,4,5] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,7,4,5] => [3,1,2,7,4,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => [1,3,2,7,4,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => [1,6,3,7,4,2,5] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => [1,7,3,2,4,6,5] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7] => [3,6,1,2,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7] => [6,1,3,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,7] => [3,1,2,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => [1,3,2,6,4,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => [1,6,3,2,4,5,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,7] => [3,1,2,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => [1,6,3,4,2,5,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5] => [3,1,2,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => [1,6,3,4,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => [1,7,3,4,2,6,5] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => [3,7,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6] => [7,1,3,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6] => [3,1,2,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => [1,3,2,7,4,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => [1,7,3,2,4,5,6] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6] => [3,1,2,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => [1,4,3,2,7,5,6] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [1,7,3,4,2,5,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [3,1,2,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => [1,7,3,4,5,2,6] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,7] => [5,1,6,4,2,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7] => [4,6,2,1,5,3,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7] => [5,6,2,4,1,3,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [4,5,7,1,2,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3] => [5,1,7,4,2,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [4,6,7,1,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3] => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3] => [6,1,7,4,5,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3] => [4,7,2,1,5,6,3] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3] => [5,7,2,4,1,6,3] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3] => [6,7,2,4,5,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[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] => [4,1,5,2,7,3,6] => [4,5,7,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6] => [5,1,7,4,2,3,6] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6] => [4,7,2,1,5,3,6] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6] => [5,7,2,4,1,3,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,5,7,1,2,3,6] => [7,1,2,4,5,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6] => [4,5,2,1,3,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [5,1,2,4,3,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6] => [4,1,5,2,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => [1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => [1,5,2,4,3,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [4,1,7,2,5,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => [1,4,7,2,5,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => [1,5,7,4,2,3,6] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [1,7,2,4,5,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [4,5,2,1,3,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7] => [4,1,5,2,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => [1,5,2,4,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7] => [4,1,6,2,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => [1,4,6,2,5,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => [1,5,6,4,2,3,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => [1,6,2,4,5,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3] => [4,1,7,2,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => [1,4,7,2,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => [1,5,7,4,2,6,3] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => [1,6,7,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => [1,7,2,4,5,6,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => [4,6,7,1,3,2,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5] => [6,1,7,4,3,2,5] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5] => [4,7,2,1,3,6,5] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5] => [6,7,2,4,3,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5] => [7,1,2,4,3,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => [4,6,2,1,7,3,5] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5] => [6,1,2,4,7,3,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [4,1,6,2,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => [1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => [1,6,2,4,7,3,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5] => [4,1,7,2,3,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => [1,4,7,2,3,6,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => [1,6,7,4,3,2,5] => [.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => [1,7,2,4,3,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => [4,6,2,1,3,5,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7] => [6,1,2,4,3,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7] => [4,1,6,2,3,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => [1,6,2,4,3,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7] => [4,1,2,3,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => [1,4,2,3,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => [1,2,6,4,3,5,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5] => [4,1,2,3,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => [1,4,2,3,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => [1,2,6,4,7,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => [1,2,7,4,3,6,5] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => [4,7,2,1,3,5,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6] => [7,1,2,4,3,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => [4,1,7,2,3,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => [1,7,2,4,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6] => [4,1,2,3,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,4,2,3,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [1,2,7,4,3,5,6] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [4,1,2,3,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => [1,4,2,3,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => [1,2,7,4,5,3,6] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4] => [5,6,7,3,1,2,4] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4] => [6,1,7,3,5,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,1,6,7,2,3,4] => [5,7,2,3,1,6,4] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4] => [6,7,2,3,5,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[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] => [5,1,6,2,3,7,4] => [5,6,2,7,1,3,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,7,4] => [6,1,2,7,5,3,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [5,1,6,7,2,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4] => [1,6,2,7,5,3,4] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4] => [5,1,7,3,2,6,4] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4] => [1,5,7,3,2,6,4] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => [1,6,7,3,5,2,4] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => [1,7,2,3,5,6,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => [5,6,2,3,1,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7] => [5,1,6,3,2,4,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7] => [1,5,6,3,2,4,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7] => [1,6,2,3,5,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7] => [5,1,2,6,3,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7] => [1,5,2,6,3,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => [1,2,6,3,5,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4] => [5,1,2,7,3,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4] => [1,5,2,7,3,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => [1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => [1,2,6,7,5,3,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => [1,2,7,3,5,6,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6] => [5,7,2,3,1,4,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6] => [7,1,2,3,5,4,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6] => [5,1,7,3,2,4,6] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => [1,5,7,3,2,4,6] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => [1,7,2,3,5,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6] => [5,1,2,7,3,4,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,5,2,7,3,4,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [1,2,7,3,5,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [5,1,2,3,4,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => [1,5,2,3,4,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => [1,2,5,3,4,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => [1,2,3,7,5,4,6] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5] => [6,7,2,3,4,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[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] => [6,1,2,7,3,4,5] => [6,1,7,3,4,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => [1,6,7,3,4,2,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => [1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5] => [6,1,2,7,4,3,5] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,6,2,7,4,3,5] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => [1,2,6,7,4,3,5] => [.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [6,1,2,3,7,4,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [1,6,2,3,7,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => [1,2,6,3,7,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[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] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
[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] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [4,2,1,3,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,8,7] => [2,1,6,4,3,5,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7] => [6,2,1,4,3,5,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,8,5,7] => [2,1,4,3,8,6,5,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7] => [4,2,1,3,8,6,5,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7] => [4,2,6,1,8,3,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,8,3,5,7] => [2,1,8,4,3,6,5,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7] => [4,2,8,1,3,6,5,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [6,2,8,4,3,1,5,7] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [8,2,1,4,3,6,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7,8] => [4,2,1,3,6,5,7,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7,8] => [2,1,6,4,3,5,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7,8] => [4,2,6,1,3,5,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7,8] => [6,2,1,4,3,5,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8] => [4,2,6,1,7,3,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [7,2,1,4,3,6,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,6,3,7,8,5] => [2,1,6,4,8,3,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => [4,2,6,1,8,3,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,3,8,5] => [2,1,7,4,8,6,3,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => [4,2,7,1,8,6,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,6,1,7,3,8,5] => [6,2,7,4,8,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,6,1,7,8,3,5] => [6,2,8,4,3,1,7,5] => [[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,6,7,1,8,3,5] => [7,2,8,4,3,6,1,5] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,8,6] => [2,1,4,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,3,7,5,8,6] => [4,2,1,3,7,8,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,7,3,5,8,6] => [2,1,7,4,3,8,5,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,7,3,5,8,6] => [4,2,7,1,3,8,5,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,5,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,7,8,