Identifier
Mp00031:
Dyck paths
—to 312-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] => [1,2] => [1,2] => [.,[.,.]]
[1,1,0,0] => [2,1] => [2,1] => [[.,.],.]
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [.,[[.,.],.]]
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [[.,.],[.,.]]
[1,1,0,1,0,0] => [2,3,1] => [3,2,1] => [[[.,.],.],.]
[1,1,1,0,0,0] => [3,2,1] => [2,3,1] => [[.,[.,.]],.]
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,3,2] => [.,[[[.,.],.],.]]
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,3,4,2] => [.,[[.,[.,.]],.]]
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,2,3,1] => [[[.,.],[.,.]],.]
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,2,4,1] => [[[.,.],[.,.]],.]
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,3,1,4] => [[.,[.,.]],[.,.]]
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [4,3,2,1] => [[[[.,.],.],.],.]
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [2,4,3,1] => [[.,[[.,.],.]],.]
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [2,3,4,1] => [[.,[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [1,3,5,4,2] => [.,[[.,[[.,.],.]],.]]
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,4,5,3] => [[.,.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [4,2,3,5,1] => [[[.,.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.]
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [3,2,5,4,1] => [[[.,.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [3,2,4,5,1] => [[[.,.],[.,[.,.]]],.]
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,3,1,5,4] => [[.,[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [4,3,2,5,1] => [[[[.,.],.],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [5,3,4,2,1] => [[[[.,.],[.,.]],.],.]
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [2,5,4,3,1] => [[.,[[[.,.],.],.]],.]
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.]
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,5,4,6,3] => [.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [.,[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,5,3,4,6,2] => [.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,4,3,5,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [1,4,3,6,5,2] => [.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,4,3,5,6,2] => [.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [.,[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,5,4,3,6,2] => [.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [1,3,5,4,2,6] => [.,[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [1,3,6,4,5,2] => [.,[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [1,3,5,4,6,2] => [.,[[.,[[.,.],[.,.]]],.]]
>>> Load all 2073 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,6,4,5,3,2] => [.,[[[[.,.],[.,.]],.],.]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [1,3,6,5,4,2] => [.,[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [1,3,4,6,5,2] => [.,[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,5,4,6,3] => [[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [2,1,4,6,5,3] => [[.,.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => [[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1,5,6,4] => [[[.,.],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [5,2,3,4,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [4,2,3,6,5,1] => [[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [4,2,3,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,4,1,6,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [5,2,4,3,1,6] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [5,2,4,3,6,1] => [[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [3,2,5,4,1,6] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [3,2,6,4,5,1] => [[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [3,2,5,4,6,1] => [[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [6,2,4,5,3,1] => [[[.,.],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [3,2,6,5,4,1] => [[[.,.],[[[.,.],.],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [3,2,4,6,5,1] => [[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [3,2,4,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [2,3,1,6,5,4] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [5,3,2,4,6,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [4,3,2,5,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [4,3,2,6,5,1] => [[[[.,.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [4,3,2,5,6,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [2,4,3,1,6,5] => [[.,[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [5,4,3,2,6,1] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [6,4,3,5,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [2,6,3,5,4,1] => [[.,[[.,.],[[.,.],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [5,3,4,2,1,6] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [6,3,4,2,5,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [5,3,4,2,6,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [2,5,4,3,1,6] => [[.,[[[.,.],.],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [2,6,4,3,5,1] => [[.,[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [6,3,5,4,2,1] => [[[[.,.],[[.,.],.]],.],.]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [2,6,5,4,3,1] => [[.,[[[[.,.],.],.],.]],.]
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [2,6,4,5,3,1] => [[.,[[[.,.],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [1,2,3,5,7,6,4] => [.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,6,4,5,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,5,4,6,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,7,4,6,5,3] => [.,[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [1,2,5,4,7,6,3] => [.,[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,5,4,6,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,4,5,3,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,7,5,4,6,3] => [.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,6,5,4,7,3] => [.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [1,2,4,6,5,3,7] => [.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [1,2,4,7,5,6,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [1,2,4,6,5,7,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,4,5,6,3,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,7,5,6,4,3] => [.,[.,[[[[.,.],[.,.]],.],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [1,2,4,7,6,5,3] => [.,[.,[[.,[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [1,2,4,5,7,6,3] => [.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [1,3,2,5,7,6,4] => [.,[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,6,3,4,5,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,5,3,4,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,7,3,4,6,5,2] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [1,5,3,4,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,5,3,4,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,4,3,5,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,4,3,5,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,6,3,5,4,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,7,3,5,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,6,3,5,4,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [1,4,3,6,5,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [1,7,3,6,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [1,4,3,7,5,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [1,4,3,6,5,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,4,3,5,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,7,3,5,6,4,2] => [.,[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [1,4,3,7,6,5,2] => [.,[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [1,4,3,5,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,4,3,5,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,3,4,2,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,3,4,2,7,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,3,4,2,6,7,5] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,6,4,3,5,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,6,4,3,5,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,5,4,3,6,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,7,4,3,6,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [1,5,4,3,7,6,2] => [.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,5,4,3,6,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [1,3,5,4,2,6,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [1,3,5,4,2,7,6] => [.,[[.,[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [1,7,5,4,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [1,6,5,4,3,7,2] => [.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [1,3,6,4,5,2,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [1,7,6,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [1,3,7,4,5,6,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [1,3,6,4,5,7,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [1,3,5,4,6,2,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [1,7,5,4,6,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [1,3,7,4,6,5,2] => [.,[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [1,3,5,4,7,6,2] => [.,[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [1,3,5,4,6,7,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,3,4,5,2,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,3,4,5,2,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,6,4,5,3,2,7] => [.,[[[[.,.],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,7,4,5,3,6,2] => [.,[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,6,4,5,3,7,2] => [.,[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [1,3,6,5,4,2,7] => [.,[[.,[[[.,.],.],.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [1,3,7,5,4,6,2] => [.,[[.,[[[.,.],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [1,3,6,5,4,7,2] => [.,[[.,[[[.,.],.],[.,.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [1,3,4,6,5,2,7] => [.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [1,7,4,6,5,3,2] => [.,[[[[.,.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [1,3,7,6,5,4,2] => [.,[[.,[[[[.,.],.],.],.]],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [1,3,4,7,5,6,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [1,3,4,6,5,7,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,3,4,5,6,2,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,7,4,5,6,3,2] => [.,[[[[.,.],[.,[.,.]]],.],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [1,3,7,5,6,4,2] => [.,[[.,[[[.,.],[.,.]],.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [1,3,4,7,6,5,2] => [.,[[.,[.,[[[.,.],.],.]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [1,3,4,5,7,6,2] => [.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,3,4,5,6,7,2] => [.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [2,1,3,5,7,6,4] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [2,1,6,4,5,7,3] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [2,1,5,4,6,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [2,1,7,4,6,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [2,1,5,4,7,6,3] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [2,1,5,4,6,7,3] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,1,4,5,3,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,1,4,5,3,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [2,1,7,5,4,6,3] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [2,1,6,5,4,7,3] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [2,1,4,6,5,3,7] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [2,1,4,7,5,6,3] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [2,1,4,6,5,7,3] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,1,4,5,6,3,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [2,1,7,5,6,4,3] => [[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [2,1,4,7,6,5,3] => [[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [2,1,4,5,7,6,3] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,1,4,5,6,7,3] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [3,2,1,4,6,7,5] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,2,1,6,5,7,4] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [3,2,1,5,6,4,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [3,2,1,5,7,6,4] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,2,1,5,6,7,4] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,2,3,1,6,7,5] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [5,2,3,4,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [4,2,3,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,2,3,5,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [6,2,3,5,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [7,2,3,5,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [6,2,3,5,4,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [4,2,3,6,5,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [7,2,3,6,5,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [4,2,3,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [4,2,3,6,5,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [7,2,3,5,6,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [4,2,3,7,6,5,1] => [[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [4,2,3,5,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [4,2,3,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [3,2,4,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [3,2,4,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [3,2,4,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,2,4,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,2,4,1,6,7,5] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [5,2,4,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [5,2,4,3,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [6,2,4,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [7,2,4,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [6,2,4,3,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [5,2,4,3,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [7,2,4,3,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [5,2,4,3,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [5,2,4,3,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [3,2,5,4,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [3,2,5,4,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [6,2,5,4,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [7,2,5,4,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [6,2,5,4,3,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [3,2,6,4,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [7,2,6,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [3,2,7,4,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [3,2,6,4,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [3,2,5,4,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [7,2,5,4,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [3,2,7,4,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [3,2,5,4,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [3,2,5,4,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [3,2,4,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [3,2,4,5,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [6,2,4,5,3,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [7,2,4,5,3,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [6,2,4,5,3,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [3,2,6,5,4,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [7,2,6,5,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [3,2,7,5,4,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [3,2,6,5,4,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [3,2,4,6,5,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [7,2,4,6,5,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [3,2,7,6,5,4,1] => [[[.,.],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [3,2,4,