Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
[1,0] => [1] => [1] => [.,.]
[1,0,1,0] => [2,1] => [2,1] => [[.,.],.]
[1,1,0,0] => [1,2] => [1,2] => [.,[.,.]]
[1,0,1,0,1,0] => [2,3,1] => [3,2,1] => [[[.,.],.],.]
[1,0,1,1,0,0] => [2,1,3] => [2,1,3] => [[.,.],[.,.]]
[1,1,0,0,1,0] => [1,3,2] => [1,3,2] => [.,[[.,.],.]]
[1,1,0,1,0,0] => [3,1,2] => [3,1,2] => [[.,[.,.]],.]
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [4,2,3,1] => [[[.,.],[.,.]],.]
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [2,1,4,3] => [[.,.],[[.,.],.]]
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [4,2,1,3] => [[[.,.],[.,.]],.]
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [1,4,3,2] => [.,[[[.,.],.],.]]
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [3,4,1,2] => [[.,[.,.]],[.,.]]
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [4,1,3,2] => [[.,[[.,.],.]],.]
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [3,1,2,4] => [[.,[.,.]],[.,.]]
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,2,3] => [.,[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [4,1,2,3] => [[.,[.,[.,.]]],.]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [5,2,3,1,4] => [[[.,.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [5,2,1,4,3] => [[[.,.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [4,2,1,3,5] => [[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [5,2,1,3,4] => [[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [1,5,3,2,4] => [.,[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [5,1,3,4,2] => [[.,[[.,.],[.,.]]],.]
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [4,1,3,2,5] => [[.,[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [3,1,2,5,4] => [[.,[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [3,5,1,2,4] => [[.,[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [5,1,3,2,4] => [[.,[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [4,1,5,2,3] => [[.,[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [4,5,2,1,3] => [[[.,.],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [5,1,2,4,3] => [[.,[.,[[.,.],.]]],.]
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [5,2,3,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [6,2,3,1,5,4] => [[[.,.],[.,[[.,.],.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [5,2,3,1,4,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [3,2,1,6,4,5] => [[[.,.],.],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [6,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [2,1,6,4,3,5] => [[.,.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [4,2,6,1,5,3] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [5,2,6,4,1,3] => [[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [6,2,1,4,5,3] => [[[.,.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [5,2,1,4,3,6] => [[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [4,2,1,3,6,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [4,2,6,1,3,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [6,2,1,4,3,5] => [[[.,.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [2,1,6,3,5,4] => [[.,.],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [5,2,1,6,3,4] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [5,2,6,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [[[.,.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]]
>>> Load all 1924 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [2,1,3,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [1,6,3,4,2,5] => [.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [1,6,3,2,5,4] => [.,[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,5,3,2,4,6] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [1,6,3,2,4,5] => [.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [3,6,1,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [3,5,1,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [3,6,1,4,2,5] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [4,6,3,1,5,2] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [6,1,3,4,5,2] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [5,1,3,4,2,6] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [4,1,3,2,6,5] => [[.,[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [4,6,3,1,2,5] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [3,1,2,6,5,4] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [3,1,2,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [3,6,1,2,5,4] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [3,5,1,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [5,1,3,6,2,4] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [5,6,3,2,1,4] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [[.,[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [3,1,2,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [3,6,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [1,6,2,4,5,3] => [.,[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,5,2,4,3,6] => [.,[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [1,6,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [4,1,6,2,5,3] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [4,1,5,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [4,6,2,1,5,3] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [4,5,2,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [5,1,6,4,2,3] => [[.,[[.,[.,.]],.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [5,6,2,4,1,3] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [4,1,6,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [4,6,2,1,3,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [1,2,6,3,5,4] => [.,[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [1,5,2,6,3,4] => [.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [1,5,6,3,2,4] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [5,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [5,1,6,3,2,4] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [5,6,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [6,2,3,4,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [7,2,3,4,1,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [4,2,3,1,7,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [3,2,1,7,5,4,6] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [5,2,3,7,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [5,2,3,6,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [6,2,3,7,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [7,2,3,1,5,6,4] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [6,2,3,1,5,4,7] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [5,2,3,1,4,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [5,2,3,7,1,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [7,2,3,1,5,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [5,2,3,1,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [3,2,1,6,7,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [3,2,1,7,4,6,5] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [3,2,1,6,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [6,2,3,1,7,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [6,2,3,7,4,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [7,2,3,1,4,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [6,2,3,1,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [3,2,1,4,7,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [3,2,1,7,4,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [7,2,3,1,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [2,1,7,4,5,3,6] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,1,6,4,7,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [2,1,7,4,