5,6] => [4,2,1,3,8,5,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,7,3,8,5,6] => [2,1,7,4,8,5,3,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,4,1,7,3,8,5,6] => [4,2,7,1,8,5,3,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,7,8,3,5,6] => [2,1,8,4,3,5,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,8,3,5,6] => [4,2,8,1,3,5,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,4,7,1,8,3,5,6] => [7,2,8,4,3,5,1,6] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [8,2,1,4,3,5,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,7,1,3,5,6,8] => [7,2,1,4,3,5,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,8] => [4,2,5,1,3,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6,8] => [5,2,7,4,1,3,6,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,7,8,6] => [4,2,1,3,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,7,8,6] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,7,8,6] => [4,2,5,1,3,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,7,8,6] => [5,2,1,4,3,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,5,7,3,8,6] => [2,1,7,4,5,8,3,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,1,5,7,3,8,6] => [4,2,7,1,5,8,3,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,1,7,3,8,6] => [5,2,7,4,1,8,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,8,6] => [7,2,1,4,5,8,3,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,4,5,7,8,3,6] => [2,1,8,4,5,3,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,7,8,3,6] => [5,2,8,4,1,3,7,6] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,5,7,1,8,3,6] => [7,2,8,4,5,3,1,6] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,8,5,6,7] => [2,1,4,3,8,5,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,8,5,6,7] => [4,2,1,3,8,5,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,8,3,5,6,7] => [4,2,8,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,4,3,5,8,6,7] => [2,1,4,3,5,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,3,5,8,6,7] => [4,2,1,3,5,8,6,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,3,8,6,7] => [4,2,5,1,3,8,6,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,4,5,8,3,6,7] => [2,1,8,4,5,3,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,5,8,3,6,7] => [4,2,8,1,5,3,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [5,2,8,4,1,3,6,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,8,7] => [4,2,5,1,3,6,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,8,7] => [4,2,6,1,5,3,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,8,7] => [5,2,6,4,1,3,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,4,1,5,6,8,3,7] => [4,2,8,1,5,6,3,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,4,5,1,6,8,3,7] => [5,2,8,4,1,6,3,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,4,5,6,1,8,3,7] => [6,2,8,4,5,1,3,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8] => [4,2,1,3,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7,8] => [4,2,5,1,3,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7,8] => [5,2,1,4,3,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7,8] => [4,2,6,1,5,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7,8] => [5,2,6,4,1,3,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [6,2,1,4,5,3,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3,8] => [4,2,7,1,5,6,3,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3,8] => [5,2,7,4,1,6,3,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3,8] => [6,2,7,4,5,1,3,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3,8] => [7,2,1,4,5,6,3,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,5,6,7,8,3] => [4,2,8,1,5,6,7,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,4,5,1,6,7,8,3] => [5,2,8,4,1,6,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,4,5,6,1,7,8,3] => [6,2,8,4,5,1,7,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,4,5,6,7,1,8,3] => [7,2,8,4,5,6,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,3] => [8,2,1,4,5,6,7,3] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,8,7] => [2,1,5,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => [5,2,1,6,3,4,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,1,6,3,5,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,8,4,7] => [2,1,5,8,3,6,4,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,8,4,7] => [5,2,1,8,3,6,4,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,8,4,7] => [5,2,6,8,1,3,4,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,5,6,1,8,3,4,7] => [6,2,8,3,5,1,4,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4,8] => [5,2,6,7,1,3,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4,8] => [5,2,7,3,1,6,4,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4,8] => [6,2,7,3,5,1,4,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [2,1,5,8,3,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,5,1,3,6,7,8,4] => [5,2,1,8,3,6,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,8,4] => [2,1,6,8,5,3,7,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => [5,2,6,8,1,3,7,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5,6,1,3,7,8,4] => [6,2,1,8,5,3,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,7,3,8,4] => [2,1,7,8,5,6,3,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => [5,2,7,8,1,6,3,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,7,3,8,4] => [6,2,7,8,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,5,6,7,8,3,4] => [2,1,8,3,5,6,7,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5,1,6,7,8,3,4] => [5,2,8,3,1,6,7,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5,6,1,7,8,3,4] => [6,2,8,3,5,1,7,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5,6,7,1,8,3,4] => [7,2,8,3,5,6,1,4] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5,6,7,8,1,3,4] => [8,2,1,3,5,6,7,4] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,8,6] => [2,1,5,7,3,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [5,2,1,7,3,8,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,7,3,4,8,6] => [2,1,7,3,5,8,4,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,7,3,4,8,6] => [5,2,7,3,1,8,4,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,5,7,1,3,4,8,6] => [7,2,1,3,5,8,4,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,8,4,6] => [5,2,1,8,3,4,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,7,3,8,4,6] => [2,1,7,8,5,4,3,6] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,7,3,8,4,6] => [5,2,7,8,1,4,3,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,7,8,3,4,6] => [2,1,8,3,5,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6,8] => [2,1,5,7,3,4,6,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6,8] => [5,2,1,7,3,4,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6,8] => [3,2,1,7,5,4,6,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,7,8,6] => [5,2,1,3,4,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,7,4,8,6] => [2,1,3,7,5,8,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,7,4,8,6] => [5,2,3,7,1,8,4,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,7,8,4,6] => [2,1,3,8,5,4,7,6] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,7,8,4,6] => [3,2,1,8,5,4,7,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,7,1,8,4,6] => [7,2,3,8,5,4,1,6] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,7,8,1,4,6] => [8,2,3,1,5,4,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,8,4,6,7] => [2,1,5,8,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,5,1,3,8,4,6,7] => [5,2,1,8,3,4,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,3,5,1,4,8,6,7] => [5,2,3,1,4,8,6,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,5,8,4,6,7] => [2,1,3,8,5,4,6,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,5,8,4,6,7] => [3,2,1,8,5,4,6,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [5,2,3,8,1,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,8,7] => [2,1,5,3,4,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,8,7] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,8,7] => [5,2,3,6,1,4,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,8,7] => [6,2,3,1,5,4,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,5,6,8,4,7] => [3,2,1,8,5,6,4,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,6,8,1,4,7] => [8,2,3,1,5,6,4,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [2,1,5,3,4,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7,8] => [5,2,1,3,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7,8] => [5,2,3,1,4,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7,8] => [3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [6,2,3,1,5,4,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4,8] => [3,2,1,7,5,6,4,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4,8] => [5,2,3,7,1,6,4,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4,8] => [6,2,3,7,5,1,4,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4,8] => [7,2,3,1,5,6,4,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,5,1,6,7,8,4] => [5,2,3,8,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,5,6,1,7,8,4] => [6,2,3,8,5,1,7,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,5,6,7,1,8,4] => [7,2,3,8,5,6,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,6,7,8,1,4] => [8,2,3,1,5,6,7,4] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5] => [2,1,6,7,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,6,7,3,4,8,5] => [2,1,7,3,8,6,4,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,6,1,7,3,4,8,5] => [6,2,7,3,8,1,4,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [7,2,1,3,8,6,4,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,6,1,3,7,8,4,5] => [6,2,1,8,4,3,7,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,1,6,7,3,8,4,5] => [2,1,7,8,4,6,3,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,6,1,7,3,8,4,5] => [6,2,7,8,4,1,3,5] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,6,7,8,3,4,5] => [2,1,8,3,4,6,7,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5,8] => [3,2,1,6,7,4,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5,8] => [3,2,1,7,4,6,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5,8] => [7,2,3,1,4,6,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [2,1,6,3,8,4,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,7,8,5] => [3,2,1,6,8,4,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [6,2,3,1,8,4,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,4,8,5] => [2,1,3,7,8,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,4,8,5] => [3,2,1,7,8,6,4,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,3,6,1,7,4,8,5] => [6,2,3,7,8,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,3,6,7,1,4,8,5] => [7,2,3,1,8,6,4,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,3,6,7,8,4,5] => [2,1,3,8,4,6,7,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,3,1,6,7,8,4,5] => [3,2,1,8,4,6,7,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => [6,2,3,8,4,1,7,5] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,8,4,5] => [7,2,3,8,4,6,1,5] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,8,4,5,7] => [2,1,6,8,4,3,5,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,6,1,8,3,4,5,7] => [6,2,8,3,4,1,5,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,6,8,1,3,4,5,7] => [8,2,1,3,4,6,5,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,8,5,7] => [2,1,6,3,8,4,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,8,5,7] => [6,2,1,3,8,4,5,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,8,5,7] => [3,2,1,6,8,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,8,4,5,7] => [3,2,1,8,4,6,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => [6,2,3,8,4,1,5,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,3,6,8,1,4,5,7] => [8,2,3,1,4,6,5,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,8,7] => [2,1,6,3,4,5,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,8,7] => [2,1,3,6,4,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,8,7] => [6,2,3,1,4,5,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,8,5,7] => [2,1,3,4,8,6,5,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,8,5,7] => [6,2,3,4,8,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7,8] => [2,1,3,6,4,5,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7,8] => [3,2,1,6,4,5,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7,8] => [6,2,3,1,4,5,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7,8] => [4,2,3,1,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5,8] => [4,2,3,1,7,6,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5,8] => [7,2,3,4,1,6,5,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,3,4,6,1,7,8,5] => [6,2,3,4,8,1,7,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,3,4,6,7,1,8,5] => [7,2,3,4,8,6,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,7,8,1,5] => [8,2,3,4,1,6,7,5] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,7,1,3,8,4,5,6] => [7,2,1,8,4,5,3,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [7,2,8,3,4,5,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,7,8,1,3,4,5,6] => [8,2,1,3,4,5,7,6] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,1,7,3,4,8,5,6] => [2,1,7,3,8,5,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,7,1,3,4,8,5,6] => [7,2,1,3,8,5,4,6] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,7,4,8,5,6] => [3,2,1,7,8,5,4,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,7,8,4,5,6] => [2,1,3,8,4,5,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,1,7,8,4,5,6] => [3,2,1,8,4,5,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [8,2,3,1,4,5,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,7,3,4,5,8,6] => [2,1,7,3,4,8,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [7,2,1,3,4,8,5,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,3,7,4,5,8,6] => [2,1,3,7,4,8,5,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,7,4,5,8,6] => [3,2,1,7,4,8,5,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,3,4,7,5,8,6] => [2,1,3,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,4,1,7,5,8,6] => [4,2,3,1,7,8,5,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,8,6] => [7,2,3,4,1,8,5,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,3,4,7,8,5,6] => [2,1,3,4,8,5,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,1,4,7,8,5,6] => [3,2,1,4,8,5,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,4,1,7,8,5,6] => [4,2,3,1,8,5,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,4,7,1,8,5,6] => [7,2,3,4,8,5,1,6] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,4,7,8,1,5,6] => [8,2,3,4,1,5,7,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6,8] => [2,1,7,3,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6,8] => [7,2,1,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,7,4,5,6,8] => [3,2,1,7,4,5,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6,8] => [7,2,3,1,4,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => [2,1,3,4,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6,8] => [7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,7,8,6] => [4,2,3,1,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,4,5,7,1,8,6] => [7,2,3,4,5,8,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,5,7,8,1,6] => [8,2,3,4,5,1,7,6] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7] => [2,1,8,3,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7] => [8,2,1,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,8,4,5,6,7] => [2,1,3,8,4,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,1,8,4,5,6,7] => [3,2,1,8,4,5,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,8,1,4,5,6,7] => [8,2,3,1,4,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,3,4,8,5,6,7] => [2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,1,4,8,5,6,7] => [3,2,1,4,8,5,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [4,2,3,1,8,5,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,3,4,5,8,6,7] => [2,1,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,3,4,1,5,8,6,7] => [4,2,3,1,5,8,6,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,3,4,5,1,8,6,7] => [5,2,3,4,1,8,6,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,3,4,5,8,1,6,7] => [8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,7] => [8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[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] => [3,1,4,2,6,5,8,7] => [3,4,1,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [4,1,3,2,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7] => [3,6,1,4,2,5,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,8,7] => [6,1,3,4,2,5,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,8,5,7] => [3,4,1,2,8,6,5,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,8,5,7] => [4,1,3,2,8,6,5,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,8,2,5,7] => [3,8,1,4,2,6,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,8,2,5,7] => [4,8,3,1,2,6,5,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [8,1,3,4,2,6,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7,8] => [3,4,1,2,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [3,4,1,6,2,5,7,8] => [4,6,3,1,2,5,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [3,4,6,1,2,5,7,8] => [6,1,3,4,2,5,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5,8] => [3,4,1,2,7,6,5,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5,8] => [3,6,1,4,7,2,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5,8] => [4,6,3,1,7,2,5,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,6,7,2,5,8] => [3,7,1,4,2,6,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [3,4,6,1,7,2,5,8] => [6,7,3,4,2,1,5,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [3,4,1,2,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,7,8,5] => [4,1,3,2,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,6,2,7,8,5] => [4,6,3,1,8,2,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,6,7,2,8,5] => [4,7,3,1,8,6,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [3,4,6,1,7,2,8,5] => [6,7,3,4,8,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,6,7,8,2,5] => [4,8,3,1,2,6,7,5] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [3,4,6,1,7,8,2,5] => [6,8,3,4,2,1,7,5] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,4,6,7,1,8,2,5] => [7,8,3,4,2,6,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,6,7,8,1,2,5] => [8,1,3,4,2,6,7,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,8,6] => [3,4,1,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,7,5,8,6] => [4,1,3,2,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,7,8,5,6] => [3,4,1,2,8,5,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6] => [4,1,3,2,8,5,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,7,2,8,5,6] => [4,7,3,1,8,5,2,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [7,8,3,4,2,5,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6,8] => [3,4,1,2,7,5,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6,8] => [3,4,1,2,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => [4,1,3,2,5,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6,8] => [3,5,1,4,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,7,6,8] => [5,1,3,4,2,7,6,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6,8] => [3,7,1,4,5,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => [3,4,1,2,5,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,7,8,6] => [3,5,1,4,2,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,7,8,6] => [4,5,3,1,2,8,7,6] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,5,7,8,2,6] => [4,8,3,1,5,2,7,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,7,1,8,2,6] => [7,8,3,4,5,2,1,6] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,2,8,5,6,7] => [3,4,1,2,8,5,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,8,5,6,7] => [4,1,3,2,8,5,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,8,6,7] => [3,4,1,2,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,2,8,6,7] => [4,5,3,1,2,8,6,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,4,5,1,2,8,6,7] => [5,1,3,4,2,8,6,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,4,5,1,8,2,6,7] => [5,8,3,4,1,2,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [8,1,3,4,5,2,6,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,8,7] => [3,4,1,2,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,8,7] => [4,5,3,1,2,6,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,8,7] => [5,1,3,4,2,6,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,8,7] => [3,6,1,4,5,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,8,7] => [4,6,3,1,5,2,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,8,7] => [5,6,3,4,1,2,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [3,8,1,4,5,6,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8] => [4,1,3,2,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7,8] => [3,5,1,4,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7,8] => [5,1,3,4,2,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7,8] => [3,6,1,4,5,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7,8] => [4,6,3,1,5,2,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7,8] => [5,6,3,4,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [6,1,3,4,5,2,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2,8] => [3,7,1,4,5,6,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2,8] => [4,7,3,1,5,6,2,8] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2,8] => [5,7,3,4,1,6,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2,8] => [6,7,3,4,5,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [7,1,3,4,5,6,2,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2] => [3,8,1,4,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,5,6,7,8,2] => [4,8,3,1,5,6,7,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,4,5,1,6,7,8,2] => [5,8,3,4,1,6,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,4,5,6,1,7,8,2] => [6,8,3,4,5,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,2] => [7,8,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[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] => [3,1,5,2,6,4,8,7] => [3,5,1,6,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => [5,1,3,6,2,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,8,7] => [5,6,3,2,1,4,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,8,7] => [6,1,3,2,5,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,8,4,7] => [3,5,1,8,2,6,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,8,4,7] => [5,1,3,8,2,6,4,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,8,4,7] => [3,6,1,8,5,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,8,4,7] => [6,1,3,8,5,2,4,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,5,6,8,2,4,7] => [3,8,1,2,5,6,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,5,1,6,8,2,4,7] => [5,8,3,2,1,6,4,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [6,8,3,2,5,1,4,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [8,1,3,2,5,6,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7,8] => [3,5,1,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7,8] => [5,6,3,2,1,4,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [5,1,3,7,2,6,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4,8] => [5,6,3,7,1,2,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4,8] => [6,1,3,7,5,2,4,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4,8] => [3,7,1,2,5,6,4,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4,8] => [5,7,3,2,1,6,4,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [7,1,3,2,5,6,4,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,5,6,2,7,8,4] => [3,6,1,8,5,2,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5,1,6,2,7,8,4] => [5,6,3,8,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5,6,1,2,7,8,4] => [6,1,3,8,5,2,7,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,5,6,7,2,8,4] => [3,7,1,8,5,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5,1,6,7,2,8,4] => [5,7,3,8,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5,6,1,7,2,8,4] => [6,7,3,8,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,5,6,7,8,2,4] => [3,8,1,2,5,6,7,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5,1,6,7,8,2,4] => [5,8,3,2,1,6,7,4] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => [6,8,3,2,5,1,7,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5,6,7,1,8,2,4] => [7,8,3,2,5,6,1,4] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5,6,7,8,1,2,4] => [8,1,3,2,5,6,7,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6] => [3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,7,8,4,6] => [3,5,1,8,2,4,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,7,8,4,6] => [5,1,3,8,2,4,7,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,7,2,8,4,6] => [5,7,3,8,1,4,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,7,8,2,4,6] => [5,8,3,2,1,4,7,6] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [8,1,3,2,5,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