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [3,2,4,6,5,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [7,2,4,5,6,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [3,2,7,5,6,4,1] => [[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [3,2,4,7,6,5,1] => [[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [3,2,4,5,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [3,2,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [2,3,1,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [2,3,1,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [2,3,1,4,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [2,3,1,4,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [2,3,1,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [2,3,1,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [2,3,1,6,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [2,3,1,7,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [2,3,1,6,5,7,4] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [2,3,1,5,6,4,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [2,3,1,7,6,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [2,3,1,5,7,6,4] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [2,3,1,5,6,7,4] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [4,3,2,1,6,7,5] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [5,3,2,4,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [7,3,2,4,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [5,3,2,4,7,6,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [4,3,2,5,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [4,3,2,5,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [6,3,2,5,4,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [7,3,2,5,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [6,3,2,5,4,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [4,3,2,6,5,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [7,3,2,6,5,4,1] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [4,3,2,7,5,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [4,3,2,6,5,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [4,3,2,5,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [7,3,2,5,6,4,1] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [4,3,2,7,6,5,1] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [4,3,2,5,7,6,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [4,3,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [2,4,3,1,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [2,4,3,1,5,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [2,4,3,1,6,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [2,4,3,1,7,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [2,4,3,1,6,7,5] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [7,4,3,2,6,5,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [5,4,3,2,7,6,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [2,5,3,4,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [2,5,3,4,1,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [2,6,3,4,5,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [2,7,3,4,5,6,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [2,6,3,4,5,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [2,5,3,4,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [2,7,3,4,6,5,1] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [2,5,3,4,7,6,1] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [2,5,3,4,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [2,4,3,5,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [2,4,3,5,1,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [6,4,3,5,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [7,4,3,5,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [6,4,3,5,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [2,6,3,5,4,1,7] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [7,6,3,5,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [2,7,3,5,4,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [2,6,3,5,4,7,1] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [2,4,3,6,5,1,7] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [7,4,3,6,5,2,1] => [[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [2,7,3,6,5,4,1] => [[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [2,4,3,7,5,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [2,4,3,6,5,7,1] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [2,4,3,5,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [7,4,3,5,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [2,7,3,5,6,4,1] => [[.,[[.,.],[[.,[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [2,4,3,7,6,5,1] => [[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [2,4,3,5,7,6,1] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [2,4,3,5,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [2,3,4,1,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [2,3,4,1,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [2,3,4,1,7,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [2,3,4,1,6,7,5] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [5,3,4,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [5,3,4,2,1,7,6] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [6,3,4,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [7,3,4,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [6,3,4,2,5,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [5,3,4,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [7,3,4,2,6,5,1] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [5,3,4,2,7,6,1] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [5,3,4,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [2,5,4,3,1,6,7] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [2,5,4,3,1,7,6] => [[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [2,6,4,3,5,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [2,7,4,3,5,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [2,6,4,3,5,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [2,5,4,3,6,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [2,7,4,3,6,5,1] => [[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [2,5,4,3,7,6,1] => [[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [2,5,4,3,6,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [2,3,5,4,1,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [2,3,5,4,1,7,6] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [6,3,5,4,2,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [7,3,5,4,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [6,3,5,4,2,7,1] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [2,6,5,4,3,1,7] => [[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [2,7,5,4,3,6,1] => [[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [2,6,5,4,3,7,1] => [[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [2,3,6,4,5,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [7,3,6,4,5,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [2,7,6,4,5,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [2,3,7,4,5,6,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [2,3,6,4,5,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [2,3,5,4,6,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [7,3,5,4,6,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [2,7,5,4,6,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [2,3,7,4,6,5,1] => [[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [2,3,5,4,7,6,1] => [[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [2,3,5,4,6,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [2,3,4,5,1,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [6,3,4,5,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [7,3,4,5,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [6,3,4,5,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [2,6,4,5,3,1,7] => [[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [2,7,4,5,3,6,1] => [[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [2,6,4,5,3,7,1] => [[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [2,3,6,5,4,1,7] => [[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [7,3,6,5,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [2,7,6,5,4,3,1] => [[.,[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [2,3,7,5,4,6,1] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [2,3,6,5,4,7,1] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [2,3,4,6,5,1,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [7,3,4,6,5,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [2,7,4,6,5,3,1] => [[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [2,3,7,6,5,4,1] => [[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [2,3,4,7,5,6,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [2,3,4,6,5,7,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [7,3,4,5,6,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [2,7,4,5,6,3,1] => [[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [2,3,7,5,6,4,1] => [[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [2,3,4,7,6,5,1] => [[.,[.,[.,[[[.,.],.],.]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [2,3,4,5,7,6,1] => [[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [1,2,3,4,7,6,8,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,7,6,5] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [1,2,3,4,6,8,7,5] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [1,2,3,5,4,7,8,6] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [1,2,3,7,5,6,8,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [1,2,3,6,5,7,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [1,2,3,8,5,7,6,4] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [1,2,3,6,5,8,7,4] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [1,2,3,6,5,7,8,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [1,2,3,7,6,5,4,8] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [1,2,3,8,6,5,7,4] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [1,2,3,7,6,5,8,4] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [1,2,3,5,7,6,4,8] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [1,2,3,8,7,6,5,4] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [1,2,3,5,8,6,7,4] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [1,2,3,5,7,6,8,4] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [1,2,3,8,6,7,5,4] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [1,2,3,5,8,7,6,4] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [1,2,3,5,6,8,7,4] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [1,2,4,3,5,7,8,6] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,6,7,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [1,2,4,3,7,6,8,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,6,5,8] => [1,2,4,3,6,7,5,8] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [1,2,4,3,8,7,6,5] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [1,2,4,3,6,7,8,5] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6,8,7] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [1,2,5,4,3,7,8,6] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [1,2,7,4,5,6,8,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [1,2,6,4,5,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,6,7,5,8,3] => [1,2,8,4,7,6,5,3] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [1,2,5,4,7,6,8,3] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,6,5,3,8] => [1,2,5,4,6,7,3,8] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [1,2,8,4,6,7,5,3] => [.,[.,[[[.,.],[[.,[.,.]],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,6,8,5,3] => [1,2,5,4,8,7,6,3] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [1,2,5,4,6,8,7,3] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [1,2,5,4,6,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,4,3,7,6,8] => [1,2,4,5,3,7,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [1,2,4,5,3,8,7,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [1,2,4,5,3,7,8,6] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,4,6,3,7,8] => [1,2,6,5,4,3,7,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [1,2,7,5,4,6,3,8] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [1,2,8,5,4,6,7,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [1,2,7,5,4,6,8,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [1,2,6,5,4,7,8,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [1,2,4,6,5,3,7,8] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,4,7,3,8] => [1,2,7,6,5,4,3,8] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [1,2,8,6,5,4,7,3] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,5,6,4,8,7,3] => [1,2,7,6,5,4,8,3] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [1,2,8,7,5,6,4,3] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [1,2,4,8,5,6,7,3] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [1,2,4,7,5,6,8,3] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => [1,2,4,6,5,7,3,8] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [1,2,8,6,5,7,4,3] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,6,4,3] => [1,2,4,6,5,8,7,3] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,5,4,3,8,7] => [1,2,4,5,6,3,8,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [1,2,8,5,6,4,7,3] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,5,7,4,8,3] => [1,2,8,7,6,5,4,3] => [.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [1,2,4,8,6,5,7,3] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [1,2,4,7,6,5,8,3] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,6,7,5,8,4,3] => [1,2,4,8,7,6,5,3] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [1,2,4,5,8,6,7,3] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [1,2,4,5,6,7,3,8] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [1,2,8,5,6,7,4,3] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [1,2,4,5,8,7,6,3] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [1,2,4,5,6,8,7,3] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [1,3,2,4,5,7,8,6] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [1,3,2,4,7,6,8,5] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [1,3,2,4,6,7,5,8] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [1,3,2,4,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,7,8,6,5] => [1,3,2,4,6,8,7,5] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [1,3,2,4,6,7,8,5] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [1,3,2,7,5,6,8,4] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [1,3,2,6,5,7,4,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [1,3,2,8,5,7,6,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [1,3,2,6,5,8,7,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [1,3,2,6,5,7,8,4] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [1,3,2,5,6,4,7,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [1,3,2,5,6,4,8,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [1,3,2,7,6,5,4,8] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [1,3,2,8,6,5,7,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [1,3,2,7,6,5,8,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,5,4,8] => [1,3,2,5,7,6,4,8] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [1,3,2,8,7,6,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [1,3,2,5,6,7,4,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [1,3,2,8,6,7,5,4] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [1,3,2,5,8,7,6,4] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,7,8,6,5,4] => [1,3,2,5,6,8,7,4] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [1,3,2,5,6,7,8,4] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [1,4,3,2,5,7,8,6] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [1,4,3,2,8,6,7,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [1,4,3,2,7,6,8,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,4,2,7,6,5,8] => [1,4,3,2,6,7,5,8] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [1,4,3,2,8,7,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [1,4,3,2,6,8,7,5] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [1,4,3,2,6,7,8,5] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [1,5,3,4,2,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [1,5,3,4,2,7,8,6] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [1,7,3,4,5,6,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [1,6,3,4,5,8,7,2] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,5,2,8,7] => [1,5,3,4,6,2,8,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,5,8,2] => [1,8,3,4,7,6,5,2] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [1,8,3,4,6,7,5,2] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [1,5,3,4,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [1,4,3,5,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [1,4,3,5,2,7,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,4,6,2,7,8] => [1,6,3,5,4,2,7,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,4,6,7,2,8] => [1,7,3,5,4,6,2,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [1,8,3,5,4,6,7,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [1,8,3,5,4,7,6,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,4,7,8,6,2] => [1,6,3,5,4,8,7,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [1,4,3,6,5,2,7,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [1,7,3,6,5,4,2,8] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,4,7,8,2] => [1,8,3,6,5,4,7,2] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,6,4,8,7,2] => [1,7,3,6,5,4,8,2] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => [1,8,3,7,5,6,4,2] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [1,4,3,8,5,6,7,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [1,4,3,6,5,7,2,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,6,8,4,2] => [1,4,3,8,5,7,6,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [1,4,3,6,5,8,7,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [1,4,3,6,5,7,8,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,5,4,2,7,8] => [1,4,3,5,6,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [1,8,3,7,6,5,4,2] => [.