3,6,5] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [2,1,6,4,3,5,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [2,1,7,4,3,5,6] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [4,2,7,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [4,2,6,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [4,2,5,1,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [4,2,7,1,5,3,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [4,2,5,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [5,2,7,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [5,2,6,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => [6,2,7,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [7,2,1,4,5,6,3] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [6,2,1,4,5,3,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [5,2,1,4,3,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [5,2,7,4,1,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [7,2,1,4,5,3,6] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [5,2,1,4,3,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [4,2,1,3,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [4,2,1,3,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [4,2,6,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [4,2,7,1,3,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [4,2,6,1,3,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [6,2,1,4,7,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [6,2,7,4,3,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [7,2,1,4,3,6,5] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [6,2,1,4,3,5,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [4,2,1,3,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [4,2,1,3,7,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [4,2,7,1,3,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [7,2,1,4,3,5,6] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [4,2,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [2,1,3,7,5,4,6] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,1,5,7,3,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,1,6,7,5,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [2,1,7,3,5,6,4] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [2,1,6,3,5,4,7] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [2,1,5,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [2,1,7,3,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [2,1,5,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [5,2,1,7,3,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [5,2,1,6,3,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [5,2,6,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [5,2,7,3,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [5,2,6,3,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => [6,2,1,7,5,3,4] => [[[.,.],[[.,[.,.]],.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => [6,2,7,3,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [7,2,1,3,5,6,4] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [6,2,1,3,5,4,7] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [5,2,1,3,4,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [5,2,1,7,3,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [5,2,7,3,1,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [7,2,1,3,5,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [5,2,1,3,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [2,1,3,7,4,6,5] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [2,1,3,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [2,1,6,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [2,1,6,7,4,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [2,1,7,3,4,6,5] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [2,1,6,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [6,2,1,3,7,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [6,2,1,7,4,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [6,2,7,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [7,2,1,3,4,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [6,2,1,3,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [2,1,3,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [2,1,7,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [7,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [1,7,3,4,5,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [1,6,3,4,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [1,7,3,4,2,6,5] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [1,6,3,4,2,5,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [1,4,3,2,7,5,6] => [.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [1,7,3,4,2,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [1,3,2,7,5,4,6] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [1,5,3,7,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [1,5,3,6,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [1,6,3,7,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [1,7,3,2,5,6,4] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [1,6,3,2,5,4,7] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [1,5,3,2,4,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [1,5,3,7,2,4,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [1,7,3,2,5,4,6] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [1,5,3,2,4,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [1,3,2,7,4,6,5] => [.,[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [1,3,2,6,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [1,6,3,2,7,4,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [1,6,3,7,4,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [1,7,3,2,4,6,5] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [1,6,3,2,4,5,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [1,3,2,7,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [1,7,3,2,4,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [3,7,1,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [3,6,1,4,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [3,5,1,4,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [3,7,1,4,5,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [3,5,1,4,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [3,4,1,2,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [3,6,1,4,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [3,7,1,4,2,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [3,6,1,4,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [3,4,1,2,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [3,7,1,4,2,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [4,7,3,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [4,6,3,1,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [4,5,3,1,2,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [4,7,3,1,5,2,6] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [5,7,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [7,1,3,4,5,6,2] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [6,1,3,4,5,2,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [5,1,3,4,2,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [5,7,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [7,1,3,4,5,2,6] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [5,1,3,4,2,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [4,1,3,2,7,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [4,1,3,2,6,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [4,6,3,1,7,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [4,7,3,1,2,6,5] => [[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [4,6,3,1,2,5,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [6,1,3,4,7,2,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [6,7,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [7,1,3,4,2,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [6,1,3,4,2,5,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [4,1,3,2,5,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [4,1,3,2,7,5,6] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [4,7,3,1,2,5,6] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [7,1,3,4,2,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [3,1,2,7,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [3,1,2,6,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [3,1,2,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [3,1,2,7,5,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [3,1,2,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [3,5,1,7,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [3,6,1,7,5,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [3,7,1,2,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [3,6,1,2,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [3,5,1,2,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [3,5,1,7,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [3,7,1,2,5,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [3,5,1,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [5,1,3,7,2,6,4] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [5,1,3,6,2,4,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [5,6,3,7,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [5,7,3,2,1,6,4] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [5,6,3,2,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => [6,1,3,7,5,2,4] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => [6,7,3,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [7,1,3,2,5,6,4] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [6,1,3,2,5,4,7] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [5,1,3,2,4,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [5,1,3,7,2,4,6] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [5,7,3,2,1,4,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [7,1,3,2,5,4,6] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [5,1,3,2,4,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [3,1,2,4,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [3,1,2,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [3,1,2,6,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [3,1,2,7,4,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [3,1,2,6,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [3,6,1,2,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [3,6,1,7,4,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [3,7,1,2,4,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [3,6,1,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [6,1,3,2,7,4,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [6,1,3,7,4,2,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [6,7,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [7,1,3,2,4,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [6,1,3,2,4,5,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [3,1,2,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [3,1,2,4,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [3,1,2,7,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [3,7,1,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [7,1,3,2,4,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [1,2,7,4,5,3,6] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [1,2,6,4,7,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [1,2,7,4,3,6,5] => [.,[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [1,2,6,4,3,5,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [1,2,7,4,3,5,6] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [1,4,7,2,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [1,4,6,2,5,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [1,4,7,2,5,3,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [1,5,7,4,2,6,3] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [1,5,6,4,2,3,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [1,6,7,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [1,7,2,4,5,6,3] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [1,6,2,4,5,3,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [1,5,2,4,3,7,6] => [.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [1,5,7,4,2,3,6] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [1,7,2,4,5,3,6] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [1,5,2,4,3,6,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [1,4,2,3,7,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [1,4,2,3,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [1,4,7,2,3,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [1,6,2,4,7,3,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [1,6,7,4,3,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [1,7,2,4,3,6,5] => [.,[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [1,6,2,4,3,5,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [1,4,2,3,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,4,2,3,7,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [1,7,2,4,3,5,6] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [1,4,2,3,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [4,1,7,2,5,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [4,1,6,2,5,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [4,1,5,2,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [4,1,7,2,5,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [4,1,5,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [4,5,7,1,2,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [4,6,7,1,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [4,7,2,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [4,6,2,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [4,5,2,1,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [4,5,7,1,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [4,7,2,1,5,3,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [4,5,2,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [5,1,7,4,2,6,3] => [[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [5,1,6,4,2,3,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [5,7,2,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [5,6,2,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [6,1,7,4,5,2,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [6,7,2,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [7,1,2,4,5,6,3] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [5,1,2,4,3,7,6] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [5,1,7,4,2,3,6] => [[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [5,7,2,4,1,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [7,1,2,4,5,3,6] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [4,1,2,3,7,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [4,1,2,3,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [4,1,6,2,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [4,1,7,2,3,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [4,1,6,2,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [4,6,2,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [4,6,7,1,3,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [4,7,2,1,3,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [4,6,2,1,3,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [6,1,2,4,7,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [6,1,7,4,3,2,5] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [6,7,2,4,3,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [7,1,2,4,3,6,5] => [[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [6,1,2,4,3,5,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [4,1,2,3,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [4,1,2,3,7,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [4,1,7,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [4,7,2,1,3,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [7,1,2,4,3,5,6] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [1,2,3,7,5,4,6] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [1,2,6,7,5,3,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [1,2,7,3,5,6,4] => [.