,8] => [3,5,1,7,2,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6,8] => [5,1,3,7,2,4,6,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6,8] => [3,7,1,2,5,4,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6,8] => [5,7,3,2,1,4,6,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6,8] => [7,1,3,2,5,4,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,8] => [3,5,1,2,4,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [5,1,3,2,4,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [3,1,2,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,8] => [1,5,3,2,4,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => [3,1,2,7,5,4,6,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6,8] => [1,3,2,7,5,4,6,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6,8] => [1,5,3,7,2,4,6,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [1,7,3,2,5,4,6,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,8,6] => [3,5,1,2,4,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,7,8,6] => [1,5,3,2,4,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,7,4,8,6] => [3,1,2,7,5,8,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,7,4,8,6] => [1,3,2,7,5,8,4,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,7,4,8,6] => [1,5,3,7,2,8,4,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,7,8,4,6] => [3,1,2,8,5,4,7,6] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,7,8,4,6] => [1,3,2,8,5,4,7,6] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,6] => [1,7,3,8,5,4,2,6] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,7,8,2,4,6] => [1,8,3,2,5,4,7,6] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [3,5,1,8,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,8,4,6,7] => [5,1,3,8,2,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,5,8,1,2,4,6,7] => [8,1,3,2,5,4,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,4,8,6,7] => [3,5,1,2,4,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,5,1,2,4,8,6,7] => [5,1,3,2,4,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,8,6,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,2,4,8,6,7] => [1,5,3,2,4,8,6,7] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,5,8,4,6,7] => [1,3,2,8,5,4,6,7] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [1,5,3,8,2,4,6,7] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [1,8,3,2,5,4,6,7] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,8,7] => [3,5,1,2,4,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,8,7] => [5,1,3,2,4,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,8,7] => [3,1,2,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,8,7] => [1,5,3,2,4,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,8,7] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,5,6,8,4,7] => [3,1,2,8,5,6,4,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,5,6,8,4,7] => [1,3,2,8,5,6,4,7] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,2,6,8,4,7] => [1,5,3,8,2,6,4,7] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,6,2,8,4,7] => [1,6,3,8,5,2,4,7] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,6,8,2,4,7] => [1,8,3,2,5,6,4,7] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7,8] => [3,5,1,2,4,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7,8] => [1,5,3,2,4,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7,8] => [1,5,3,6,2,4,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [1,6,3,2,5,4,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4,8] => [1,5,3,7,2,6,4,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,8] => [1,6,3,7,5,2,4,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4,8] => [1,7,3,2,5,6,4,8] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,5,6,7,8,4] => [3,1,2,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,5,2,6,7,8,4] => [1,5,3,8,2,6,7,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,5,6,2,7,8,4] => [1,6,3,8,5,2,7,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,5,6,7,2,8,4] => [1,7,3,8,5,6,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5,6,7,8,2,4] => [1,8,3,2,5,6,7,4] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5] => [3,6,1,7,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,6,1,7,2,4,8,5] => [6,7,3,2,8,1,4,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,6,7,1,2,4,8,5] => [7,1,3,2,8,6,4,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,6,1,2,7,8,4,5] => [6,1,3,8,4,2,7,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,6,7,2,8,4,5] => [3,7,1,8,4,6,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,6,1,7,2,8,4,5] => [6,7,3,8,4,1,2,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,6,7,1,2,8,4,5] => [7,1,3,8,4,6,2,5] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,6,1,7,8,2,4,5] => [6,8,3,2,4,1,7,5] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,6,7,1,8,2,4,5] => [7,8,3,2,4,6,1,5] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [8,1,3,2,4,6,7,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,6,1,2,7,4,5,8] => [6,1,3,7,4,2,5,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5,8] => [3,7,1,2,4,6,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5,8] => [1,3,2,6,7,4,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5,8] => [1,6,3,2,7,4,5,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5,8] => [1,3,2,7,4,6,5,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5,8] => [1,6,3,7,4,2,5,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5,8] => [1,7,3,2,4,6,5,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,7,8,5] => [6,1,3,2,8,4,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,7,8,5] => [3,1,2,6,8,4,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,7,8,5] => [1,3,2,6,8,4,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,7,8,5] => [1,6,3,2,8,4,7,5] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,6,7,4,8,5] => [3,1,2,7,8,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,6,2,7,4,8,5] => [1,6,3,7,8,2,4,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,6,7,2,4,8,5] => [1,7,3,2,8,6,4,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,2,6,7,8,4,5] => [3,1,2,8,4,6,7,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,2,6,7,8,4,5] => [1,3,2,8,4,6,7,5] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => [1,6,3,8,4,2,7,5] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,8,4,5] => [1,7,3,8,4,6,2,5] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,6,8,2,4,5,7] => [3,8,1,2,4,6,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,6,8,1,2,4,5,7] => [8,1,3,2,4,6,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,8,5,7] => [3,6,1,2,8,4,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,2,6,4,8,5,7] => [3,1,2,6,8,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,8,5,7] => [1,3,2,6,8,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,8,5,7] => [1,6,3,2,8,4,5,7] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,8,4,5,7] => [1,3,2,8,4,6,5,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,8,4,5,7] => [1,6,3,8,4,2,5,7] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,8,7] => [3,6,1,2,4,5,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,8,7] => [3,1,2,6,4,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,8,7] => [3,1,2,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,8,7] => [1,6,3,4,2,5,8,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,8,5,7] => [3,1,2,4,8,6,5,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,8,5,7] => [1,3,2,4,8,6,5,7] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => [3,6,1,2,4,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7,8] => [1,3,2,6,4,5,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7,8] => [1,6,3,2,4,5,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => [1,6,3,4,2,5,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5,8] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5,8] => [1,7,3,4,2,6,5,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,6,7,8,5] => [3,1,2,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,6,7,8,5] => [1,4,3,2,8,6,7,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,3,4,6,2,7,8,5] => [1,6,3,4,8,2,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,4,6,7,2,8,5] => [1,7,3,4,8,6,2,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4,6,7,8,2,5] => [1,8,3,4,2,6,7,5] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [3,7,1,2,8,4,5,6] => [7,1,3,8,4,5,2,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,7,8,2,4,5,6] => [3,8,1,2,4,5,7,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,7,8,1,2,4,5,6] => [8,1,3,2,4,5,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [3,7,1,2,4,8,5,6] => [7,1,3,2,8,5,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,3,2,7,8,5,4,6] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,3,7,2,4,8,5,6] => [1,7,3,2,8,5,4,6] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,7,8,4,5,6] => [3,1,2,8,4,5,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,3,2,7,8,4,5,6] => [1,3,2,8,4,5,7,6] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [1,7,3,8,4,5,2,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => [1,8,3,2,4,5,7,6] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,7,2,4,5,8,6] => [3,7,1,2,4,8,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,7,1,2,4,5,8,6] => [7,1,3,2,4,8,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,2,7,4,5,8,6] => [3,1,2,7,4,8,5,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,3,2,7,4,5,8,6] => [1,3,2,7,4,8,5,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,3,7,2,4,5,8,6] => [1,7,3,2,4,8,5,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [3,1,2,4,7,5,8,6] => [3,1,2,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,3,2,4,7,5,8,6] => [1,3,2,4,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,3,4,2,7,5,8,6] => [1,4,3,2,7,8,5,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,8,6] => [1,7,3,4,2,8,5,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,2,4,7,8,5,6] => [3,1,2,4,8,5,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,3,2,4,7,8,5,6] => [1,3,2,4,8,5,7,6] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,3,4,7,2,8,5,6] => [1,7,3,4,8,5,2,6] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6,8] => [3,7,1,2,4,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6,8] => [7,1,3,2,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6,8] => [3,1,2,7,4,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6,8] => [1,3,2,7,4,5,6,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6,8] => [1,7,3,2,4,5,6,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [3,1,2,4,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [1,7,3,4,2,5,6,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6,8] => [3,1,2,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,7,8,6] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,7,8,6] => [1,5,3,4,2,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,4,5,7,2,8,6] => [1,7,3,4,5,8,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,3,4,5,7,8,2,6] => [1,8,3,4,5,2,7,6] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [3,8,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,8,1,2,4,5,6,7] => [8,1,3,2,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,8,4,5,6,7] => [3,1,2,8,4,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,3,2,8,4,5,6,7] => [1,3,2,8,4,5,6,7] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,3,8,2,4,5,6,7] => [1,8,3,2,4,5,6,7] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,4,8,5,6,7] => [3,1,2,4,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,3,2,4,8,5,6,7] => [1,3,2,4,8,5,6,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [1,4,3,2,8,5,6,7] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [1,8,3,4,2,5,6,7] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,2,4,5,8,6,7] => [3,1,2,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,6,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,3,4,2,5,8,6,7] => [1,4,3,2,5,8,6,7] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,3,4,5,8,2,6,7] => [1,8,3,4,5,2,6,7] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [3,1,2,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,3,4,5,6,8,2,7] => [1,8,3,4,5,6,2,7] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7] => [4,5,6,1,2,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,8,7] => [4,6,2,1,5,3,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,8,7] => [5,6,2,4,1,3,