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [1,4,3,8,6,5,7,2] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => [1,4,3,5,7,6,2,8] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [1,4,3,8,7,6,5,2] => [.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [1,4,3,5,8,6,7,2] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [1,4,3,5,6,7,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,6,5,8,4,2] => [1,4,3,8,6,7,5,2] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [1,4,3,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [1,3,4,2,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [1,3,4,2,5,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [1,3,4,2,5,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [1,3,4,2,5,7,8,6] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,3,2,6,5,8,7] => [1,3,4,2,6,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [1,3,4,2,8,6,7,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [1,3,4,2,7,6,8,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [1,3,4,2,8,7,6,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,7,8,6,5] => [1,3,4,2,6,8,7,5] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [1,3,4,2,6,7,8,5] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [1,5,4,3,2,6,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [1,5,4,3,2,7,6,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => [1,5,4,3,2,8,7,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [1,5,4,3,2,7,8,6] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [1,6,4,3,5,2,7,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [1,8,4,3,5,6,7,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,3,5,7,6,8,2] => [1,8,4,3,5,7,6,2] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [1,6,4,3,5,8,7,2] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [1,5,4,3,6,2,7,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [1,8,4,3,6,5,7,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [1,7,4,3,6,5,8,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,3,7,6,5,2,8] => [1,5,4,3,6,7,2,8] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [1,5,4,3,8,7,6,2] => [.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [1,5,4,3,6,8,7,2] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [1,5,4,3,6,7,8,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,5,3,2,6,8,7] => [1,3,5,4,2,6,8,7] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => [1,3,5,4,2,7,6,8] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [1,3,5,4,2,7,8,6] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [1,6,5,4,3,2,7,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [1,8,5,4,3,6,7,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [1,7,5,4,3,6,8,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => [1,6,5,4,3,8,7,2] => [.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,4,5,6,3,2,8,7] => [1,3,6,4,5,2,8,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,3,7,2,8] => [1,7,6,4,5,3,2,8] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,5,6,3,7,8,2] => [1,8,6,4,5,3,7,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [1,3,7,4,5,6,2,8] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [1,8,7,4,5,6,3,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [1,3,8,4,5,6,7,2] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,5,7,6,3,8,2] => [1,8,6,4,5,7,3,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [1,3,6,4,5,7,8,2] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,6,5,3,7,8,2] => [1,8,5,4,6,3,7,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,5,3,2,8] => [1,3,5,4,7,6,2,8] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [1,8,5,4,7,6,3,2] => [.,[[[[[.,.],.],[[.,.],.]],.],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [1,3,5,4,7,6,8,2] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,7,6,5,3,8,2] => [1,8,5,4,6,7,3,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [1,3,8,4,6,7,5,2] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,4,7,6,8,5,3,2] => [1,3,5,4,8,7,6,2] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [1,3,4,5,2,6,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [1,3,4,5,2,7,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [1,3,4,5,2,8,7,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [1,3,4,5,2,7,8,6] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [1,6,4,5,3,2,7,8] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [1,8,4,5,3,6,7,2] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [1,7,4,5,3,6,8,2] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,4,3,7,8,6,2] => [1,6,4,5,3,8,7,2] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,4,6,3,2,8,7] => [1,3,6,5,4,2,8,7] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [1,7,6,5,4,3,2,8] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [1,8,6,5,4,3,7,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,4,6,3,8,7,2] => [1,7,6,5,4,3,8,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [1,8,7,5,4,6,3,2] => [.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [1,3,8,5,4,6,7,2] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,4,7,6,3,2,8] => [1,3,6,5,4,7,2,8] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,4,7,6,3,8,2] => [1,8,6,5,4,7,3,2] => [.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,4,7,6,8,3,2] => [1,3,8,5,4,7,6,2] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,5,6,4,3,7,2,8] => [1,7,4,6,5,3,2,8] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,5,6,7,4,8,3,2] => [1,3,8,7,5,6,4,2] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [1,3,4,8,5,6,7,2] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,5,7,6,4,3,2,8] => [1,3,4,6,5,7,2,8] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,7,6,4,3,8,2] => [1,8,4,6,5,7,3,2] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [1,3,4,6,5,7,8,2] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [1,3,4,5,6,2,7,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [1,3,4,5,6,2,8,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [1,8,4,5,6,3,7,2] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [1,7,4,5,6,3,8,2] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [1,8,4,7,6,5,3,2] => [.,[[[[.,.],[[[.,.],.],.]],.],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,5,7,4,8,3,2] => [1,3,8,7,6,5,4,2] => [.,[[.,[[[[[.,.],.],.],.],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [1,3,4,5,7,6,2,8] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,6,7,5,4,8,3,2] => [1,3,8,5,7,6,4,2] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [1,3,4,8,7,6,5,2] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [1,3,4,5,8,6,7,2] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [1,3,4,5,7,6,8,2] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [1,3,4,5,6,7,2,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [1,8,4,5,6,7,3,2] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [1,3,8,5,6,7,4,2] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [1,3,4,5,8,7,6,2] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [1,3,4,5,6,8,7,2] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,2] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,4,6,8,7,5] => [2,1,3,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [2,1,3,5,4,7,8,6] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [2,1,3,8,5,7,6,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,7,8,6,4] => [2,1,3,6,5,8,7,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,5,7,8,4] => [2,1,3,8,6,5,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,6,7,5,8,4] => [2,1,3,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [2,1,3,5,8,6,7,4] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,7,6,5,8,4] => [2,1,3,8,6,7,5,4] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [2,1,3,5,6,7,8,4] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [2,1,4,3,5,7,8,6] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,6,8,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,7,6,5,8] => [2,1,4,3,6,7,5,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [2,1,4,3,6,8,7,5] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3,7,8,6] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,6,8,3] => [2,1,8,4,5,7,6,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [2,1,6,4,5,8,7,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [2,1,6,4,5,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [2,1,5,4,6,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,5,7,8,3] => [2,1,8,4,6,5,7,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [2,1,7,4,6,5,8,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [2,1,8,4,7,6,5,3] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [2,1,5,4,8,6,7,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [2,1,5,4,7,6,8,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,4,7,6,5,3,8] => [2,1,5,4,6,7,3,8] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [2,1,8,4,6,7,5,3] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,7,6,8,5,3] => [2,1,5,4,8,7,6,3] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [2,1,5,4,6,8,7,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [2,1,5,4,6,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [2,1,4,5,3,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,1,4,5,3,6,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,5,4,3,7,8,6] => [2,1,4,5,3,8,7,6] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [2,1,8,5,4,6,7,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [2,1,8,5,4,7,6,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [2,1,6,5,4,8,7,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [2,1,4,6,5,3,7,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [2,1,4,6,5,3,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,5,6,4,7,3,8] => [2,1,7,6,5,4,3,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [2,1,8,6,5,4,7,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [2,1,7,6,5,4,8,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [2,1,8,7,5,6,4,3] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [2,1,4,8,5,6,7,3] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [2,1,8,6,5,7,4,3] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [2,1,4,8,5,7,6,3] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [2,1,4,6,5,8,7,3] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,5,4,7,8,3] => [2,1,8,5,6,4,7,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [2,1,7,5,6,4,8,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [2,1,4,8,6,5,7,3] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [2,1,4,7,6,5,8,3] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => [2,1,8,5,7,6,4,3] => [[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [2,1,4,8,7,6,5,3] => [[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [2,1,4,5,8,6,7,3] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [2,1,4,5,6,7,3,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [2,1,8,5,6,7,4,3] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [2,1,4,8,6,7,5,3] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [2,1,4,5,8,7,6,3] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [2,1,4,5,6,8,7,3] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,7,6] => [3,2,1,4,5,7,8,6] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,3,1,4,6,8,7,5] => [3,2,1,4,7,6,8,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [3,2,1,4,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [3,2,1,4,6,8,7,5] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [3,2,1,4,6,7,8,5] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [3,2,1,7,5,6,4,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,7,4] => [3,2,1,7,5,6,8,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [3,2,1,8,5,7,6,4] => [[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [3,2,1,6,5,8,7,4] => [[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,3,1,5,8,7,6,4] => [3,2,1,6,5,7,8,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [3,2,1,5,6,4,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [3,2,1,7,6,5,4,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,5,7,8,4] => [3,2,1,8,6,5,7,4] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [3,2,1,7,6,5,8,4] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,5,4,8] => [3,2,1,5,7,6,4,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => [3,2,1,8,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [3,2,1,5,8,6,7,4] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => [3,2,1,5,7,6,8,4] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [3,2,1,8,6,7,5,4] => [[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [3,2,1,5,8,7,6,4] => [[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [3,2,1,5,6,8,7,4] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,2,1,5,6,7,8,4] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [4,2,3,1,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [4,2,3,1,5,7,8,6] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [4,2,3,1,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [4,2,3,1,7,6,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [4,2,3,1,7,6,8,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,2,3,1,8,7,6,5] => [[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [4,2,3,1,6,8,7,5] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,3,1,6,7,8,5] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,2,3,4,1,7,8,6] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [8,2,3,4,5,7,6,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [6,2,3,4,5,8,7,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,4,6,5,1,8,7] => [5,2,3,4,6,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [7,2,3,4,6,5,1,8] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [5,2,3,4,7,6,1,8] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [8,2,3,4,7,6,5,1] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [5,2,3,4,8,6,7,1] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,3,5,4,1,7,8,6] => [4,2,3,5,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [6,2,3,5,4,1,7,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [7,2,3,5,4,6,1,8] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [8,2,3,5,4,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,3,5,4,7,6,1,8] => [6,2,3,5,4,7,1,8] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [8,2,3,5,4,7,6,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [6,2,3,5,4,7,8,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => [7,2,3,6,5,4,1,8] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [8,2,3,6,5,4,7,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [8,2,3,7,5,6,4,1] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [4,2,3,8,5,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [4,2,3,7,5,6,8,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => [4,2,3,8,5,7,6,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [4,2,3,6,5,8,7,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [4,2,3,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [4,2,3,5,6,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [4,2,3,7,6,5,8,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,6,7,5,4,8,1] => [8,2,3,5,7,6,4,1] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,5,8,4,1] => [4,2,3,8,7,6,5,1] => [[[.,.],[.,[[[[.,.],.],.],.