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [1,2,6,3,5,4,7] => [.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [1,2,5,3,4,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [1,2,7,3,5,4,6] => [.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [1,2,5,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [1,5,2,7,3,6,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [1,5,2,6,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [1,5,7,3,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [1,5,6,3,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [1,6,2,7,5,3,4] => [.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [1,6,7,3,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [1,7,2,3,5,6,4] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [1,6,2,3,5,4,7] => [.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [1,5,2,3,4,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,5,2,7,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [1,5,7,3,2,4,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [1,7,2,3,5,4,6] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [1,5,2,3,4,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [5,1,2,7,3,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [5,1,2,6,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [5,1,6,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [5,1,7,3,2,6,4] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [5,1,6,3,2,4,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [5,6,2,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [5,6,7,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [5,7,2,3,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [5,6,2,3,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [6,1,2,7,5,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [6,1,7,3,5,2,4] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [6,7,2,3,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [5,1,2,3,4,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [5,1,2,7,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [5,1,7,3,2,4,6] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [5,7,2,3,1,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [7,1,2,3,5,4,6] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [1,2,6,3,7,4,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [1,2,6,7,4,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [1,2,7,3,4,6,5] => [.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [1,6,2,3,7,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,6,2,7,4,3,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [1,6,7,3,4,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [1,7,2,3,4,6,5] => [.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [1,6,2,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [6,1,2,3,7,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [6,1,2,7,4,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [6,1,7,3,4,2,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [6,7,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => [[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [1,2,7,3,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => [8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,7,1,8,6] => [7,2,3,4,5,8,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => [8,2,3,4,5,1,7,6] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6,8] => [7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,7] => [5,2,3,4,1,8,6,7] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => [8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,1,6,7,5,8] => [4,2,3,1,7,6,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8] => [4,2,3,1,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,6,1,7,8,5] => [6,2,3,4,8,1,7,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,4,6,7,1,8,5] => [7,2,3,4,8,6,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,1,5] => [8,2,3,4,1,6,7,5] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,4,6,7,1,5,8] => [7,2,3,4,1,6,5,8] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,8,5,7] => [6,2,3,4,8,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,4,1,5,7,8,6] => [4,2,3,1,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => [4,2,3,1,7,8,5,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => [4,2,3,1,8,5,7,6] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,4,7,1,5,8,6] => [7,2,3,4,1,8,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,4,7,1,8,5,6] => [7,2,3,4,8,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,7,8,1,5,6] => [8,2,3,4,1,5,7,6] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,4,1,5,8,6,7] => [4,2,3,1,5,8,6,7] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [4,2,3,1,8,5,6,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,5,6,7,4,8] => [3,2,1,7,5,6,4,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,5,6,4,8,7] => [3,2,1,6,5,4,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,5,6,8,4,7] => [3,2,1,8,5,6,4,7] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,5,6,4,7,8] => [3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,7,8,4,6] => [3,2,1,8,5,4,7,6] => [[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6,8] => [3,2,1,7,5,4,6,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,5,8,4,6,7] => [3,2,1,8,5,4,6,7] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,5,4,6,7,8] => [3,2,1,5,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,4] => [5,2,3,8,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,5,1,6,7,4,8] => [5,2,3,7,1,6,4,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,5,1,6,4,8,7] => [5,2,3,6,1,4,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,5,1,6,4,7,8] => [5,2,3,6,1,4,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,5,6,1,7,8,4] => [6,2,3,8,5,1,7,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,5,6,1,7,4,8] => [6,2,3,7,5,1,4,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,5,6,7,1,8,4] => [7,2,3,8,5,6,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,1,4] => [8,2,3,1,5,6,7,4] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,6,7,1,4,8] => [7,2,3,1,5,6,4,8] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,6,1,4,8,7] => [6,2,3,1,5,4,8,7] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,8,1,4,7] => [8,2,3,1,5,6,4,7] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [6,2,3,1,5,4,7,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,7,1,8,4,6] => [7,2,3,8,5,4,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,7,8,1,4,6] => [8,2,3,1,5,4,7,6] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,5,1,4,8,6,7] => [5,2,3,1,4,8,6,7] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [5,2,3,8,1,4,6,7] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,1,4,6,7,8] => [5,2,3,1,4,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,3,1,6,4,7,8,5] => [3,2,1,6,8,4,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [3,2,1,6,7,4,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