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,8,7] => [6,1,2,4,5,3,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,8,3,7] => [4,5,8,1,2,6,3,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,8,3,7] => [5,1,8,4,2,6,3,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,8,3,7] => [5,6,8,4,1,2,3,7] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,8,3,7] => [6,1,8,4,5,2,3,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,5,6,8,2,3,7] => [4,8,2,1,5,6,3,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [4,5,1,6,8,2,3,7] => [5,8,2,4,1,6,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [6,8,2,4,5,1,3,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [8,1,2,4,5,6,3,7] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7,8] => [4,5,6,1,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7,8] => [4,6,2,1,5,3,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7,8] => [5,6,2,4,1,3,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3,8] => [4,5,7,1,2,6,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [5,1,7,4,2,6,3,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3,8] => [4,6,7,1,5,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3,8] => [5,6,7,4,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3,8] => [5,7,2,4,1,6,3,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [7,1,2,4,5,6,3,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [4,5,8,1,2,6,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [4,5,1,6,2,7,8,3] => [5,6,8,4,1,2,7,3] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [4,5,6,1,2,7,8,3] => [6,1,8,4,5,2,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [4,1,5,6,7,2,8,3] => [4,7,8,1,5,6,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5,1,6,7,2,8,3] => [5,7,8,4,1,6,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5,6,1,7,2,8,3] => [6,7,8,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,1,5,6,7,8,2,3] => [4,8,2,1,5,6,7,3] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,5,1,6,7,8,2,3] => [5,8,2,4,1,6,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [4,5,6,1,7,8,2,3] => [6,8,2,4,5,1,7,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,3] => [7,8,2,4,5,6,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[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] => [4,1,5,2,7,3,8,6] => [4,5,7,1,2,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,7,8,3,6] => [4,5,8,1,2,3,7,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,7,8,3,6] => [5,1,8,4,2,3,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,1,5,7,2,8,3,6] => [4,7,8,1,5,3,2,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,5,1,7,2,8,3,6] => [5,7,8,4,1,3,2,6] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,5,7,1,2,8,3,6] => [7,1,8,4,5,3,2,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,5,1,7,8,2,3,6] => [5,8,2,4,1,3,7,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [8,1,2,4,5,3,7,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6,8] => [5,1,7,4,2,3,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6,8] => [4,5,2,1,3,7,6,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6,8] => [4,1,5,2,3,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,8] => [1,4,5,2,3,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6,8] => [1,5,2,4,3,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6,8] => [1,4,7,2,5,3,6,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6,8] => [1,5,7,4,2,3,6,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => [1,7,2,4,5,3,6,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [4,5,2,1,3,8,7,6] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,7,8,6] => [4,1,5,2,3,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,7,8,6] => [1,5,2,4,3,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [1,4,7,2,5,8,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,7,3,8,6] => [1,5,7,4,2,8,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,8,6] => [1,7,2,4,5,8,3,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,7,8,3,6] => [4,1,8,2,5,3,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,4,5,7,2,8,3,6] => [1,7,8,4,5,3,2,6] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,8,3,6,7] => [4,5,8,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,8,3,6,7] => [5,1,8,4,2,3,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,8,2,3,6,7] => [5,8,2,4,1,3,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [4,5,8,1,2,3,6,7] => [8,1,2,4,5,3,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,8,6,7] => [4,1,5,2,3,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,4,5,2,3,8,6,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [1,5,2,4,3,8,6,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [1,5,8,4,2,3,6,7] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,8,7] => [5,1,2,4,3,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,8,7] => [4,1,6,2,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,5,6,8,3,7] => [1,4,8,2,5,6,3,7] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,5,2,6,8,3,7] => [1,5,8,4,2,6,3,7] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,5,6,2,8,3,7] => [1,6,8,4,5,2,3,7] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => [4,5,2,1,3,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7,8] => [5,1,2,4,3,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7,8] => [4,1,5,2,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7,8] => [1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7,8] => [1,5,2,4,3,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7,8] => [1,4,6,2,5,3,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,5,6,4,2,3,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => [1,6,2,4,5,3,7,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3,8] => [1,4,7,2,5,6,3,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3,8] => [1,5,7,4,2,6,3,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3,8] => [1,6,7,4,5,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3,8] => [1,7,2,4,5,6,3,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,8,3] => [4,1,8,2,5,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,3] => [1,4,8,2,5,6,7,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,5,2,6,7,8,3] => [1,5,8,4,2,6,7,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,5,6,2,7,8,3] => [1,6,8,4,5,2,7,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,5,6,7,2,8,3] => [1,7,8,4,5,6,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,5,6,7,8,2,3] => [1,8,2,4,5,6,7,3] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5] => [4,6,7,1,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,6,1,2,7,3,8,5] => [6,1,7,4,8,2,3,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,6,7,2,8,3,5] => [4,7,8,1,3,6,2,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,6,1,7,2,8,3,5] => [6,7,8,4,3,1,2,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,6,7,1,2,8,3,5] => [7,1,8,4,3,6,2,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,6,7,8,2,3,5] => [4,8,2,1,3,6,7,5] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [7,8,2,4,3,6,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5,8] => [4,6,7,1,3,2,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5,8] => [4,7,2,1,3,6,5,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5,8] => [6,7,2,4,3,1,5,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5,8] => [4,6,2,1,7,3,5,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [6,1,2,4,7,3,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => [4,1,6,2,7,3,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5,8] => [1,4,6,2,7,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5,8] => [1,6,2,4,7,3,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5,8] => [4,1,7,2,3,6,5,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5,8] => [1,4,7,2,3,6,5,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5,8] => [1,6,7,4,3,2,5,8] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [1,7,2,4,3,6,5,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [4,6,2,1,8,3,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,6,1,2,3,7,8,5] => [6,1,2,4,8,3,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,8,5] => [4,1,6,2,8,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,3,7,8,5] => [1,4,6,2,8,3,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,6,2,3,7,8,5] => [1,6,2,4,8,3,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,6,7,3,8,5] => [1,4,7,2,8,6,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,2,7,3,8,5] => [1,6,7,4,8,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,8,5] => [1,7,2,4,8,6,3,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,6,7,8,3,5] => [1,4,8,2,3,6,7,5] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,6,2,7,8,3,5] => [1,6,8,4,3,2,7,5] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,6,7,2,8,3,5] => [1,7,8,4,3,6,2,5] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,8,3,5,7] => [6,1,8,4,3,2,5,7] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,8,2,3,5,7] => [4,8,2,1,3,6,5,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,8,2,3,5,7] => [6,8,2,4,3,1,5,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,8,1,2,3,5,7] => [8,1,2,4,3,6,5,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,8,5,7] => [6,1,2,4,8,3,5,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [4,1,6,2,8,3,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,4,6,2,8,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [1,6,2,4,8,3,5,7] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,6,8,3,5,7] => [4,1,8,2,3,6,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,8,3,5,7] => [1,4,8,2,3,6,5,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => [1,6,8,4,3,2,5,7] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [1,8,2,4,3,6,5,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,8,7] => [4,6,2,1,3,5,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7] => [6,1,2,4,3,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,8,7] => [4,1,6,2,3,5,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,8,7] => [1,4,6,2,3,5,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,8,7] => [1,6,2,4,3,5,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7] => [4,1,2,3,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7] => [1,4,2,3,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,8,5,7] => [4,1,2,3,8,6,5,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,8,5,7] => [1,4,2,3,8,6,5,7] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,8,3,5,7] => [1,2,8,4,3,6,5,7] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [4,6,2,1,3,5,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7,8] => [6,1,2,4,3,5,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7,8] => [4,1,6,2,3,5,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7,8] => [1,4,6,2,3,5,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7,8] => [1,6,2,4,3,5,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7,8] => [4,1,2,3,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7,8] => [1,4,2,3,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [1,2,6,4,3,5,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5,8] => [4,1,2,3,7,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5,8] => [1,2,6,4,7,3,5,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,6,7,8,5] => [4,1,2,3,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,6,7,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,6,3,7,8,5] => [1,2,6,4,8,3,7,5] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,6,7,3,8,5] => [1,2,7,4,8,6,3,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,6,7,8,3,5] => [1,2,8,4,3,6,7,5] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,7,1,2,8,3,5,6] => [7,1,8,4,3,5,2,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,7,8,2,3,5,6] => [4,8,2,1,3,5,7,6] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,7,1,8,2,3,5,6] => [7,8,2,4,3,5,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,7,8,1,2,3,5,6] => [8,1,2,4,3,5,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,7,2,3,8,5,6] => [4,7,2,1,8,5,3,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,7,3,8,5,6] => [4,1,7,2,8,5,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,2,7,3,8,5,6] => [1,4,7,2,8,5,3,6] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,7,8,3,5,6] => [4,1,8,2,3,5,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,7,8,3,5,6] => [1,4,8,2,3,5,7,6] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => [1,7,8,4,3,5,2,6] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,2,7,3,5,8,6] => [4,1,7,2,3,8,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,2,7,3,5,8,6] => [1,4,7,2,3,8,5,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,7,2,3,5,8,6] => [1,7,2,4,3,8,5,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,2,3,7,5,8,6] => [4,1,2,3,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,2,3,7,5,8,6] => [1,4,2,3,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,4,3,7,5,8,6] => [1,2,4,3,7,8,5,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,3,7,8,5,6] => [4,1,2,3,8,5,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,3,7,8,5,6] => [1,4,2,3,8,5,7,6] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [1,2,4,3,8,5,7,6] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,4,7,3,8,5,6] => [1,2,7,4,8,5,3,6] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,4,7,8,3,5,6] => [1,2,8,4,3,5,7,6] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6,8] => [7,1,2,4,3,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6,8] => [4,1,7,2,3,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6,8] => [1,4,7,2,3,5,6,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6,8] => [1,7,2,4,3,5,6,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => [4,1,2,3,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6,8] => [1,4,2,3,7,5,6,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6,8] => [1,2,4,3,7,5,6,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [1,2,7,4,3,5,6,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6,8] => [4,1,2,3,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6,8] => [1,4,2,3,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,8,6] => [4,1,2,3,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,7,8,6] => [1,4,2,3,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,7,8,6] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,4,5,7,3,8,6] => [1,2,7,4,5,8,3,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,4,5,7,8,3,6] => [1,2,8,4,5,3,7,6] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,8,2,3,5,6,7] => [4,8,2,1,3,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,8,1,2,3,5,6,7] => [8,1,2,4,3,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,8,3,5,6,7] => [4,1,8,2,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,4,2,8,3,5,6,7] => [1,4,8,2,3,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,4,8,2,3,5,6,7] => [1,8,2,4,3,5,6,7] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,3,8,5,6,7] => [4,1,2,3,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,4,2,3,8,5,6,7] => [1,4,2,3,8,5,6,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [1,2,4,3,8,5,6,7] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [1,2,8,4,3,5,6,7] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,2,3,5,8,6,7] => [4,1,2,3,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,4,2,3,5,8,6,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,4,3,5,8,6,7] => [1,2,4,3,5,8,6,7] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,4,5,3,8,6,7] => [1,2,5,4,3,8,6,7] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [4,1,2,3,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,8,7] => [1,4,2,3,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,8,7] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,4,5,6,8,3,7] => [1,2,8,4,5,6,3,7] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [5,6,1,2,7,3,8,4] => [6,1,7,8,5,2,3,4] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,6,7,2,3,8,4] => [5,7,2,8,1,6,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [5,6,1,7,2,3,8,4] => [6,7,2,8,5,1,3,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,1,2,3,8,4] => [7,1,2,8,5,6,3,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [5,1,6,2,7,8,3,4] => [5,6,8,3,1,2,7,4] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,6,1,2,7,8,3,4] => [6,1,8,3,5,2,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [5,1,6,7,2,8,3,4] => [5,7,8,3,1,6,2,4] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [5,6,1,7,2,8,3,4] => [6,7,8,3,5,1,2,4] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,6,7,1,2,8,3,4] => [7,1,8,3,5,6,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,1,6,7,8,2,3,4] => [5,8,2,3,1,6,7,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [5,6,1,7,8,2,3,4] => [6,8,2,3,5,1,7,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [7,8,2,3,5,6,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[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] => [5,1,6,2,7,3,4,8] => [5,6,7,3,1,2,4,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4,8] => [7,1,2,3,5,6,4,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4,8] => [5,6,2,7,1,3,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4,8] => [1,5,6,7,2,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4,8] => [1,6,2,7,5,3,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4,8] => [1,5,7,3,2,6,4,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [5,6,2,8,1,3,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [5,6,1,2,3,7,8,4] => [6,1,2,8,5,3,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [1,5,6,8,2,3,7,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,5,6,2,3,7,8,4] => [1,6,2,8,5,3,7,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,5,2,6,7,3,8,4] => [1,5,7,8,2,6,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,5,6,2,7,3,8,4] => [1,6,7,8,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,8,4] => [1,7,2,8,5,6,3,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [5,1,2,6,7,8,3,4] => [5,1,8,3,2,6,7,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,5,2,6,7,8,3,4] => [1,5,8,3,2,6,7,4] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [1,6,8,3,5,2,7,4] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,5,6,7,2,8,3,4] => [1,7,8,3,5,6,2,4] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,5,6,7,8,2,3,4] => [1,8,2,3,5,6,7,4] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,1,6,8,2,3,4,7] => [5,8,2,3,1,6,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,6,1,8,2,3,4,7] => [6,8,2,3,5,1,4,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,6,8,1,2,3,4,7] => [8,1,2,3,5,6,4,7] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,8,4,7] => [5,6,2,8,1,3,4,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,8,4,7] => [6,1,2,8,5,3,4,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,8,4,7] => [1,5,6,8,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [1,6,2,8,5,3,4,7] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,1,2,6,8,3,4,7] => [5,1,8,3,2,6,4,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => [1,6,8,3,5,2,4,7] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => [1,8,2,3,5,6,4,7] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,8,7] => [5,1,6,3,2,4,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,8,7] => [5,1,2,6,3,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,8,7] => [1,5,2,6,3,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,8,7] => [1,2,5,6,3,4,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,8,4,7] => [1,5,2,8,3,6,4,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,8,4,7] => [1,2,5,8,3,6,4,7] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,8,4,7] => [1,2,6,8,5,3,4,7] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,2,5,6,8,3,4,7] => [1,2,8,3,5,6,4,7] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7,8] => [6,1,2,3,5,4,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7,8] => [5,1,6,3,2,4,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7,8] => [1,5,6,3,2,4,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7,8] => [5,1,2,6,3,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7,8] => [1,5,2,6,3,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7,8] => [1,2,5,6,3,4,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,2,6,3,5,4,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4,8] => [5,1,2,7,3,6,4,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4,8] => [1,5,2,7,3,6,4,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4,8] => [1,2,5,7,3,6,4,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4,8] => [1,2,6,7,5,3,4,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,6,7,8,4] => [5,1,2,8,3,6,7,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,2,5,3,6,7,8,4] => [1,2,5,8,3,6,7,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,2,5,6,3,7,8,4] => [1,2,6,8,5,3,7,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,2,5,6,7,3,8,4] => [1,2,7,8,5,6,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,5,6,7,8,3,4] => [1,2,8,3,5,6,7,4] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,7,2,8,3,4,6] => [5,7,8,3,1,4,2,6] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,7,1,2,8,3,4,6] => [7,1,8,3,5,4,2,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,7,1,8,2,3,4,6] => [7,8,2,3,5,4,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,7,8,1,2,3,4,6] => [8,1,2,3,5,4,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,7,2,3,8,4,6] => [5,7,2,8,1,4,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,7,3,8,4,6] => [5,1,7,8,2,4,3,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,5,7,8,2,4,3,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,5,7,2,3,8,4,6] => [1,7,2,8,5,4,3,6] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,7,8,3,4,6] => [5,1,8,3,2,4,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,7,8,3,4,6] => [1,5,8,3,2,4,7,6] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [1,7,8,3,5,4,2,6] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [7,1,2,3,5,8,4,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,7,3,4,8,6] => [5,1,7,3,2,8,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,7,3,4,8,6] => [1,5,7,3,2,8,4,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,5,7,2,3,4,8,6] => [1,7,2,3,5,8,4,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,7,4,8,6] => [5,1,2,7,3,8,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,7,4,8,6] => [1,5,2,7,3,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,7,4,8,6] => [1,2,5,7,3,8,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,8,6] => [1,2,7,3,5,8,4,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,8,4,6] => [1,5,2,8,3,4,7,6] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,7,8,4,6] => [1,2,5,8,3,4,7,6] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,7,3,8,4,6] => [1,2,7,8,5,4,3,6] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,7,8,3,4,6] => [1,2,8,3,5,4,7,6] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6,8] => [7,1,2,3,5,4,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6,8] => [5,1,7,3,2,4,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6,8] => [1,5,7,3,2,4,6,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6,8] => [1,7,2,3,5,4,6,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6,8] => [5,1,2,7,3,4,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6,8] => [1,5,2,7,3,4,6,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6,8] => [1,2,5,7,3,4,6,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [1,2,7,3,5,4,6,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6,8] => [1,5,2,3,4,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6,8] => [1,2,5,3,4,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,8] => [1,2,3,7,5,4,6,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,8,6] => [5,1,2,3,4,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,7,8,6] => [1,5,2,3,4,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,7,8,6] => [1,2,5,3,4,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,7,4,8,6] => [1,2,3,7,5,8,4,6] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,7,8,4,6] => [1,2,3,8,5,4,7,6] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,8,2,3,4,6,7] => [5,8,2,3,1,4,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,8,1,2,3,4,6,7] => [8,1,2,3,5,4,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,8,3,4,6,7] => [5,1,8,3,2,4,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,5,2,8,3,4,6,7] => [1,5,8,3,2,4,6,7] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,5,8,2,3,4,6,7] => [1,8,2,3,5,4,6,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,3,8,4,6,7] => [5,1,2,8,3,4,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,5,2,3,8,4,6,7] => [1,5,2,8,3,4,6,7] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [1,2,5,8,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [1,2,8,3,5,4,6,7] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,2,3,4,8,6,7] => [5,1,2,3,4,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,5,2,3,4,8,6,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,2,5,3,4,8,6,7] => [1,2,5,3,4,8,6,7] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,8,6,7] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,5,8,4,6,7] => [1,2,3,8,5,4,6,7] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [5,1,2,3,4,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,8,7] => [1,5,2,3,4,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,8,7] => [1,2,5,3,4,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,5,6,8,4,7] => [1,2,3,8,5,6,4,7] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7,8] => [1,2,5,3,4,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,5] => [6,7,8,3,4,1,2,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,7,1,2,8,3,4,5] => [7,1,8,3,4,6,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [6,1,7,8,2,3,4,5] => [6,8,2,3,4,1,7,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,7,1,8,2,3,4,5] => [7,8,2,3,4,6,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[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] => [6,1,7,2,3,8,4,5] => [6,7,2,8,4,1,3,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [6,1,2,7,3,8,4,5] => [6,1,7,8,4,2,3,5] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,5] => [1,6,7,8,4,2,3,5] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,6,7,2,3,8,4,5] => [1,7,2,8,4,6,3,5] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [6,1,2,7,8,3,4,5] => [6,1,8,3,4,2,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,6,2,7,8,3,4,5] => [1,6,8,3,4,2,7,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,8,2,3,4,6,7,5] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,7,2,3,4,8,5] => [6,7,2,3,8,1,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [6,1,2,7,3,4,8,5] => [6,1,7,3,8,2,4,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,6,7,2,3,4,8,5] => [1,7,2,3,8,6,4,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [6,1,2,3,7,4,8,5] => [6,1,2,7,8,3,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,6,2,3,7,4,8,5] => [1,6,2,7,8,3,4,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,3,7,4,8,5] => [1,2,6,7,8,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,8,5] => [1,2,7,3,8,6,4,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [6,1,2,3,7,8,4,5] => [6,1,2,8,4,3,7,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,6,2,3,7,8,4,5] => [1,6,2,8,4,3,7,5] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [1,2,6,8,4,3,7,5] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,7,3,8,4,5] => [1,2,7,8,4,6,3,5] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,7,8,3,4,5] => [1,2,8,3,4,6,7,5] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5,8] => [6,7,2,3,4,1,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5,8] => [7,1,2,3,4,6,5,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5,8] => [6,1,7,3,4,2,5,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5,8] => [1,6,7,3,4,2,5,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5,8] => [1,7,2,3,4,6,5,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5,8] => [1,2,6,7,4,3,5,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => [1,2,7,3,4,6,5,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5,8] => [6,1,2,3,7,4,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5,8] => [1,6,2,3,7,4,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5,8] => [1,2,6,3,7,4,5,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,8] => [1,2,3,6,7,4,5,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5,8] => [1,2,3,7,4,6,5,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,8,5] => [6,1,2,3,8,4,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,7,8,5] => [1,2,6,3,8,4,7,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,7,8,5] => [1,2,3,6,8,4,7,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,2,3,6,7,4,8,5] => [1,2,3,7,8,6,4,5] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,6,7,8,4,5] => [1,2,3,8,4,6,7,5] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,8,2,3,4,5,7] => [6,8,2,3,4,1,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,8,1,2,3,4,5,7] => [8,1,2,3,4,6,5,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,8,3,4,5,7] => [6,1,8,3,4,2,5,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,6,2,8,3,4,5,7] => [1,6,8,3,4,2,5,7] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,6,8,2,3,4,5,7] => [1,8,2,3,4,6,5,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,8,4,5,7] => [6,1,2,8,4,3,5,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,8,4,5,7] => [1,6,2,8,4,3,5,7] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [1,2,6,8,4,3,5,7] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [1,2,8,3,4,6,5,7] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,8,5,7] => [6,1,2,3,8,4,5,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [1,6,2,3,8,4,5,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,8,5,7] => [1,2,6,3,8,4,5,7] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,8,5,7] => [1,2,3,6,8,4,5,7] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,8,4,5,7] => [1,2,3,8,4,6,5,7] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [6,1,2,3,4,5,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,8,7] => [1,6,2,3,4,5,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,8,7] => [1,2,6,3,4,5,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,8,7] => [1,2,3,6,4,5,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7] => [1,2,3,4,8,6,5,7] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7,8] => [1,2,6,3,4,5,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6] => [7,8,2,3,4,5,1,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[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] => [7,1,2,8,3,4,5,6] => [7,1,8,3,4,5,2,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,7,2,8,3,4,5,6] => [1,7,8,3,4,5,2,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,8,2,3,4,5,6] => [1,8,2,3,4,5,7,6] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1,2,3,8,4,5,6] => [7,1,2,8,4,5,3,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,7,2,3,8,4,5,6] => [1,7,2,8,4,5,3,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [1,2,7,8,4,5,3,6] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,2,8,3,4,5,7,6] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1,2,3,4,8,5,6] => [7,1,2,3,8,5,4,6] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [1,7,2,3,8,5,4,6] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [1,2,7,3,8,5,4,6] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,6] => [1,2,3,7,8,5,4,6] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,7,8,4,5,6] => [1,2,3,8,4,5,7,6] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [7,1,2,3,4,8,5,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [1,7,2,3,4,8,5,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,2,7,3,4,5,8,6] => [1,2,7,3,4,8,5,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,2,3,7,4,5,8,6] => [1,2,3,7,4,8,5,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6] => [1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6] => [1,2,3,4,8,5,7,6] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6,8] => [1,2,7,3,4,5,6,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6,8] => [1,2,3,4,7,5,6,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,8,3,4,5,6,7] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,8,5,6,7] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[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] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [8,1,2,3,4,5,9,6,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8,9] => [7,1,2,3,4,5,6,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,1,8] => [9,2,3,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [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] => [10,1,2,3,4,5,6,7,8,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [9,1,2,3,4,5,6,10,7,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [7,1,2,3,4,5,6,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,9,8] => [7,2,3,4,5,6,1,9,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,10,1,9] => [10,2,3,4,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,11,9] => [10,1,2,3,4,5,6,7,11,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => [8,1,2,3,4,5,6,7,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,9,6] => [7,1,2,3,4,9,5,8,6] => [[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,9,1,7,8] => [9,2,3,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,9,7] => [8,2,3,4,5,6,9,1,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,11,1,10] => [11,2,3,4,5,6,7,8,9,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1,2,3,9,4,5,6,7] => [8,1,2,9,4,5,6,3,7] => [[.,.],[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,9,7,8] => [6,1,2,3,4,5,9,7,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,9,7] => [6,1,2,3,4,5,9,8,7] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => [10,2,3,4,5,6,7,1,8,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,1,10,8] => [9,2,3,4,5,6,7,10,1,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,1,2,3,4,10,5,6,7,8] => [9,1,2,3,10,5,6,7,4,8] => [[.,.],[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [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] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [2,3,4,5,9,1,6,7,8] => [9,2,3,4,5,1,6,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[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] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,9,2,3,4,5,6,7] => [8,9,2,3,4,5,6,1,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [5,1,2,3,4,9,6,7,8] => [5,1,2,3,4,9,6,7,8] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,9,1,2,3,4,5,6,8] => [9,1,2,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,10,1,7,8,9] => [10,2,3,4,5,6,1,7,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,9,2] => [8,9,3,4,5,6,7,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [10,1,2,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7,9] => [4,1,2,3,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6,9] => [8,1,2,3,4,5,7,6,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,9,2] => [7,9,3,4,5,6,1,8,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,9,3] => [8,2,9,4,5,6,7,1,3] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],[.,.]]
[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] => [9,1,10,2,3,4,5,6,7,8] => [9,10,2,3,4,5,6,7,1,8] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [4,1,2,3,9,5,6,7,8] => [4,1,2,3,9,5,6,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,9,7,8] => [2,1,3,4,5,6,9,7,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [5,9,1,2,3,4,6,7,8] => [9,1,2,3,5,4,6,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,10,2] => [9,10,3,4,5,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[] => [] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,9,8] => [1,5,3,2,4,7,6,9,8] => [.,[[[.,.],.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,3,9,2,4,5,6,7,8] => [1,9,3,2,4,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,3,4,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,9,8] => [1,4,5,2,3,7,6,9,8] => [.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,9,3] => [1,4,9,2,5,6,7,8,3] => [.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7,9] => [1,4,2,3,6,5,8,7,9] => [.,[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [1,2,9,4,3,5,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [1,2,3,9,5,4,6,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,9,5] => [1,6,7,8,9,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,6,5,8,7,9] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7,9] => [1,2,3,4,8,6,5,7,9] => [.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,9,5,7,8] => [1,2,3,4,9,6,5,7,8] => [.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,9,6] => [1,2,3,7,8,9,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6,9] => [1,2,3,4,7,8,5,6,9] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,9,6] => [1,2,3,4,7,9,5,8,6] => [.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [1,7,9,2,3,4,5,6,8] => [1,9,2,3,4,5,7,6,8] => [.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,9,8] => [1,7,2,3,4,5,6,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6,9,8] => [1,2,3,4,7,5,6,9,8] => [.