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [4,2,3,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [8,2,3,5,6,7,4,1] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,7,6,8,5,4,1] => [4,2,3,5,8,7,6,1] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,7,8,6,5,4,1] => [4,2,3,5,6,8,7,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [4,2,3,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,4,3,1,5,6,8,7] => [3,2,4,1,5,6,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,4,3,1,5,7,6,8] => [3,2,4,1,5,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,4,3,1,5,7,8,6] => [3,2,4,1,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [3,2,4,1,5,7,8,6] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [3,2,4,1,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [3,2,4,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [3,2,4,1,7,6,8,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [3,2,4,1,8,7,6,5] => [[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [3,2,4,1,6,8,7,5] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [3,2,4,1,6,7,8,5] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [5,2,4,3,1,6,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [5,2,4,3,1,6,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [5,2,4,3,1,7,6,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [5,2,4,3,1,8,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [6,2,4,3,5,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [5,2,4,3,6,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [7,2,4,3,6,5,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [8,2,4,3,6,5,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [7,2,4,3,6,5,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => [8,2,4,3,7,6,5,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [5,2,4,3,7,6,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,4,3,7,6,5,1,8] => [5,2,4,3,6,7,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [8,2,4,3,6,7,5,1] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,7,6,8,5,1] => [5,2,4,3,8,7,6,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [3,2,5,4,1,6,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => [3,2,5,4,1,6,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,3,1,7,6,8] => [3,2,5,4,1,7,6,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [3,2,5,4,1,8,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [3,2,5,4,1,7,8,6] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => [6,2,5,4,3,1,8,7] => [[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,4,5,3,6,7,1,8] => [7,2,5,4,3,6,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [8,2,5,4,3,6,7,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,4,5,3,7,6,8,1] => [8,2,5,4,3,7,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,3,8,7,6,1] => [6,2,5,4,3,7,8,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => [3,2,6,4,5,1,7,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,4,5,6,3,1,8,7] => [3,2,6,4,5,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,3,7,1,8] => [7,2,6,4,5,3,1,8] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [8,2,6,4,5,3,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [7,2,6,4,5,3,8,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [3,2,7,4,5,6,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [8,2,7,4,5,6,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [3,2,8,4,5,6,7,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,4,5,7,6,3,8,1] => [8,2,6,4,5,7,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [3,2,5,4,6,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [7,2,5,4,6,3,8,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [8,2,7,4,6,5,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [3,2,8,4,6,5,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [3,2,7,4,6,5,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [3,2,5,4,7,6,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [8,2,5,4,7,6,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [3,2,5,4,8,6,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [3,2,5,4,7,6,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [3,2,5,4,6,8,7,1] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [3,2,5,4,6,7,8,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [3,2,4,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [3,2,4,5,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,4,3,6,1,7,8] => [6,2,4,5,3,1,7,8] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [7,2,4,5,3,6,1,8] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [7,2,4,5,3,6,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [8,2,4,5,3,7,6,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,5,4,6,3,1,8,7] => [3,2,6,5,4,1,8,7] => [[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [7,2,6,5,4,3,1,8] => [[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,4,6,3,7,8,1] => [8,2,6,5,4,3,7,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [3,2,7,5,4,6,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [8,2,7,5,4,6,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => [3,2,8,5,4,6,7,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => [3,2,6,5,4,7,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => [8,2,6,5,4,7,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [3,2,8,5,4,7,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [3,2,6,5,4,8,7,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [3,2,7,6,5,4,1,8] => [[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,5,6,4,7,3,8,1] => [8,2,7,6,5,4,3,1] => [[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [3,2,7,6,5,4,8,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [8,2,4,7,5,6,3,1] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [3,2,8,7,5,6,4,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [3,2,4,8,5,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,5,6,8,7,4,3,1] => [3,2,4,7,5,6,8,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,5,7,6,4,8,3,1] => [3,2,8,6,5,7,4,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,5,7,8,6,4,3,1] => [3,2,4,6,5,8,7,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [3,2,8,5,6,4,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [3,2,7,5,6,4,8,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [8,2,4,7,6,5,3,1] => [[[.,.],[[.,[[[.,.],.],.]],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,6,5,7,4,8,3,1] => [3,2,8,7,6,5,4,1] => [[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,5,8,7,4,3,1] => [3,2,4,7,6,5,8,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,6,7,5,4,8,3,1] => [3,2,8,5,7,6,4,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [3,2,4,8,7,6,5,1] => [[[.,.],[.,[[[[.,.],.],.],.]]],.]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [3,2,4,5,8,6,7,1] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [3,2,4,5,7,6,8,1] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [3,2,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [8,2,4,5,6,7,3,1] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,6,5,8,4,3,1] => [3,2,4,8,6,7,5,1] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [3,2,4,5,6,8,7,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [2,3,1,4,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,2,1,4,6,5,8,7] => [2,3,1,4,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [2,3,1,4,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [2,3,1,4,6,7,5,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [2,3,1,4,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [2,3,1,4,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [2,3,1,5,4,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [2,3,1,6,5,4,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,5,6,4,8,7] => [2,3,1,6,5,4,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => [2,3,1,7,5,6,4,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [2,3,1,8,5,6,7,4] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [2,3,1,6,5,7,4,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [2,3,1,6,5,8,7,4] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [2,3,1,5,6,4,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [2,3,1,7,6,5,8,4] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [2,3,1,8,7,6,5,4] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [2,3,1,5,7,6,8,4] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [2,3,1,5,6,7,4,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [2,3,1,8,6,7,5,4] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [2,3,1,5,6,7,8,4] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [4,3,2,1,5,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [4,3,2,1,5,7,8,6] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [4,3,2,1,7,6,5,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [4,3,2,1,8,6,7,5] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [4,3,2,1,7,6,8,5] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [4,3,2,1,6,7,5,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [4,3,2,1,6,8,7,5] => [[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [4,3,2,1,6,7,8,5] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,2,4,5,1,6,8,7] => [5,3,2,4,1,6,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,2,4,5,1,7,6,8] => [5,3,2,4,1,7,6,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,2,4,5,1,7,8,6] => [5,3,2,4,1,8,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [7,3,2,4,5,6,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => [5,3,2,4,7,6,1,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,6,7,5,8,1] => [8,3,2,4,7,6,5,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [8,3,2,4,6,7,5,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [5,3,2,4,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [4,3,2,5,1,8,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [4,3,2,5,1,7,8,6] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,5,4,6,1,7,8] => [6,3,2,5,4,1,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,5,4,6,7,1,8] => [7,3,2,5,4,6,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [6,3,2,5,4,7,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [8,3,2,5,4,7,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => [6,3,2,5,4,8,7,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [4,3,2,6,5,1,8,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [8,3,2,7,5,6,4,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [4,3,2,8,5,6,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,5,6,8,7,4,1] => [4,3,2,7,5,6,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [8,3,2,6,5,7,4,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,5,7,6,8,4,1] => [4,3,2,8,5,7,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [4,3,2,6,5,8,7,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,2,5,8,7,6,4,1] => [4,3,2,6,5,7,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [4,3,2,5,6,1,8,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [7,3,2,5,6,4,8,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [8,3,2,7,6,5,4,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,6,5,8,7,4,1] => [4,3,2,7,6,5,8,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [4,3,2,5,7,6,1,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [8,3,2,5,7,6,4,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,6,7,5,8,4,1] => [4,3,2,8,7,6,5,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [4,3,2,5,7,6,8,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [8,3,2,5,6,7,4,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,2,7,6,5,8,4,1] => [4,3,2,8,6,7,5,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,7,6,8,5,4,1] => [4,3,2,5,8,7,6,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [4,3,2,5,6,8,7,1] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [2,4,3,1,5,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,4,2,1,5,7,8,6] => [2,4,3,1,5,8,7,6] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,4,2,1,6,5,7,8] => [2,4,3,1,6,5,7,8] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [2,4,3,1,6,5,8,7] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [2,4,3,1,7,6,8,5] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [2,4,3,1,8,7,6,5] => [[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [2,4,3,1,6,8,7,5] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [2,4,3,1,6,7,8,5] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,4,2,5,1,6,8,7] => [5,4,3,2,1,6,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [5,4,3,2,1,7,6,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [5,4,3,2,1,8,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [5,4,3,2,1,7,8,6] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [6,4,3,2,5,1,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [7,4,3,2,5,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => [8,4,3,2,5,7,6,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [6,4,3,2,5,8,7,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,4,2,6,5,1,7,8] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [5,4,3,2,6,1,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [7,4,3,2,6,5,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [8,4,3,2,6,5,7,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,2,6,5,8,7,1] => [7,4,3,2,6,5,8,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => [5,4,3,2,7,6,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [8,4,3,2,7,6,5,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,4,2,6,7,8,5,1] => [5,4,3,2,8,6,7,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,4,2,6,8,7,5,1] => [5,4,3,2,7,6,8,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,4,2,7,6,5,1,8] => [5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,4,2,7,6,8,5,1] => [5,4,3,2,8,7,6,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,2,7,8,6,5,1] => [5,4,3,2,6,8,7,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [2,5,3,4,1,6,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,2,1,7,8,6] => [2,5,3,4,1,8,7,6] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [6,5,3,4,2,1,8,7] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [8,5,3,4,2,6,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [8,5,3,4,2,7,6,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,5,2,8,7,6,1] => [6,5,3,4,2,7,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [2,6,3,4,5,1,7,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [8,6,3,4,5,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [7,6,3,4,5,