,6,7,4,8,5] => [3,2,1,7,8,6,4,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,4,5] => [3,2,1,8,4,6,7,5] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,6,7,4,5,8] => [3,2,1,7,4,6,5,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => [3,2,1,6,8,4,5,7] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,4,5,7] => [3,2,1,8,4,6,5,7] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,1,6,4,5,7,8] => [3,2,1,6,4,5,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,1,4,7,8,5] => [6,2,3,1,8,4,7,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,6,1,7,4,8,5] => [6,2,3,7,8,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,1,7,8,4,5] => [6,2,3,8,4,1,7,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,7,4,5,8] => [6,2,3,7,4,1,5,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,6,7,1,4,8,5] => [7,2,3,1,8,6,4,5] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,6,7,1,8,4,5] => [7,2,3,8,4,6,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,6,7,1,4,5,8] => [7,2,3,1,4,6,5,8] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,8,7] => [6,2,3,1,4,5,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => [6,2,3,8,4,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,6,8,1,4,5,7] => [8,2,3,1,4,6,5,7] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,6,1,4,5,7,8] => [6,2,3,1,4,5,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [3,2,1,4,8,5,7,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,7,4,5,8,6] => [3,2,1,7,4,8,5,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [3,2,1,7,8,5,4,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,7,8,4,5,6] => [3,2,1,8,4,5,7,6] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,1,7,4,5,6,8] => [3,2,1,7,4,5,6,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [8,2,3,1,4,5,7,6] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6,8] => [7,2,3,1,4,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,1,4,8,5,6,7] => [3,2,1,4,8,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,1,8,4,5,6,7] => [3,2,1,8,4,5,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [8,2,3,1,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3,7,8,6] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,7,3,8,6] => [2,1,7,4,5,8,3,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4,5,7,8,3,6] => [2,1,8,4,5,3,7,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4,5,8,3,6,7] => [2,1,8,4,5,3,6,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [2,1,4,3,8,6,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,6,3,7,8,5] => [2,1,6,4,8,3,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,7,3,8,5] => [2,1,7,4,8,6,3,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,8,7] => [2,1,6,4,3,5,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,8,3,5,7] => [2,1,8,4,3,6,5,7] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,6,3,5,7,8] => [2,1,6,4,3,5,7,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [2,1,4,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,7,3,5,8,6] => [2,1,7,4,3,8,5,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,4,7,3,8,5,6] => [2,1,7,4,8,5,3,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,4,7,8,3,5,6] => [2,1,8,4,3,5,7,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => [2,1,4,3,5,8,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [2,1,4,3,8,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,3] => [4,2,8,1,5,6,7,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,5,6,7,3,8] => [4,2,7,1,5,6,3,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,5,6,8,3,7] => [4,2,8,1,5,6,3,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,5,6,3,7,8] => [4,2,6,1,5,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => [4,2,5,1,3,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,4,1,5,7,8,3,6] => [4,2,8,1,5,3,7,6] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,3,6,8,7] => [4,2,5,1,3,6,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => [4,2,5,1,3,8,6,7] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,4,1,5,8,3,6,7] => [4,2,8,1,5,3,6,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,3,6,7,8] => [4,2,5,1,3,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,4,5,1,6,7,8,3] => [5,2,8,4,1,6,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,4,5,1,6,7,3,8] => [5,2,7,4,1,6,3,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,4,5,1,6,3,8,7] => [5,2,6,4,1,3,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,4,5,1,6,8,3,7] => [5,2,8,4,1,6,3,7] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,4,5,1,6,3,7,8] => [5,2,6,4,1,3,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,6,1,7,8,3] => [6,2,8,4,5,1,7,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,6,1,7,3,8] => [6,2,7,4,5,1,3,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,1,8,3] => [7,2,8,4,5,6,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,1,3] => [8,2,1,4,5,6,7,3] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,7,1,3,8] => [7,2,1,4,5,6,3,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,6,1,8,3,7] => [6,2,8,4,5,1,3,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [6,2,1,4,5,3,7,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,4,5,1,3,7,8,6] => [5,2,1,4,3,8,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,4,5,1,7,3,8,6] => [5,2,7,4,1,8,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,4,5,1,7,8,3,6] => [5,2,8,4,1,3,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6,8] => [5,2,7,4,1,3,6,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,7,1,3,8,6] => [7,2,1,4,5,8,3,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,7,1,8,3,6] => [7,2,8,4,5,3,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [5,2,8,4,1,3,6,7] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => [5,2,1,4,3,6,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7] => [4,2,1,3,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,8,5,7] => [4,2,1,3,8,6,5,7] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,6,5,7,8] => [4,2,1,3,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => [4,2,6,1,8,3,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => [4,2,6,1,7,3,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,6,7,3,8,5] => [4,2,7,1,8,6,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [4,2,6,1,8,3,5,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,8,3,5,7] => [4,2,8,1,3,6,5,7] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,6,3,5,7,8] => [4,2,6,1,3,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => [6,2,7,4,8,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,6,1,7,8,3,5] => [6,2,8,4,3,1,7,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,6,7,1,8,3,5] => [7,2,8,4,3,6,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [7,2,1,4,3,6,5,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => [6,2,1,4,3,5,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [6,2,8,4,3,1,5,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [8,2,1,4,3,6,5,7] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,6,1,3,5,7,8] => [6,2,1,4,3,5,7,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,3,5,7,8,6] => [4,2,1,3,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,3,7,5,8,6] => [4,2,1,3,7,8,5,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,3,7,8,5,6] => [4,2,1,3,8,5,7,6] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,7,3,5,8,6] => [4,2,7,1,3,8,5,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,7,3,8,5,6] => [4,2,7,1,8,5,3,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,7,8,3,5,6] => [4,2,8,1,3,5,7,6] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,4,7,1,8,