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,9,6,8] => [1,2,3,4,5,9,7,6,8] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8,9] => [1,7,2,3,4,5,6,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,8,9,2,3,4,5,6,7] => [1,9,2,3,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,8,9,5,6,7] => [1,2,3,4,9,5,6,8,7] => [.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,9,7] => [1,8,2,3,4,5,9,6,7] => [.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,9,7] => [1,2,3,8,4,5,9,6,7] => [.,[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,8,5,6,9,7] => [1,2,3,4,8,5,9,6,7] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,9,7] => [1,2,3,4,5,8,9,6,7] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,8,9,6,7] => [1,2,3,4,5,9,6,8,7] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7,9] => [1,8,2,3,4,5,6,7,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8] => [1,9,2,3,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,9,3,4,5,6,7,8] => [1,2,9,3,4,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [1,2,3,9,4,5,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [1,2,3,4,9,5,6,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => [1,2,3,4,5,9,6,7,8] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,9,7,8] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[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] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7] => [4,2,6,1,8,3,9,5,7] => [[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,9,8] => [4,2,6,1,7,3,5,9,8] => [[[.,.],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,9,8] => [4,2,5,1,3,7,6,9,8] => [[[.,.],[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,9,8] => [3,2,1,5,4,7,6,9,8] => [[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8,9] => [4,2,6,1,7,3,5,8,9] => [[[.,.],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7,10] => [4,2,6,1,8,3,9,5,7,10] => [[[.,.],[.,.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,8,6,9,7] => [4,2,5,1,3,8,9,6,7] => [[[.,.],[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,9,8,10] => [4,2,6,1,7,3,5,9,8,10] => [[[.,.],[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5,9,8] => [3,2,1,6,7,4,5,9,8] => [[[.,.],.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [4,2,5,1,3,7,6,9,8,10] => [[[.,.],[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,1,5,4,7,6,9,8,10] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7,9] => [8,2,1,4,3,6,5,7,9] => [[[.,.],.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [1,3,2,5,4,7,6,9,8,11,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7,8,9] => [4,2,5,1,3,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => [1,4,2,3,6,5,8,7,10,9] => [.,[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,9,7,8] => [2,1,4,3,6,5,9,7,8] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,4,5,6,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,1,9,3,4,5,6,7,8] => [2,1,9,3,4,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,9,1,3,4,5,6,7,8] => [9,2,1,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,9] => [3,4,1,2,6,5,8,7,9] => [[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,4,8,9,2,5,6,7] => [3,9,1,4,2,5,6,8,7] => [[.,[.,.]],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,2] => [3,9,1,4,5,6,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7,8,9] => [4,5,6,1,2,3,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,9] => [5,6,7,8,1,2,3,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,8,2,9,3,4,5,6] => [7,8,9,3,4,5,1,2,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[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] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,9,7,10,8] => [2,1,4,3,6,5,9,10,7,8] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,10,7,9,8] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,10,7,8,9] => [2,1,4,3,6,5,10,7,8,9] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,8,6,10,9] => [2,1,4,3,7,8,5,6,10,9] => [[.,.],[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,8,5,9,6,10,7] => [2,1,4,3,8,9,10,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,1,4,3,10,5,6,7,8,9] => [2,1,4,3,10,5,6,7,8,9] => [[.,.],[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,8,7,10,9] => [2,1,5,6,3,4,8,7,10,9] => [[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,8,7,10,9] => [2,1,6,3,5,4,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,9,7,10,8] => [2,1,5,6,3,4,9,10,7,8] => [[.,.],[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4,9,10,7,8] => [2,1,6,3,5,4,10,7,9,8] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5,10,9] => [2,1,6,7,8,3,4,5,10,9] => [[.,.],[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,7,3,8,4,9,5,10,6] => [2,1,7,8,9,10,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,1,10,3,4,5,6,7,8,9] => [2,1,10,3,4,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,10,1,3,4,5,6,7,8,9] => [10,2,1,3,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [3,4,1,2,6,5,8,7,10,9] => [[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7,10,9] => [4,1,3,2,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,9,7,10,8] => [3,4,1,2,6,5,9,10,7,8] => [[.,[.,.]],[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,8,6,10,9] => [3,4,1,2,7,8,5,6,10,9] => [[.,[.,.]],[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6,10,9] => [4,1,3,2,8,5,7,6,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,8,5,9,6,10,7] => [3,4,1,2,8,9,10,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,8,9,10,5,6,7] => [4,1,3,2,10,5,6,8,9,7] => [[.,.],[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9,10] => [3,4,1,2,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [3,10,1,4,5,6,7,8,9,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7,10,9] => [4,5,6,1,2,3,8,7,10,9] => [[.,[.,[.,.]]],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,9,7,10,8] => [4,5,6,1,2,3,9,10,7,8] => [[.,[.,[.,.]]],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,9,10,7,8] => [6,1,2,4,5,3,10,7,9,8] => [[.,.],[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,10,9] => [5,6,7,8,1,2,3,4,10,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4,10,9] => [8,1,2,3,5,6,7,4,10,9] => [[.,.],[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [6,7,8,9,10,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[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] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [8,1,9,2,10,3,4,5,6,7] => [8,9,10,3,4,5,6,1,2,7] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],[.,[.,.]]]
[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] => [3,1,5,2,6,4,8,7,9] => [3,5,1,6,2,4,8,7,9] => [[.,[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,9,8] => [3,5,1,2,4,7,6,9,8] => [[.,[.,.]],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [3,1,2,5,4,7,6,9,8] => [[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7,10,9] => [3,5,1,6,2,4,8,7,10,9] => [[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6,10,9] => [3,5,1,7,2,8,4,6,10,9] => [[.,[.,.]],[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,9,6,10,8] => [3,5,1,7,2,9,4,10,6,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,9,8] => [3,1,2,7,5,4,6,9,8] => [[.,.],[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => [3,1,2,5,4,7,6,9,8,10] => [[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,10,8,9] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,10,8] => [1,2,3,4,5,6,9,10,7,8] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [1,2,3,4,5,6,7,8,11,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => [4,1,2,3,6,5,8,7,9] => [[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,3,4,5,6,7,8,9,2] => [.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,10,2,3,4,5,6,7,8,9] => [1,10,2,3,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [1,11,2,3,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8,10] => [1,9,2,3,4,5,6,7,8,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,9,4,8] => [5,6,7,9,1,2,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7] => [.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6] => [.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5] => [.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4] => [.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3] => [.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,8,7,9] => [3,1,2,4,6,5,8,7,9] => [[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [1,3,2,5,4,7,6,10,8,9] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [1,2,10,3,4,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [1,2,3,10,4,5,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [1,2,3,4,10,5,6,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [1,2,3,4,5,10,6,7,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [1,2,3,4,5,6,10,7,8,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,9,6,10,8] => [2,1,4,3,7,9,5,10,6,8] => [[.,.],[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,9,6,10,8] => [2,1,5,7,3,9,4,10,6,8] => [[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,9,8] => [.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,9,10,6,7,8] => [1,2,3,4,5,10,6,7,9,8] => [.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]]
[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] => [4,1,2,3,6,5,8,7,10,9] => [4,1,2,3,6,5,8,7,10,9] => [[.,.],[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7,10,9] => [6,1,2,3,4,5,8,7,10,9] => [[.,.],[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,6,5,8,7,10,9] => [.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,9,3] => [7,8,9,4,5,6,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [2,6,1,7,3,8,4,9,5] => [6,2,7,8,9,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,1,10,3] => [9,2,10,4,5,6,7,8,1,3] => [[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9,10,11] => [3,1,2,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2,9] => [3,8,1,4,5,6,7,2,9] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [1,10,2,3,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,9,6,7,10,8] => [1,2,3,4,5,9,6,10,7,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,6,2,8,3,9,5,10,7] => [4,6,8,1,9,2,10,3,5,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5,10,9] => [4,6,7,1,8,2,3,5,10,9] => [[.,[.,[.,.]]],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,8,6,10,9] => [2,1,5,7,3,8,4,6,10,9] => [[.,.],[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,9,6,10,8] => [3,4,1,2,7,9,5,10,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,3,9,1,4,5,6,7,8] => [9,2,3,1,4,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [2,3,4,10,1,5,6,7,8,9] => [10,2,3,4,1,5,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5,10,9] => [3,6,1,7,8,2,4,5,10,9] => [[.,[.,.]],[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6,10,9] => [4,5,7,1,2,8,3,6,10,9] => [[.,[.,[.,.]]],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,6,3,8,5,9,7] => [4,1,6,2,8,3,9,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7,9] => [8,2,1,3,4,5,6,7,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7,9] => [2,1,8,3,4,5,6,7,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [2,9,1,3,4,5,6,7,8,10] => [9,2,1,3,4,5,6,7,8,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7,10,9,12,11] => [4,5,6,1,2,3,8,7,10,9,12,11] => [[.,[.,[.,.]]],[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6,11,12,9,10] => [4,1,3,2,8,5,7,6,12,9,11,10] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,12,10,11] => [1,2,3,4,5,6,7,8,9,12,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,10,11,2] => [3,11,1,4,5,6,7,8,9,10,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,8,7,10,9,12,11] => [2,1,5,6,3,4,8,7,10,9,12,11] => [[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7,10,9,12,11] => [3,5,1,6,2,4,8,7,10,9,12,11] => [[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [3,1,2,9,4,5,6,7,8] => [3,1,2,9,4,5,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,11,1,3,4,5,6,7,8,9,10] => [11,2,1,3,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,9,10,2] => [8,10,3,4,5,6,7,1,9,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,10,9,12,11] => [3,4,1,2,6,5,8,7,10,9,12,11] => [[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,7,2,8,3,9,5,10,6] => [4,7,8,1,9,10,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
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.