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [2,7,3,4,5,6,1,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [2,8,3,4,5,6,7,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [2,8,3,4,5,7,6,1] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [2,6,3,4,5,8,7,1] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [2,6,3,4,5,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [8,7,3,4,6,5,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [8,5,3,4,7,6,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [2,5,3,4,8,6,7,1] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,7,5,2,1] => [2,5,3,4,7,6,8,1] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [8,5,3,4,6,7,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,6,5,2,1] => [2,5,3,4,6,8,7,1] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [2,5,3,4,6,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [2,4,3,5,1,6,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [2,4,3,5,1,7,6,8] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [2,4,3,5,1,8,7,6] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [2,4,3,5,1,7,8,6] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,4,2,6,1,8,7] => [6,4,3,5,2,1,8,7] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => [7,4,3,5,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,4,2,6,8,7,1] => [7,4,3,5,2,6,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,4,2,7,6,8,1] => [8,4,3,5,2,7,6,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,4,6,2,1,8,7] => [2,6,3,5,4,1,8,7] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [7,6,3,5,4,2,1,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,4,6,2,7,8,1] => [8,6,3,5,4,2,7,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,5,4,6,2,8,7,1] => [7,6,3,5,4,2,8,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => [8,7,3,5,4,6,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,5,4,6,8,7,2,1] => [2,7,3,5,4,6,8,1] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [8,6,3,5,4,7,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [2,8,3,5,4,7,6,1] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [2,6,3,5,4,8,7,1] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,5,6,4,2,1,7,8] => [2,4,3,6,5,1,7,8] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [2,4,3,6,5,1,8,7] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [7,4,3,6,5,2,1,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => [7,4,3,6,5,2,8,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,4,7,2,1,8] => [2,7,3,6,5,4,1,8] => [[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [8,7,3,6,5,4,2,1] => [[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [8,4,3,7,5,6,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [2,8,3,7,5,6,4,1] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [2,4,3,8,5,6,7,1] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [2,4,3,7,5,6,8,1] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [2,4,3,6,5,7,1,8] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => [2,4,3,8,5,7,6,1] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [2,4,3,6,5,8,7,1] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [2,4,3,6,5,7,8,1] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [2,4,3,5,6,1,8,7] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,5,4,2,7,8,1] => [8,4,3,5,6,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [8,7,3,5,6,4,2,1] => [[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,5,4,8,7,2,1] => [2,7,3,5,6,4,8,1] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,6,5,7,4,2,8,1] => [8,4,3,7,6,5,2,1] => [[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,6,5,7,4,8,2,1] => [2,8,3,7,6,5,4,1] => [[.,[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,5,7,8,4,2,1] => [2,4,3,8,6,5,7,1] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,6,5,8,7,4,2,1] => [2,4,3,7,6,5,8,1] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,6,7,5,4,2,8,1] => [8,4,3,5,7,6,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,5,4,8,2,1] => [2,8,3,5,7,6,4,1] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,6,7,5,8,4,2,1] => [2,4,3,8,7,6,5,1] => [[.,[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,5,4,2,1] => [2,4,3,5,8,6,7,1] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,7,6,5,4,2,1,8] => [2,4,3,5,6,7,1,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,7,6,5,4,2,8,1] => [8,4,3,5,6,7,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [2,8,3,5,6,7,4,1] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [2,4,3,5,6,8,7,1] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [2,4,3,5,6,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [2,3,4,1,5,6,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [2,3,4,1,5,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [2,3,4,1,5,8,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [2,3,4,1,5,7,8,6] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [2,3,4,1,6,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [2,3,4,1,7,6,5,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [2,3,4,1,8,6,7,5] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [2,3,4,1,7,6,8,5] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [2,3,4,1,6,7,5,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [2,3,4,1,8,7,6,5] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [2,3,4,1,6,8,7,5] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [5,3,4,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,3,2,5,1,6,8,7] => [5,3,4,2,1,6,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [5,3,4,2,1,8,7,6] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [5,3,4,2,1,7,8,6] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [6,3,4,2,5,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [8,3,4,2,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [5,3,4,2,6,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [7,3,4,2,6,5,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [8,3,4,2,6,5,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [7,3,4,2,6,5,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,6,7,5,1,8] => [5,3,4,2,7,6,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,6,7,8,5,1] => [5,3,4,2,8,6,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [5,3,4,2,7,6,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [5,3,4,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [2,5,4,3,1,6,7,8] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [2,5,4,3,1,6,8,7] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,3,5,2,1,7,8,6] => [2,5,4,3,1,8,7,6] => [[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,3,5,2,6,7,1,8] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,3,5,2,6,8,7,1] => [7,5,4,3,2,6,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [8,5,4,3,2,7,6,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [2,6,4,3,5,1,8,7] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => [8,7,4,3,5,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [2,8,4,3,5,6,7,1] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,3,5,6,8,7,2,1] => [2,7,4,3,5,6,8,1] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,3,5,7,6,2,8,1] => [8,6,4,3,5,7,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [2,8,4,3,5,7,6,1] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => [2,6,4,3,5,8,7,1] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [2,5,4,3,6,1,8,7] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,3,6,5,2,7,1,8] => [7,5,4,3,6,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [7,5,4,3,6,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [8,7,4,3,6,5,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [2,8,4,3,6,5,7,1] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [2,7,4,3,6,5,8,1] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,6,7,5,2,8,1] => [8,5,4,3,7,6,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,3,6,7,5,8,2,1] => [2,8,4,3,7,6,5,1] => [[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [2,5,4,3,8,6,7,1] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => [2,8,4,3,6,7,5,1] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,7,6,8,5,2,1] => [2,5,4,3,8,7,6,1] => [[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [2,3,5,4,1,6,7,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => [2,3,5,4,1,6,8,7] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,5,3,2,1,7,8,6] => [2,3,5,4,1,8,7,6] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,3,2,6,1,8,7] => [6,3,5,4,2,1,8,7] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,5,3,2,6,7,1,8] => [7,3,5,4,2,6,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => [8,3,5,4,2,6,7,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [6,3,5,4,2,7,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,5,3,2,7,6,8,1] => [8,3,5,4,2,7,6,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,5,3,2,7,8,6,1] => [6,3,5,4,2,8,7,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,3,2,8,7,6,1] => [6,3,5,4,2,7,8,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [2,6,5,4,3,1,8,7] => [[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,5,3,6,2,7,8,1] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,3,6,7,8,2,1] => [2,8,5,4,3,6,7,1] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [2,7,5,4,3,6,8,1] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,3,7,6,2,8,1] => [8,6,5,4,3,7,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [2,8,5,4,3,7,6,1] => [[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [2,6,5,4,3,8,7,1] => [[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,3,8,7,6,2,1] => [2,6,5,4,3,7,8,1] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [2,3,6,4,5,1,7,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [2,3,6,4,5,1,8,7] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [8,3,6,4,5,2,7,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => [7,3,6,4,5,2,8,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [2,7,6,4,5,3,8,1] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [8,3,7,4,5,6,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [2,8,7,4,5,6,3,1] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [2,3,8,4,5,6,7,1] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [2,3,7,4,5,6,8,1] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,6,3,2,1] => [2,3,6,4,5,8,7,1] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [2,3,6,4,5,7,8,1] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [7,3,5,4,6,2,8,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [8,7,5,4,6,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,5,3,8,7,2,1] => [2,7,5,4,6,3,8,1] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [8,3,7,4,6,5,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,6,5,7,3,8,2,1] => [2,8,7,4,6,5,3,1] => [[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [2,3,7,4,6,5,8,1] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [8,3,5,4,7,6,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,6,7,5,3,8,2,1] => [2,8,5,4,7,6,3,1] => [[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,5,3,2,1] => [2,3,5,4,8,6,7,1] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [2,3,5,4,7,6,8,1] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [2,3,5,4,6,7,1,8] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [8,3,5,4,6,7,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [2,8,5,4,6,7,3,1] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [2,3,8,4,6,7,5,1] => [[.,[.,[[.,.],[[.,[.,.]],.]]]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [2,3,5,4,6,7,8,1] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [2,3,4,5,1,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [2,3,4,5,1,6,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [2,3,4,5,1,7,6,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [2,3,4,5,1,8,7,6] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [2,3,4,5,1,7,8,6] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [6,3,4,5,2,1,7,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [6,3,4,5,2,1,8,7] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [8,3,4,5,2,6,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [6,3,4,5,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [8,3,4,5,2,7,6,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [6,3,4,5,2,8,7,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [6,3,4,5,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => [2,6,4,5,3,1,7,8] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [7,6,4,5,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [7,6,4,5,3,2,8,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [2,8,4,5,3,6,7,1] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [2,3,6,5,4,1,7,8] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [2,3,6,5,4,1,8,7] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => [7,3,6,5,4,2,1,8] => [[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [7,3,6,5,4,2,8,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [2,7,6,5,4,3,1,8] => [[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,4,6,3,8,7,2,1] => [2,7,6,5,4,3,8,1] => [[.,[[[[[.,.],.],.],.],[.,.]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [2,3,7,5,4,6,1,8] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,4,6,7,3,2,8,1] => [8,3,7,5,4,6,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [2,8,7,5,4,6,3,1] => [[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [2,3,8,5,4,6,7,1] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,4,6,8,7,3,2,1] => [2,3,7,5,4,6,8,1] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,4,7,6,3,2,8,1] => [8,3,6,5,4,7,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,4,8,7,6,3,2,1] => [2,3,6,5,4,7,8,1] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [2,3,4,6,5,1,7,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [2,7,4,6,5,3,1,8] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,4,3,7,2,8,1] => [8,7,4,6,5,3,2,1] => [[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,4,3,7,8,2,1] => [2,8,4,6,5,3,7,1] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [2,7,4,6,5,3,8,1] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => [2,3,7,6,5,4,1,8] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,6,4,7,3,2,8,1] => [8,3,7,6,5,4,2,1] => [[[[.,.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,6,4,7,3,8,2,1] => [2,8,7,6,5,4,3,1] => [[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [2,3,8,6,5,4,7,1] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [2,3,7,6,5,4,8,1] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [2,3,4,7,5,6,1,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [2,3,4,8,5,6,7,1] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [2,3,4,7,5,6,8,1] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [2,3,4,6,5,7,1,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [2,3,4,8,5,7,6,1] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [2,3,4,6,5,8,7,1] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [2,3,4,6,5,7,8,1] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [2,3,4,5,6,1,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [7,3,4,5,6,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [2,7,4,5,6,3,1,8] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [2,8,4,5,6,3,7,1] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [2,7,4,5,6,3,8,1] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [2,3,7,5,6,4,1,8] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [8,3,7,5,6,4,2,1] => [[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [2,8,7,5,6,4,3,1] => [[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [2,3,8,5,6,4,7,1] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,5,4,8,7,3,2,1] => [2,3,7,5,6,4,8,1] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [2,3,4,7,6,5,1,8] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [8,3,4,7,6,5,2,1] => [[[[.,.],[.,[[[.,.],.],.]]],.],.]