3,5,6] => [7,2,8,4,3,5,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [8,2,1,4,3,5,7,6] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6,8] => [7,2,1,4,3,5,6,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,3,5,8,6,7] => [4,2,1,3,5,8,6,7] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,3,8,5,6,7] => [4,2,1,3,8,5,6,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1,8,3,5,6,7] => [4,2,8,1,3,5,6,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8] => [4,2,1,3,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,6,4,8,7] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,1,3,5,7,4,8,6] => [2,1,3,7,5,8,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,1,3,5,7,8,4,6] => [2,1,3,8,5,4,7,6] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,1,3,5,8,4,6,7] => [2,1,3,8,5,4,6,7] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [2,1,5,8,3,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [2,1,5,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,1,5,3,6,8,4,7] => [2,1,5,8,3,6,4,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,1,5,3,6,4,7,8] => [2,1,5,6,3,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,5,6,3,7,8,4] => [2,1,6,8,5,3,7,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => [2,1,8,3,5,6,7,4] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,1,6,3,5,4,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => [2,1,5,7,3,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6,8] => [2,1,5,7,3,4,6,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,5,7,3,4,8,6] => [2,1,7,3,5,8,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [2,1,7,8,5,4,3,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,5,7,8,3,4,6] => [2,1,8,3,5,4,7,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,5,3,4,6,8,7] => [2,1,5,3,4,6,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,1,5,3,8,4,6,7] => [2,1,5,8,3,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,5,3,4,6,7,8] => [2,1,5,3,4,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,1,3,6,7,8,4] => [5,2,1,8,3,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,5,1,3,6,4,8,7] => [5,2,1,6,3,4,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,1,3,6,8,4,7] => [5,2,1,8,3,6,4,7] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,1,3,6,4,7,8] => [5,2,1,6,3,4,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,5,1,6,3,7,8,4] => [5,2,6,8,1,3,7,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,1,6,3,7,4,8] => [5,2,6,7,1,3,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => [5,2,7,8,1,6,3,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,1,6,7,8,3,4] => [5,2,8,3,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,1,6,7,3,4,8] => [5,2,7,3,1,6,4,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,1,6,3,8,4,7] => [5,2,6,8,1,3,4,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,5,6,1,3,7,8,4] => [6,2,1,8,5,3,7,4] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,5,6,1,7,3,8,4] => [6,2,7,8,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,5,6,1,7,8,3,4] => [6,2,8,3,5,1,7,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,5,6,1,7,3,4,8] => [6,2,7,3,5,1,4,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,5,6,7,1,8,3,4] => [7,2,8,3,5,6,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,1,3,4] => [8,2,1,3,5,6,7,4] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,5,6,1,8,3,4,7] => [6,2,8,3,5,1,4,7] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,7,8,6] => [5,2,1,3,4,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,7,4,8,6] => [5,2,1,7,3,8,4,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,7,8,4,6] => [5,2,1,8,3,4,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6,8] => [5,2,1,7,3,4,6,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,5,1,7,3,4,8,6] => [5,2,7,3,1,8,4,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,5,1,7,3,8,4,6] => [5,2,7,8,1,4,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,5,1,7,8,3,4,6] => [5,2,8,3,1,4,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,5,7,1,3,4,8,6] => [7,2,1,3,5,8,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,5,1,3,8,4,6,7] => [5,2,1,8,3,4,6,7] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,5,1,8,3,4,6,7] => [5,2,8,3,1,4,6,7] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,4,6,7,8] => [5,2,1,3,4,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,1,3,4,6,8,5,7] => [2,1,3,4,8,6,5,7] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,1,3,6,7,4,8,5] => [2,1,3,7,8,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,6,7,8,4,5] => [2,1,3,8,4,6,7,5] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,6,4,5,8,7] => [2,1,3,6,4,5,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,1,3,6,4,5,7,8] => [2,1,3,6,4,5,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [2,1,6,3,8,4,7,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [2,1,6,7,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,6,7,3,4,8,5] => [2,1,7,3,8,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,1,6,7,3,8,4,5] => [2,1,7,8,4,6,3,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => [2,1,8,3,4,6,7,5] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [2,1,6,3,4,5,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,1,6,3,4,8,5,7] => [2,1,6,3,8,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,1,6,3,8,4,5,7] => [2,1,6,8,4,3,5,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,1,3,7,8,4,5] => [6,2,1,8,4,3,7,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,6,1,7,3,4,8,5] => [6,2,7,3,8,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,6,1,7,3,8,4,5] => [6,2,7,8,4,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => [7,2,1,3,8,6,4,5] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,8,5,7] => [6,2,1,3,8,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,6,1,8,3,4,5,7] => [6,2,8,3,4,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [8,2,1,3,4,6,5,7] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,4,7,5,8,6] => [2,1,3,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,1,3,4,7,8,5,6] => [2,1,3,4,8,5,7,6] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,3,4,7,5,6,8] => [2,1,3,4,7,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,3,7,4,5,8,6] => [2,1,3,7,4,8,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,3,7,8,4,5,6] => [2,1,3,8,4,5,7,6] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,7,3,4,5,8,6] => [2,1,7,3,4,8,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,1,7,3,4,8,5,6] => [2,1,7,3,8,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6,8] => [2,1,7,3,4,5,6,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,7,1,3,4,5,8,6] => [7,2,1,3,4,8,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,1,3,4,8,5,6] => [7,2,1,3,8,5,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,7,1,3,8,4,5,6] => [7,2,1,8,4,5,3,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,7,1,8,3,4,5,6] => [7,2,8,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [8,2,1,3,4,5,7,6] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => [7,2,1,3,4,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [2,1,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => [2,1,3,8,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [2,1,8,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [8,2,1,3,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,8,2,7] => [1,8,3,4,5,6,2,7] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,2,7,8,6] => [1,5,3,4,2,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,5,7,2,8,6] => [1,7,3,4,5,8,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,7,8,2,6] => [1,8,3,4,5,2,7,6] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,5,8,2,6,7] => [1,8,3,4,5,2,6,7] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,5] => [1,4,3,2,8,6,7,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,6,2,7,8,5] => [1,6,3,4,8,2,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,6,7,2,8,5] => [1,7,3,4,8,6,2,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,6,7,8,2,5] => [1,8,3,4,2,6,7,5] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,7,2,5,8] => [1,7,3,4,2,6,5,8] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,8,7] => [1,6,3,4,2,5,8,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => [1,6,3,4,2,5,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,4,2,5,7,8,6] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,4,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,2,7,5,8,6] => [1,4,3,2,7,8,5,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,4,7,2,5,8,6] => [1,7,3,4,2,8,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,4,7,2,8,5,6] => [1,7,3,4,8,5,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [1,7,3,4,2,5,6,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,3,4,2,5,8,6,7] => [1,4,3,2,5,8,6,7] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [1,4,3,2,8,5,6,7] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [1,8,3,4,2,5,6,7] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,6,4,8,7] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,5,6,8,4,7] => [1,3,2,8,5,6,4,7] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,7,4,8,6] => [1,3,2,7,5,8,4,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,7,8,4,6] => [1,3,2,8,5,4,7,6] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6,8] => [1,3,2,7,5,4,6,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,8,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => [1,3,2,8,5,4,6,7] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,5,2,6,7,8,4] => [1,5,3,8,2,6,7,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,5,2,6,7,4,8] => [1,5,3,7,2,6,4,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,5,2,6,8,4,7] => [1,5,3,8,2,6,4,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,5,2,6,4,7,8] => [1,5,3,6,2,4,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,5,6,2,7,8,4] => [1,6,3,8,5,2,7,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,5,6,2,7,4,8] => [1,6,3,7,5,2,4,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,5,6,7,2,8,4] => [1,7,3,8,5,6,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,2,4] => [1,8,3,2,5,6,7,4] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,6,7,2,4,8] => [1,7,3,2,5,6,4,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,5,6,2,8,4,7] => [1,6,3,8,5,2,4,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,6,8,2,4,7] => [1,8,3,2,5,6,4,7] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [1,6,3,2,5,4,7,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,7,8,6] => [1,5,3,2,4,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6,8] => [1,5,3,2,4,7,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6,8] => [1,5,3,7,2,4,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,7,2,8,4,6] => [1,7,3,8,5,4,2,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,7,8,2,4,6] => [1,8,3,2,5,4,7,6] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [1,7,3,2,5,4,6,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,5,2,4,6,8,7] => [1,5,3,2,4,6,8,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,5,2,4,8,6,7] => [1,5,3,2,4,8,6,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [1,5,3,8,2,4,6,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [1,8,3,2,5,4,6,7] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,2,4,6,7,8] => [1,5,3,2,4,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,6,7,5] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,2,4,6,7,5,8] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,4,6,8,5,7] => [1,3,2,4,8,6,5,7] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,2,6,4,7,8,5] => [1,3,2,6,8,4,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [1,3,2,6,7,4,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,7,8,4,5] => [1,3,2,8,4,6,7,5] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,2,6,7,4,5,8] => [1,3,2,7,4,6,5,8] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => [1,3,2,6,8,4,5,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,6,8,4,5,7] => [1,3,2,8,4,6,5,7] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [1,3,2,6,4,5,7,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,6,2,4,7,8,5] => [1,6,3,2,8,4,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,2,4,7,5,8] => [1,6,3,2,7,4,5,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,2,7,4,8,5] => [1,6,3,7,8,2,4,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,2,7,8,4,5] => [1,6,3,8,4,2,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,7,4,5,8] => [1,6,3,7,4,2,5,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,6,7,2,4,8,5] => [1,7,3,2,8,6,4,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,6,7,2,8,4,5] => [1,7,3,8,4,6,2,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,6,7,2,4,5,8] => [1,7,3,2,4,6,5,8] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,6,2,4,8,5,7] => [1,6,3,2,8,4,5,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,6,2,8,4,5,7] => [1,6,3,8,4,2,5,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,6,2,4,5,7,8] => [1,6,3,2,4,5,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,3,2,4,7,5,8,6] => [1,3,2,4,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,4,7,8,5,6] => [1,3,2,4,8,5,7,6] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,3,2,7,4,5,8,6] => [1,3,2,7,4,8,5,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,3,2,7,8,5,4,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,3,2,7,8,4,5,6] => [1,3,2,8,4,5,7,6] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [1,3,2,7,4,5,6,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,2,4,5,8,6] => [1,7,3,2,4,8,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,7,2,4,8,5,6] => [1,7,3,2,8,5,4,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [1,7,3,8,4,5,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => [1,8,3,2,4,5,7,6] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6,8] => [1,7,3,2,4,5,6,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [1,3,2,4,8,5,6,7] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [1,3,2,8,4,5,6,7] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [1,8,3,2,4,5,6,7] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => [3,8,1,4,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,2,8] => [3,7,1,4,5,6,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,5,6,2,8,7] => [3,6,1,4,5,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,8,2,7] => [3,8,1,4,5,6,2,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,4,5,6,2,7,8] => [3,6,1,4,5,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,5,2,7,8,6] => [3,5,1,4,2,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6,8] => [3,5,1,4,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6,8] => [3,7,1,4,5,2,6,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,2,6,7,8] => [3,5,1,4,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [3,4,1,2,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,4,2,6,7,5,8] => [3,4,1,2,7,6,5,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [3,4,1,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => [3,4,1,2,8,6,5,7] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,1,4,2,6,5,7,8] => [3,4,1,2,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,1,4,6,2,7,5,8] => [3,6,1,4,7,2,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