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [2,8,4,7,6,5,3,1] => [[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [2,3,8,7,6,5,4,1] => [[.,[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [2,3,4,8,6,5,7,1] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [2,3,4,7,6,5,8,1] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [2,3,4,5,7,6,1,8] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [8,3,4,5,7,6,2,1] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [2,3,8,5,7,6,4,1] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [2,3,4,8,7,6,5,1] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [2,3,4,5,8,6,7,1] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [2,3,4,5,7,6,8,1] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,1,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [8,3,4,5,6,7,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [2,8,4,5,6,7,3,1] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [2,3,8,5,6,7,4,1] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [2,3,4,8,6,7,5,1] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [2,3,4,5,8,7,6,1] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [2,3,4,5,6,8,7,1] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,1,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,2] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,1,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,6,5,4,3,2,1,9] => [2,3,4,5,6,8,7,1,9] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [1,3,4,5,6,7,9,8,2] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,2] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,9,10,1,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,9,8,1,10] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,7,5,4,3,2,1,9] => [2,3,4,5,7,6,8,1,9] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => [1,3,4,5,6,8,7,9,2] => [.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,10,9,2] => [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,11,2] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,8,4,3,2,1,9] => [2,3,4,8,5,6,7,1,9] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [3,2,4,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [2,3,4,5,6,7,1,9,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,3] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [1,4,3,5,6,7,8,9,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,1,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [1,3,4,5,6,7,8,2,9] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,3] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [2,3,4,5,6,7,8,1,10,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9] => [2,3,4,5,7,6,1,8,9] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,3] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [2,3,4,5,6,7,8,1,9,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [1,3,4,5,6,7,8,9,2,10] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,10,3] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[] => [] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [8,2,3,4,5,6,7,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,7,1] => [7,2,3,4,5,6,9,8,1] => [[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,6,1] => [6,2,3,4,5,9,7,8,1] => [[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,5,1] => [5,2,3,4,9,6,7,8,1] => [[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,4,1] => [4,2,3,9,5,6,7,8,1] => [[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [4,2,3,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,3,1] => [3,2,9,4,5,6,7,8,1] => [[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [9,3,2,4,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => [4,3,2,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [9,4,3,2,5,6,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [2,9,3,4,5,6,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,8,7,6,5,4,2,1] => [2,4,3,5,6,7,8,9,1] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [9,3,4,2,5,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,9,2,1] => [2,9,4,3,5,6,7,8,1] => [[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [2,3,9,4,5,6,7,8,1] => [[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [9,3,4,5,2,6,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => [2,3,9,5,4,6,7,8,1] => [[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [2,3,4,9,5,6,7,8,1] => [[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => [2,3,4,6,5,7,8,9,1] => [[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [2,3,4,9,6,5,7,8,1] => [[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [2,3,4,5,9,6,7,8,1] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,8,5,4,3,2,1] => [2,3,4,5,8,6,7,9,1] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,8,7,9,5,4,3,2,1] => [2,3,4,5,9,6,8,7,1] => [[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]],.]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,9,8,7,5,4,3,2,1] => [2,3,4,5,7,6,8,9,1] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,6,8,9,5,4,3,2,1] => [2,3,4,5,9,7,6,8,1] => [[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,6,9,8,5,4,3,2,1] => [2,3,4,5,8,7,6,9,1] => [[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,6,5,4,3,2,9,1] => [9,3,4,5,6,8,7,2,1] => [[[[.,.],[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => [2,3,4,5,6,9,7,8,1] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [2,3,4,5,6,8,7,9,1] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [9,3,4,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1] => [2,9,4,5,6,7,8,3,1] => [[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,7,6,5,4,9,3,2,1] => [2,3,9,5,6,7,8,4,1] => [[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,7,6,5,9,4,3,2,1] => [2,3,4,9,6,7,8,5,1] => [[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,7,6,9,5,4,3,2,1] => [2,3,4,5,9,7,8,6,1] => [[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => [2,3,4,5,6,9,8,7,1] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [2,3,4,5,6,7,9,8,1] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,1] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,3,4,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,9,7] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,9,8,7,6] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7] => [.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [1,2,3,4,9,7,6,8,5] => [.,[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6] => [.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [1,2,3,9,6,5,7,8,4] => [.,[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5] => [.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [1,2,9,5,4,6,7,8,3] => [.,[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4] => [.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [1,9,4,3,5,6,7,8,2] => [.,[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3] => [.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,3,4,5,6,7,8,9,2] => [.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,9,10,8] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,7,6] => [1,2,3,4,5,7,9,8,6] => [.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,7,8,9,6] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [10,3,2,4,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [1,2,3,4,5,6,7,8,10,11,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [1,2,3,4,5,6,8,9,10,7] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [1,2,3,4,6,7,8,9,5] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [1,2,3,4,5,7,8,9,10,6] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,8,3,9,2] => [1,9,8,4,5,6,7,3,2] => [.,[[[[[.,.],.],[.,[.,[.,.]]]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,3,2] => [1,3,9,4,5,6,7,8,2] => [.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,4] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [1,2,3,4,6,7,8,9,10,5] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,6,5,8,7,9] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => [1,3,2,4,5,6,8,9,7] => [.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,7,6,5,4,3,2,8,9] => [1,3,4,5,6,7,2,8,9] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,8,7] => [2,1,3,4,5,6,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,9,8,7,6,5] => [2,1,4,3,6,7,8,9,5] => [[.,.],[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [2,1,4,5,6,7,8,3,9] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,7,9,8] => [2,3,1,4,5,6,7,9,8] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => [2,3,1,5,4,6,7,8,9] => [[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => [2,3,1,5,4,7,6,9,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [2,3,1,5,6,7,8,9,4] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,3,2,1,6,5,7,8,9] => [2,3,4,1,6,5,7,8,9] => [[.,[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => [2,3,4,1,6,5,8,7,9] => [[.,[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [2,3,4,1,6,7,8,9,5] => [[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => [2,3,4,5,1,7,6,8,9] => [[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [2,3,4,5,1,7,8,9,6] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => [2,3,4,5,6,1,8,7,9] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [2,3,4,5,6,1,8,9,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,10,4] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [1,3,2,5,4,7,6,9,10,8] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [2,1,4,5,6,3,8,9,10,7] => [[.,.],[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [2,1,4,5,6,7,8,3,10,9] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => [2,3,1,5,4,7,6,9,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [2,3,1,5,6,7,8,9,10,4] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9] => [[.,[.,[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => [2,3,4,1,6,5,8,9,10,7] => [[.,[.,[.,.]]],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [2,3,4,1,6,7,8,5,10,9] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,5] => [[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,9,8,10] => [2,3,4,5,1,7,6,9,8,10] => [[.,[.,[.,[.,.]]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [2,3,4,5,1,7,8,9,10,6] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [2,3,4,5,6,1,8,9,10,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => [2,3,4,5,6,7,1,9,8,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [2,3,4,5,6,7,1,9,10,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,8,10,9,4,3,2,1] => [2,3,4,9,5,6,7,8,10,1] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [9,2,3,4,5,6,7,8,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => [2,3,4,5,6,7,10,9,8,1] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,8,7] => [.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,2,1,9] => [2,8,3,4,5,6,7,1,9] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [10,3,4,5,6,7,8,9,2,1] => [[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [11,3,4,5,6,7,8,9,10,2,1] => [[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,9,7,6,5,4,3,2,10,1] => [10,3,4,5,6,7,9,8,2,1] => [[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,10,9,1] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => [2,3,4,6,5,7,8,9,10,1] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,9,4,3] => [2,1,4,9,5,6,7,8,3] => [[.,.],[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,3,1] => [3,2,10,4,5,6,7,8,9,1] => [[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,11,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [3,2,1,5,6,7,8,9,4] => [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [1,8,3,4,5,6,7,9,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [7,2,3,4,5,6,1,9,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,4,5,6,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [6,2,3,4,5,1,8,9,7] => [[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [2,3,10,4,5,6,7,8,9,1] => [[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => [2,3,4,5,6,1,9,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [2,10,4,5,6,7,8,9,3,1] => [[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,8,7,6,5,4,10,3,2,1] => [2,3,10,5,6,7,8,9,4,1] => [[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,8,7,6,5,10,4,3,2,1] => [2,3,4,10,6,7,8,9,5,1] => [[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,8,7,6,10,5,4,3,2,1] => [2,3,4,5,10,7,8,9,6,1] => [[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,8,7,10,6,5,4,3,2,1] => [2,3,4,5,6,10,8,9,7,1] => [[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,10,6,1] => [6,2,3,4,5,10,7,8,9,1] => [[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,8,7,9] => [3,2,4,1,6,5,8,7,9] => [[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [3,2,1,5,4,7,6,9,8] => [[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => [3,2,4,1,6,5,8,7,10,9] => [[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,1,5,4,7,6,9,8,10] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,9,10,8,1] => [8,2,3,4,5,6,7,10,9,1] => [[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,8,9,10,7,1] => [7,2,3,4,5,6,10,8,9,1] => [[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,10,5,1] => [5,2,3,4,10,6,7,8,9,1] => [[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,10,4,1] => [4,2,3,10,5,6,7,8,9,1] => [[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [2,10,3,4,5,6,7,8,9,1] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [10,2,3,4,5,6,7,8,9,11,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,5,7,9,10,8,6,4,2] => [1,4,3,6,5,8,7,10,9,2] => [.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,3,6,7,5,9,10,8,4,2] => [1,4,3,8,7,6,5,10,9,2] => [.,[[[.,.],[[[[.,.],.],.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,5,3,7,9,10,8,6,2] => [1,6,5,4,3,8,7,10,9,2] => [.,[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,4,6,7,5,3,9,10,8,2] => [1,8,5,4,7,6,3,10,9,2] => [.,[[[[[.,.],.],[[.,.],.]],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,6,4,7,3,9,10,8,2] => [1,8,7,6,5,4,3,10,9,2] => [.,[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,4,6,8,9,7,5,3,10,2] => [1,10,5,4,7,6,9,8,3,2] => [.,[[[[[.,.],.],[[.,.],[[.,.],.]]],.],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,4,7,8,6,9,5,3,10,2] => [1,10,5,4,9,8,7,6,3,2] => [.,[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,8,9,7,3,10,2] => [1,10,7,6,5,4,9,8,3,2] => [.,[[[[[[[.,.],.],.],.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,5,7,8,6,4,9,3,10,2] => [1,10,9,6,5,8,7,4,3,2] => [.,[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,7,5,8,4,9,3,10,2] => [1,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,1,5,7,9,10,8,6,4] => [3,2,1,6,5,8,7,10,9,4] => [[[.,.],.],[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,7,5,9,10,8,4] => [3,2,1,8,7,6,5,10,9,4] => [[[.,.],.],[[[[[.,.],.],.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,6,8,9,7,5,10,4] => [3,2,1,10,7,6,9,8,5,4] => [[[.,.],.],[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,7,8,6,9,5,10,4] => [3,2,1,10,9,8,7,6,5,4] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1,7,9,10,8,6] => [3,2,5,4,1,8,7,10,9,6] => [[[.,.],[[.,.],.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [2,4,5,3,1,8,9,7,10,6] => [3,2,5,4,1,10,9,8,7,6] => [[[.,.],[[.,.],.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,2,5,1,7,9,10,8,6] => [5,4,3,2,1,8,7,10,9,6] => [[[[[.,.],.],.],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1,8,9,7,10,6] => [5,4,3,2,1,10,9,8,7,6] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [2,4,6,7,5,3,1,9,10,8] => [3,2,5,4,7,6,1,10,9,8] => [[[.,.],[[.,.],[[.,.],.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [2,5,6,4,7,3,1,9,10,8] => [3,2,7,6,5,4,1,10,9,8] => [[[.,.],[[[[.,.],.],.],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,6,7,5,1,9,10,8] => [5,4,3,2,7,6,1,10,9,8] => [[[[[.,.],.],.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [3,5,6,4,2,7,1,9,10,8] => [7,4,3,6,5,2,1,10,9,8] => [[[[[.,.],.],[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,3,6,2,7,1,9,10,8] => [7,6,5,4,3,2,1,10,9,8] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,3,5,7,9,11,12,10,8,6,4,2] => [1,4,3,6,5,8,7,10,9,12,11,2] => [.,[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [1,3,5,8,9,7,11,12,10,6,4,2] => [1,4,3,6,5,10,9,8,7,12,11,2] => [.,[[[.,.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,6,7,5,9,11,12,10,8,4,2] => [1,4,3,8,7,6,5,10,9,12,11,2] => [.,[[[.,.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [1,3,6,8,9,7,5,11,12,10,4,2] => [1,4,3,10,7,6,9,8,5,12,11,2] => [.,[[[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [1,3,7,8,6,9,5,11,12,10,4,2] => [1,4,3,10,9,8,7,6,5,12,11,2] => [.,[[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,4,5,3,7,9,11,12,10,8,6,2] => [1,6,5,4,3,8,7,10,9,12,11,2] => [.,[[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,4,5,3,8,9,7,11,12,10,6,2] => [1,6,5,4,3,10,9,8,7,12,11,2] => [.,[[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,9,11,12,10,8,2] => [1,8,5,4,7,6,3,10,9,12,11,2] => [.,[[[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,5,6,4,7,3,9,11,12,10,8,2] => [1,8,7,6,5,4,3,10,9,12,11,2] => [.,[[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => [1,4,6,8,9,7,5,3,11,12,10,2] => [1,10,5,4,7,6,9,8,3,12,11,2] => [.,[[[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [1,4,7,8,6,9,5,3,11,12,10,2] => [1,10,5,4,9,8,7,6,3,12,11,2] => [.,[[[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,4,8,9,7,3,11,12,10,2] => [1,10,7,6,5,4,9,8,3,12,11,2] => [.,[[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,7,8,6,4,9,3,11,12,10,2] => [1,10,9,6,5,8,7,4,3,12,11,2] => [.,[[[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,6,7,5,8,4,9,3,11,12,10,2] => [1,10,9,8,7,6,5,4,3,12,11,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [1,4,6,8,10,11,9,7,5,3,12,2] => [1,12,5,4,7,6,9,8,11,10,3,2] => [.,[[[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],.],.]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [1,4,6,9,10,8,11,7,5,3,12,2] => [1,12,5,4,7,6,11,10,9,8,3,2] => [.,[[[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],.],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [1,4,7,8,6,10,11,9,5,3,12,2] => [1,12,5,4,9,8,7,6,11,10,3,2] => [.,[[[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],.],.]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [1,4,7,9,10,8,6,11,5,3,12,2] => [1,12,5,4,11,8,7,10,9,6,3,2] => [.,[[[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],.],.]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [1,4,8,9,7,10,6,11,5,3,12,2] => [1,12,5,4,11,10,9,8,7,6,3,2] => [.,[[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,5,6,4,8,10,11,9,7,3,12,2] => [1,12,7,6,5,4,9,8,11,10,3,2] => [.,[[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,5,6,4,9,10,8,11,7,3,12,2] => [1,12,7,6,5,4,11,10,9,8,3,2] => [.,[[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,8,6,4,10,11,9,3,12,2] => [1,12,9,6,5,8,7,4,11,10,3,2] => [.,[[[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],.],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,6,7,5,8,4,10,11,9,3,12,2] => [1,12,9,8,7,6,5,4,11,10,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [1,5,7,9,10,8,6,4,11,3,12,2] => [1,12,11,6,5,8,7,10,9,4,3,2] => [.,[[[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],.],.]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [1,5,8,9,7,10,6,4,11,3,12,2] => [1,12,11,6,5,10,9,8,7,4,3,2] => [.,[[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,6,7,5,9,10,8,4,11,3,12,2] => [1,12,11,8,7,6,5,10,9,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [1,6,8,9,7,5,10,4,11,3,12,2] => [1,12,11,10,7,6,9,8,5,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,7,8,6,9,5,10,4,11,3,12,2] => [1,12,11,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,1,5,7,9,11,12,10,8,6,4] => [3,2,1,6,5,8,7,10,9,12,11,4] => [[[.,.],.],[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [2,3,1,5,8,9,7,11,12,10,6,4] => [3,2,1,6,5,10,9,8,7,12,11,4] => [[[.,.],.],[[[.,.],[[[[.,.],.],.],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,1,6,7,5,9,11,12,10,8,4] => [3,2,1,8,7,6,5,10,9,12,11,4] => [[[.,.],.],[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,9,7,5,11,12,10,4] => [3,2,1,10,7,6,9,8,5,12,11,4] => [[[.,.],.],[[[[[.,.],.],[[.,.],.]],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [2,3,1,7,8,6,9,5,11,12,10,4] => [3,2,1,10,9,8,7,6,5,12,11,4] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [2,3,1,6,8,10,11,9,7,5,12,4] => [3,2,1,12,7,6,9,8,11,10,5,4] => [[[.,.],.],[[[[[.,.],.],[[.,.],[[.,.],.]]],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [2,3,1,6,9,10,8,11,7,5,12,4] => [3,2,1,12,7,6,11,10,9,8,5,4] => [[[.,.],.],[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,7,8,6,10,11,9,5,12,4] => [3,2,1,12,9,8,7,6,11,10,5,4] => [[[.,.],.],[[[[[[[.,.],.],.],.],[[.,.],.]],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [2,3,1,7,9,10,8,6,11,5,12,4] => [3,2,1,12,11,8,7,10,9,6,5,4] => [[[.,.],.],[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,3,1,8,9,7,10,6,11,5,12,4] => [3,2,1,12,11,10,9,8,7,6,5,4] => [[[.,.],.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,5,3,1,7,9,11,12,10,8,6] => [3,2,5,4,1,8,7,10,9,12,11,6] => [[[.,.],[[.,.],.]],[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,1,8,9,7,11,12,10,6] => [3,2,5,4,1,10,9,8,7,12,11,6] => [[[.,.],[[.,.],.]],[[[[[.,.],.],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,5,3,1,8,10,11,9,7,12,6] => [3,2,5,4,1,12,9,8,11,10,7,6] => [[[.,.],[[.,.],.]],[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,4,5,3,1,9,10,8,11,7,12,6] => [3,2,5,4,1,12,11,10,9,8,7,6] => [[[.,.],[[.,.],.]],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,2,5,1,7,9,11,12,10,8,6] => [5,4,3,2,1,8,7,10,9,12,11,6] => [[[[[.,.],.],.],.],[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,5,1,8,9,7,11,12,10,6] => [5,4,3,2,1,10,9,8,7,12,11,6] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,2,5,1,8,10,11,9,7,12,6] => [5,4,3,2,1,12,9,8,11,10,7,6] => [[[[[.,.],.],.],.],[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,4,2,5,1,9,10,8,11,7,12,6] => [5,4,3,2,1,12,11,10,9,8,7,6] => [[[[[.,.],.],.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,7,5,3,1,9,11,12,10,8] => [3,2,5,4,7,6,1,10,9,12,11,8] => [[[.,.],[[.,.],[[.,.],.]]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [2,4,6,7,5,3,1,10,11,9,12,8] => [3,2,5,4,7,6,1,12,11,10,9,8] => [[[.,.],[[.,.],[[.,.],.]]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5,6,4,7,3,1,9,11,12,10,8] => [3,2,7,6,5,4,1,10,9,12,11,8] => [[[.,.],[[[[.,.],.],.],.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5,6,4,7,3,1,10,11,9,12,8] => [3,2,7,6,5,4,1,12,11,10,9,8] => [[[.,.],[[[[.,.],.],.],.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1,9,11,12,10,8] => [5,4,3,2,7,6,1,10,9,12,11,8] => [[[[[.,.],.],.],[[.,.],.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,1,10,11,9,12,8] => [5,4,3,2,7,6,1,12,11,10,9,8] => [[[[[.,.],.],.],[[.,.],.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5,6,4,2,7,1,9,11,12,10,8] => [7,4,3,6,5,2,1,10,9,12,11,8] => [[[[[.,.],.],[[.,.],.]],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5,6,4,2,7,1,10,11,9,12,8] => [7,4,3,6,5,2,1,12,11,10,9,8] => [[[[[.,.],.],[[.,.],.]],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,5,3,6,2,7,1,9,11,12,10,8] => [7,6,5,4,3,2,1,10,9,12,11,8] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1,10,11,9,12,8] => [7,6,5,4,3,2,1,12,11,10,9,8] => [[[[[[[.,.],.],.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [2,4,6,8,9,7,5,3,1,11,12,10] => [3,2,5,4,7,6,9,8,1,12,11,10] => [[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [2,4,7,8,6,9,5,3,1,11,12,10] => [3,2,5,4,9,8,7,6,1,12,11,10] => [[[.,.],[[.,.],[[[[.,.],.],.],.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [2,5,6,4,8,9,7,3,1,11,12,10] => [3,2,7,6,5,4,9,8,1,12,11,10] => [[[.,.],[[[[.,.],.],.],[[.,.],.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [2,5,7,8,6,4,9,3,1,11,12,10] => [3,2,9,6,5,8,7,4,1,12,11,10] => [[[.,.],[[[[.,.],.],[[.,.],.]],.]],[[[.,.],.],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [2,6,7,5,8,4,9,3,1,11,12,10] => [3,2,9,8,7,6,5,4,1,12,11,10] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [3,4,2,6,8,9,7,5,1,11,12,10] => [5,4,3,2,7,6,9,8,1,12,11,10] => [[[[[.,.],.],.],[[.,.],[[.,.],.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,7,8,6,9,5,1,11,12,10] => [5,4,3,2,9,8,7,6,1,12,11,10] => [[[[[.,.],.],.],[[[[.,.],.],.],.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,6,4,2,8,9,7,1,11,12,10] => [7,4,3,6,5,2,9,8,1,12,11,10] => [[[[[.,.],.],[[.,.],.]],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,5,3,6,2,8,9,7,1,11,12,10] => [7,6,5,4,3,2,9,8,1,12,11,10] => [[[[[[[.,.],.],.],.],.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [3,5,7,8,6,4,2,9,1,11,12,10] => [9,4,3,6,5,8,7,2,1,12,11,10] => [[[[[.,.],.],[[.,.],[[.,.],.]]],.],[[[.,.],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [3,6,7,5,8,4,2,9,1,11,12,10] => [9,4,3,8,7,6,5,2,1,12,11,10] => [[[[[.,.],.],[[[[.,.],.],.],.]],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,5,3,7,8,6,2,9,1,11,12,10] => [9,6,5,4,3,8,7,2,1,12,11,10] => [[[[[[[.,.],.],.],.],[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,6,7,5,3,8,2,9,1,11,12,10] => [9,8,5,4,7,6,3,2,1,12,11,10] => [[[[[[[.,.],.],.],[[.,.],.]],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [5,6,4,7,3,8,2,9,1,11,12,10] => [9,8,7,6,5,4,3,2,1,12,11,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,9,10,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,10,9,1] => [[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,11,10,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,10,11,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [1,2,5,4,6,7,8,9,3] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [1,2,3,6,5,7,8,9,4] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [1,2,3,4,7,6,8,9,5] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,8,7,9,6] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => [2,3,4,5,6,7,8,9,1,11,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [2,3,4,10,5,6,7,8,9,1] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9] => [2,3,4,6,5,1,7,8,9] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8,9] => [2,3,5,4,1,6,7,8,9] => [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [2,3,4,5,6,7,10,8,9,1] => [[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [2,3,4,5,10,6,7,8,9,1] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [2,3,4,5,6,10,7,8,9,1] => [[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => [4,3,2,5,6,7,8,9,10,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9,10] => [2,4,3,1,5,6,7,8,9,10] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [1,3,2,5,4,7,6,9,8,11,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7,10,9] => [2,4,3,1,6,5,8,7,10,9] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7,10,9] => [6,3,2,5,4,1,8,7,10,9] => [[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,7,6,8,1,10,9] => [8,3,2,5,4,7,6,1,10,9] => [[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => [10,3,2,5,4,7,6,9,8,1] => [[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,10,7] => [2,1,4,3,6,5,10,9,8,7] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,6,9,8,10,5] => [2,1,4,3,10,7,6,9,8,5] => [[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,9,8,10,3] => [2,1,10,5,4,7,6,9,8,3] => [[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,9,8] => [.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,5,7,9,8,6,4,2] => [1,4,3,6,5,8,7,9,2] => [.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7,10,9] => [6,5,4,3,2,1,8,7,10,9] => [[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7,10,9] => [2,1,6,5,4,3,8,7,10,9] => [[.,.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,6,5,7,4,8,3,10,9] => [2,1,8,7,6,5,4,3,10,9] => [[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,6,5,7,4,8,1,10,9] => [8,3,2,7,6,5,4,1,10,9] => [[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,6,5,7,2,8,1,10,9] => [8,7,4,3,6,5,2,1,10,9] => [[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,4,6,3,7,2,8,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,6,8,5,10,9] => [2,1,4,3,8,7,6,5,10,9] => [[.,.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,7,6,8,5,10,9] => [4,3,2,1,8,7,6,5,10,9] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,7,6,8,1,10,9] => [8,5,4,3,2,7,6,1,10,9] => [[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,7,6,8,3,10,9] => [2,1,8,5,4,7,6,3,10,9] => [[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,8,7,9,6,10,5] => [2,1,4,3,10,9,8,7,6,5] => [[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,2,4,1,8,7,9,6,10,5] => [4,3,2,1,10,9,8,7,6,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,8,7,9,6,10,1] => [10,5,4,3,2,9,8,7,6,1] => [[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,8,7,9,6,10,3] => [2,1,10,5,4,9,8,7,6,3] => [[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,8,7,9,6,10,1] => [10,3,2,5,4,9,8,7,6,1] => [[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,8,7,9,2,10,1] => [10,9,4,3,6,5,8,7,2,1] => [[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,4,6,3,8,7,9,2,10,1] => [10,9,6,5,4,3,8,7,2,1] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,7,6,8,5,9,2,10,1] => [10,9,4,3,8,7,6,5,2,1] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,7,6,8,3,9,2,10,1] => [10,9,8,5,4,7,6,3,2,1] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,8,7,9,4,10,3] => [2,1,10,9,6,5,8,7,4,3] => [[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,8,7,9,4,10,1] => [10,3,2,9,6,5,8,7,4,1] => [[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,10,1] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,7,6,8,5,9,4,10,3] => [2,1,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,7,6,8,5,9,4,10,1] => [10,3,2,9,8,7,6,5,4,1] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,6,5,9,8,10,7] => [4,3,2,1,6,5,10,9,8,7] => [[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,3,5,2,6,1,9,8,10,7] => [6,5,4,3,2,1,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3,9,8,10,7] => [2,1,6,5,4,3,10,9,8,7] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,5,4,6,1,9,8,10,7] => [6,3,2,5,4,1,10,9,8,7] => [[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,6,5,7,4,9,8,10,3] => [2,1,10,7,6,5,4,9,8,3] => [[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,6,5,7,4,9,8,10,1] => [10,3,2,7,6,5,4,9,8,1] => [[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,6,5,7,2,9,8,10,1] => [10,7,4,3,6,5,2,9,8,1] => [[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,4,6,3,7,2,9,8,10,1] => [10,7,6,5,4,3,2,9,8,1] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,7,6,9,8,10,5] => [4,3,2,1,10,7,6,9,8,5] => [[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,9,8,10,1] => [10,5,4,3,2,7,6,9,8,1] => [[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9,12,11] => [4,3,2,1,6,5,8,7,10,9,12,11] => [[[[.,.],.],.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7,10,9,12,11] => [6,5,4,3,2,1,8,7,10,9,12,11] => [[[[[[.,.],.],.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7,10,9,12,11] => [2,1,6,5,4,3,8,7,10,9,12,11] => [[.,.],[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7,10,9,12,11] => [6,3,2,5,4,1,8,7,10,9,12,11] => [[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,6,5,7,4,8,3,10,9,12,11] => [2,1,8,7,6,5,4,3,10,9,12,11] => [[.,.],[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,6,5,7,4,8,1,10,9,12,11] => [8,3,2,7,6,5,4,1,10,9,12,11] => [[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,3,6,5,7,2,8,1,10,9,12,11] => [8,7,4,3,6,5,2,1,10,9,12,11] => [[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,4,6,3,7,2,8,1,10,9,12,11] => [8,7,6,5,4,3,2,1,10,9,12,11] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,7,6,8,5,10,9,12,11] => [2,1,4,3,8,7,6,5,10,9,12,11] => [[.,.],[[.,.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,7,6,8,5,10,9,12,11] => [4,3,2,1,8,7,6,5,10,9,12,11] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,3,5,2,7,6,8,1,10,9,12,11] => [8,5,4,3,2,7,6,1,10,9,12,11] => [[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,7,6,8,3,10,9,12,11] => [2,1,8,5,4,7,6,3,10,9,12,11] => [[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,5,4,7,6,8,1,10,9,12,11] => [8,3,2,5,4,7,6,1,10,9,12,11] => [[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,8,7,9,6,10,5,12,11] => [2,1,4,3,10,9,8,7,6,5,12,11] => [[.,.],[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,8,7,9,6,10,5,12,11] => [4,3,2,1,10,9,8,7,6,5,12,11] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,8,7,9,6,10,1,12,11] => [10,5,4,3,2,9,8,7,6,1,12,11] => [[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,8,7,9,6,10,3,12,11] => [2,1,10,5,4,9,8,7,6,3,12,11] => [[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,8,7,9,6,10,1,12,11] => [10,3,2,5,4,9,8,7,6,1,12,11] => [[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,6,5,8,7,9,2,10,1,12,11] => [10,9,4,3,6,5,8,7,2,1,12,11] => [[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,4,6,3,8,7,9,2,10,1,12,11] => [10,9,6,5,4,3,8,7,2,1,12,11] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,7,6,8,5,9,2,10,1,12,11] => [10,9,4,3,8,7,6,5,2,1,12,11] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,4,7,6,8,3,9,2,10,1,12,11] => [10,9,8,5,4,7,6,3,2,1,12,11] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,6,5,8,7,9,4,10,3,12,11] => [2,1,10,9,6,5,8,7,4,3,12,11] => [[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,6,5,8,7,9,4,10,1,12,11] => [10,3,2,9,6,5,8,7,4,1,12,11] => [[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [6,5,7,4,8,3,9,2,10,1,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,7,6,8,5,9,4,10,3,12,11] => [2,1,10,9,8,7,6,5,4,3,12,11] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,7,6,8,5,9,4,10,1,12,11] => [10,3,2,9,8,7,6,5,4,1,12,11] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,6,5,9,8,10,7,12,11] => [2,1,4,3,6,5,10,9,8,7,12,11] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5,9,8,10,7,12,11] => [4,3,2,1,6,5,10,9,8,7,12,11] => [[[[.,.],.],.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,9,8,10,7,12,11] => [6,5,4,3,2,1,10,9,8,7,12,11] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,9,8,10,7,12,11] => [2,1,6,5,4,3,10,9,8,7,12,11] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,9,8,10,7,12,11] => [6,3,2,5,4,1,10,9,8,7,12,11] => [[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,6,5,7,4,9,8,10,3,12,11] => [2,1,10,7,6,5,4,9,8,3,12,11] => [[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,6,5,7,4,9,8,10,1,12,11] => [10,3,2,7,6,5,4,9,8,1,12,11] => [[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,3,6,5,7,2,9,8,10,1,12,11] => [10,7,4,3,6,5,2,9,8,1,12,11] => [[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [5,4,6,3,7,2,9,8,10,1,12,11] => [10,7,6,5,4,3,2,9,8,1,12,11] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,6,9,8,10,5,12,11] => [2,1,4,3,10,7,6,9,8,5,12,11] => [[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,7,6,9,8,10,5,12,11] => [4,3,2,1,10,7,6,9,8,5,12,11] => [[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,7,6,9,8,10,1,12,11] => [10,5,4,3,2,7,6,9,8,1,12,11] => [[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,7,6,9,8,10,3,12,11] => [2,1,10,5,4,7,6,9,8,3,12,11] => [[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,7,6,9,8,10,1,12,11] => [10,3,2,5,4,7,6,9,8,1,12,11] => [[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,6,5,10,9,11,8,12,7] => [2,1,4,3,6,5,12,11,10,9,8,7] => [[.,.],[[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,2,4,1,6,5,10,9,11,8,12,7] => [4,3,2,1,6,5,12,11,10,9,8,7] => [[[[.,.],.],.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1,10,9,11,8,12,7] => [6,5,4,3,2,1,12,11,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,6,3,10,9,11,8,12,7] => [2,1,6,5,4,3,12,11,10,9,8,7] => [[.,.],[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,6,1,10,9,11,8,12,7] => [6,3,2,5,4,1,12,11,10,9,8,7] => [[[[.,.],.],[[.,.],.]],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,10,9,11,8,12,3] => [2,1,12,7,6,5,4,11,10,9,8,3] => [[.,.],[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,10,9,11,8,12,1] => [12,3,2,7,6,5,4,11,10,9,8,1] => [[[[.,.],.],[[[[.,.],.],.],[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,10,9,11,8,12,1] => [12,7,4,3,6,5,2,11,10,9,8,1] => [[[[[[.,.],.],.],[[.,.],.]],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,10,9,11,8,12,1] => [12,7,6,5,4,3,2,11,10,9,8,1] => [[[[[[[[.,.],.],.],.],.],.],[[[[.,.],.],.],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,7,6,10,9,11,8,12,5] => [2,1,4,3,12,7,6,11,10,9,8,5] => [[.,.],[[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,4,1,7,6,10,9,11,8,12,5] => [4,3,2,1,12,7,6,11,10,9,8,5] => [[[[.,.],.],.],[[[[.,.],.],[[[[.,.],.],.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,7,6,10,9,11,8,12,1] => [12,5,4,3,2,7,6,11,10,9,8,1] => [[[[[[.,.],.],.],.],[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,7,6,10,9,11,8,12,3] => [2,1,12,5,4,7,6,11,10,9,8,3] => [[.,.],[[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,7,6,10,9,11,8,12,1] => [12,3,2,5,4,7,6,11,10,9,8,1] => [[[[.,.],.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,8,7,10,9,11,4,12,3] => [2,1,12,11,6,5,8,7,10,9,4,3] => [[.,.],[[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,8,7,10,9,11,4,12,1] => [12,3,2,11,6,5,8,7,10,9,4,1] => [[[[.,.],.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,10,9,11,2,12,1] => [12,11,8,7,6,5,4,3,10,9,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]],.],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,7,6,8,5,10,9,11,4,12,3] => [2,1,12,11,8,7,6,5,10,9,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,7,6,8,5,10,9,11,4,12,1] => [12,3,2,11,8,7,6,5,10,9,4,1] => [[[[.,.],.],[[[[[[.,.],.],.],.],[[.,.],.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,6,5,9,8,10,7,11,4,12,3] => [2,1,12,11,6,5,10,9,8,7,4,3] => [[.,.],[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,6,5,9,8,10,7,11,4,12,1] => [12,3,2,11,6,5,10,9,8,7,4,1] => [[[[.,.],.],[[[[.,.],.],[[[[.,.],.],.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,9,8,10,3,11,2,12,1] => [12,11,10,7,6,5,4,9,8,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.],.],.]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,7,6,9,8,10,5,11,4,12,3] => [2,1,12,11,10,7,6,9,8,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,7,6,9,8,10,5,11,4,12,1] => [12,3,2,11,10,7,6,9,8,5,4,1] => [[[[.,.],.],[[[[[[.,.],.],.],[[.,.],.]],.],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,8,7,10,9,11,2,12,1] => [12,11,4,3,6,5,8,7,10,9,2,1] => [[[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,7,6,8,5,10,9,11,2,12,1] => [12,11,4,3,8,7,6,5,10,9,2,1] => [[[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,4,6,3,8,7,10,9,11,2,12,1] => [12,11,6,5,4,3,8,7,10,9,2,1] => [[[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,4,7,6,8,3,10,9,11,2,12,1] => [12,11,8,5,4,7,6,3,10,9,2,1] => [[[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]],.],.]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,8,7,9,4,10,3,11,2,12,1] => [12,11,10,9,6,5,8,7,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,6,5,9,8,10,7,11,2,12,1] => [12,11,4,3,6,5,10,9,8,7,2,1] => [[[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,7,6,9,8,10,5,11,2,12,1] => [12,11,4,3,10,7,6,9,8,5,2,1] => [[[[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,9,8,10,7,11,2,12,1] => [12,11,6,5,4,3,10,9,8,7,2,1] => [[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,7,6,9,8,10,3,11,2,12,1] => [12,11,10,5,4,7,6,9,8,3,2,1] => [[[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.],.],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,8,7,10,9,11,6,12,5] => [2,1,4,3,12,11,8,7,10,9,6,5] => [[.,.],[[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,4,1,8,7,10,9,11,6,12,5] => [4,3,2,1,12,11,8,7,10,9,6,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],[[.,.],.]],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,8,7,10,9,11,6,12,1] => [12,5,4,3,2,11,8,7,10,9,6,1] => [[[[[[.,.],.],.],.],[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,8,7,10,9,11,6,12,3] => [2,1,12,5,4,11,8,7,10,9,6,3] => [[.,.],[[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,8,7,10,9,11,6,12,1] => [12,3,2,5,4,11,8,7,10,9,6,1] => [[[[.,.],.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,8,7,9,6,10,5,11,4,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,8,7,9,6,10,5,11,4,12,1] => [12,3,2,11,10,9,8,7,6,5,4,1] => [[[[.,.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,8,7,9,6,10,5,11,2,12,1] => [12,11,4,3,10,9,8,7,6,5,2,1] => [[[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]],.],.]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,8,7,9,6,10,3,11,2,12,1] => [12,11,10,5,4,9,8,7,6,3,2,1] => [[[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.],.],.]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,4,3,9,8,10,7,11,6,12,5] => [2,1,4,3,12,11,10,9,8,7,6,5] => [[.,.],[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,4,1,9,8,10,7,11,6,12,5] => [4,3,2,1,12,11,10,9,8,7,6,5] => [[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,5,2,9,8,10,7,11,6,12,1] => [12,5,4,3,2,11,10,9,8,7,6,1] => [[[[[[.,.],.],.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,5,4,9,8,10,7,11,6,12,3] => [2,1,12,5,4,11,10,9,8,7,6,3] => [[.,.],[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,5,4,9,8,10,7,11,6,12,1] => [12,3,2,5,4,11,10,9,8,7,6,1] => [[[[.,.],.],[[.,.],[[[[[[.,.],.],.],.],.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,8,7,11,10,12,9] => [2,1,4,3,6,5,8,7,12,11,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,6,5,8,7,11,10,12,9] => [4,3,2,1,6,5,8,7,12,11,10,9] => [[[[.,.],.],.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [4,3,5,2,6,1,8,7,11,10,12,9] => [6,5,4,3,2,1,8,7,12,11,10,9] => [[[[[[.,.],.],.],.],.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3,8,7,11,10,12,9] => [2,1,6,5,4,3,8,7,12,11,10,9] => [[.,.],[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,2,5,4,6,1,8,7,11,10,12,9] => [6,3,2,5,4,1,8,7,12,11,10,9] => [[[[.,.],.],[[.,.],.]],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3,11,10,12,9] => [2,1,8,7,6,5,4,3,12,11,10,9] => [[.,.],[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1,11,10,12,9] => [8,3,2,7,6,5,4,1,12,11,10,9] => [[[[.,.],.],[[[[.,.],.],.],.]],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1,11,10,12,9] => [8,7,4,3,6,5,2,1,12,11,10,9] => [[[[[[.,.],.],.],[[.,.],.]],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1,11,10,12,9] => [8,7,6,5,4,3,2,1,12,11,10,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5,11,10,12,9] => [2,1,4,3,8,7,6,5,12,11,10,9] => [[.,.],[[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5,11,10,12,9] => [4,3,2,1,8,7,6,5,12,11,10,9] => [[[[.,.],.],.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1,11,10,12,9] => [8,5,4,3,2,7,6,1,12,11,10,9] => [[[[[[.,.],.],.],.],[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3,11,10,12,9] => [2,1,8,5,4,7,6,3,12,11,10,9] => [[.,.],[[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1,11,10,12,9] => [8,3,2,5,4,7,6,1,12,11,10,9] => [[[[.,.],.],[[.,.],[[.,.],.]]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,8,7,9,6,11,10,12,5] => [2,1,4,3,12,9,8,7,6,11,10,5] => [[.,.],[[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,8,7,9,6,11,10,12,5] => [4,3,2,1,12,9,8,7,6,11,10,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,8,7,9,6,11,10,12,1] => [12,5,4,3,2,9,8,7,6,11,10,1] => [[[[[[.,.],.],.],.],[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,8,7,9,6,11,10,12,3] => [2,1,12,5,4,9,8,7,6,11,10,3] => [[.,.],[[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,8,7,9,6,11,10,12,1] => [12,3,2,5,4,9,8,7,6,11,10,1] => [[[[.,.],.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,6,5,8,7,9,2,11,10,12,1] => [12,9,4,3,6,5,8,7,2,11,10,1] => [[[[[[.,.],.],.],[[.,.],[[.,.],.]]],[[.,.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,4,6,3,8,7,9,2,11,10,12,1] => [12,9,6,5,4,3,8,7,2,11,10,1] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,7,6,8,5,9,2,11,10,12,1] => [12,9,4,3,8,7,6,5,2,11,10,1] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],[[.,.],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,4,7,6,8,3,9,2,11,10,12,1] => [12,9,8,5,4,7,6,3,2,11,10,1] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],[[.,.],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,6,5,8,7,9,4,11,10,12,3] => [2,1,12,9,6,5,8,7,4,11,10,3] => [[.,.],[[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,6,5,8,7,9,4,11,10,12,1] => [12,3,2,9,6,5,8,7,4,11,10,1] => [[[[.,.],.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,11,10,12,1] => [12,9,8,7,6,5,4,3,2,11,10,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,7,6,8,5,9,4,11,10,12,3] => [2,1,12,9,8,7,6,5,4,11,10,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,7,6,8,5,9,4,11,10,12,1] => [12,3,2,9,8,7,6,5,4,11,10,1] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,11,10,12,7] => [2,1,4,3,6,5,12,9,8,11,10,7] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,6,5,9,8,11,10,12,7] => [4,3,2,1,6,5,12,9,8,11,10,7] => [[[[.,.],.],.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,6,1,9,8,11,10,12,7] => [6,5,4,3,2,1,12,9,8,11,10,7] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,6,3,9,8,11,10,12,7] => [2,1,6,5,4,3,12,9,8,11,10,7] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1,9,8,11,10,12,7] => [6,3,2,5,4,1,12,9,8,11,10,7] => [[[[.,.],.],[[.,.],.]],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,6,5,7,4,9,8,11,10,12,3] => [2,1,12,7,6,5,4,9,8,11,10,3] => [[.,.],[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,6,5,7,4,9,8,11,10,12,1] => [12,3,2,7,6,5,4,9,8,11,10,1] => [[[[.,.],.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,3,6,5,7,2,9,8,11,10,12,1] => [12,7,4,3,6,5,2,9,8,11,10,1] => [[[[[[.,.],.],.],[[.,.],.]],[[.,.],[[.,.],.]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [5,4,6,3,7,2,9,8,11,10,12,1] => [12,7,6,5,4,3,2,9,8,11,10,1] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,6,9,8,11,10,12,5] => [2,1,4,3,12,7,6,9,8,11,10,5] => [[.,.],[[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,7,6,9,8,11,10,12,5] => [4,3,2,1,12,7,6,9,8,11,10,5] => [[[[.,.],.],.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,9,8,11,10,12,1] => [12,5,4,3,2,7,6,9,8,11,10,1] => [[[[[[.,.],.],.],.],[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,9,8,11,10,12,3] => [2,1,12,5,4,7,6,9,8,11,10,3] => [[.,.],[[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,11,10,12,1] => [12,3,2,5,4,7,6,9,8,11,10,1] => [[[[.,.],.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => [2,1,5,4,6,3,8,7,10,9] => [[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => [2,1,4,3,7,6,8,5,10,9] => [[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [2,1,4,3,6,5,9,8,10,7] => [[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,4,6,3,7,2,8,1,9] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,5,7,4,8,3,9,2] => [1,9,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,1,7,8,9,10,6,5,4,3] => [2,1,4,5,6,10,7,8,9,3] => [[.,.],[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,6,5,9,10,8,7] => [2,4,3,1,6,5,8,10,9,7] => [[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [5,6,4,7,3,8,2,10,9,1] => [9,8,7,6,5,4,3,2,10,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,5,3,6,2,7,1,8,9] => [7,6,5,4,3,2,1,8,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [5,7,6,4,8,3,9,2,10,1] => [10,9,8,6,5,7,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
Map
to 312-avoiding permutation
Description
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.