,1,4,6,7,2,5,8] => [3,7,1,4,2,6,5,8] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,8,7] => [3,6,1,4,2,5,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,4,6,8,2,5,7] => [3,8,1,4,2,6,5,7] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => [3,4,1,2,5,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,2,5,7,6,8] => [3,4,1,2,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [3,4,1,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,4,2,7,8,5,6] => [3,4,1,2,8,5,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,4,2,7,5,6,8] => [3,4,1,2,7,5,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,7,2,5,8,6] => [3,7,1,4,2,8,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,2,5,6,8,7] => [3,4,1,2,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,2,5,8,6,7] => [3,4,1,2,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => [3,4,1,2,8,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [4,8,3,1,5,6,7,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,5,6,7,2,8] => [4,7,3,1,5,6,2,8] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,4,1,5,6,2,8,7] => [4,6,3,1,5,2,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,4,1,5,6,2,7,8] => [4,6,3,1,5,2,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,4,1,5,2,7,8,6] => [4,5,3,1,2,8,7,6] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,7,8,2,6] => [4,8,3,1,5,2,7,6] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,4,1,5,2,6,8,7] => [4,5,3,1,2,6,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,2,8,6,7] => [4,5,3,1,2,8,6,7] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => [5,8,3,4,1,6,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,5,1,6,7,2,8] => [5,7,3,4,1,6,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,5,1,6,8,2,7] => [5,8,3,4,1,6,2,7] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,1,6,2,7,8] => [5,6,3,4,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,8,2] => [6,8,3,4,5,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,8] => [6,7,3,4,5,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => [7,8,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,1,2] => [8,1,3,4,5,6,7,2] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,1,2,8] => [7,1,3,4,5,6,2,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [6,1,3,4,5,2,7,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6,8] => [5,1,3,4,2,7,6,8] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,5,1,7,2,8,6] => [5,7,3,4,1,8,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => [7,1,3,4,5,8,2,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,5,7,1,8,2,6] => [7,8,3,4,5,2,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,5,1,2,6,8,7] => [5,1,3,4,2,6,8,7] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,5,1,2,8,6,7] => [5,1,3,4,2,8,6,7] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,5,1,8,2,6,7] => [5,8,3,4,1,2,6,7] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [8,1,3,4,5,2,6,7] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [5,1,3,4,2,6,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,5] => [4,1,3,2,8,6,7,5] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [4,1,3,2,6,5,8,7] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,8,5,7] => [4,1,3,2,8,6,5,7] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,4,1,6,2,7,8,5] => [4,6,3,1,8,2,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,6,2,7,5,8] => [4,6,3,1,7,2,5,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,4,1,6,7,2,8,5] => [4,7,3,1,8,6,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,6,7,8,2,5] => [4,8,3,1,2,6,7,5] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,8,2,5,7] => [4,8,3,1,2,6,5,7] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,4,1,6,2,5,7,8] => [4,6,3,1,2,5,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,4,6,1,2,7,5,8] => [6,1,3,4,7,2,5,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => [6,7,3,4,8,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,4,6,1,7,8,2,5] => [6,8,3,4,2,1,7,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,4,6,1,7,2,5,8] => [6,7,3,4,2,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,4,6,7,1,8,2,5] => [7,8,3,4,2,6,1,5] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,1,2,5] => [8,1,3,4,2,6,7,5] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,8,7] => [6,1,3,4,2,5,8,7] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [8,1,3,4,2,6,5,7] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,6,1,2,5,7,8] => [6,1,3,4,2,5,7,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => [4,1,3,2,5,7,6,8] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,4,1,2,7,5,8,6] => [4,1,3,2,7,8,5,6] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => [4,1,3,2,8,5,7,6] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,4,1,7,2,5,8,6] => [4,7,3,1,2,8,5,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,7,2,8,5,6] => [4,7,3,1,8,5,2,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,4,7,1,2,5,8,6] => [7,1,3,4,2,8,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [7,8,3,4,2,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1,2,8,5,6,7] => [4,1,3,2,8,5,6,7] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [4,1,3,2,5,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,4] => [3,1,2,8,5,6,7,4] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,5,6,8,4,7] => [3,1,2,8,5,6,4,7] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,8] => [3,1,2,5,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,7,4,8,6] => [3,1,2,7,5,8,4,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,7,8,4,6] => [3,1,2,8,5,4,7,6] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6,8] => [3,1,2,7,5,4,6,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,5,4,6,8,7] => [3,1,2,5,4,6,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [3,5,1,6,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,5,2,6,8,4,7] => [3,5,1,8,2,6,4,7] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,4,7,8] => [3,5,1,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,5,6,2,7,8,4] => [3,6,1,8,5,2,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,5,6,7,2,8,4] => [3,7,1,8,5,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,2,4] => [3,8,1,2,5,6,7,4] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,5,6,7,2,4,8] => [3,7,1,2,5,6,4,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,5,6,2,8,4,7] => [3,6,1,8,5,2,4,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,5,6,8,2,4,7] => [3,8,1,2,5,6,4,7] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,8,6] => [3,5,1,2,4,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6,8] => [3,5,1,2,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,7,8,4,6] => [3,5,1,8,2,4,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6,8] => [3,5,1,7,2,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,7,8,2,4,6] => [3,8,1,2,5,4,7,6] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6,8] => [3,7,1,2,5,4,6,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,5,2,4,6,8,7] => [3,5,1,2,4,6,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,5,2,4,8,6,7] => [3,5,1,2,4,8,6,7] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => [3,5,1,8,2,4,6,7] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,5,2,4,6,7,8] => [3,5,1,2,4,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [5,1,3,7,2,6,4,8] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,5,1,2,6,4,8,7] => [5,1,3,6,2,4,8,7] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,1,2,6,8,4,7] => [5,1,3,8,2,6,4,7] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,5,1,2,6,4,7,8] => [5,1,3,6,2,4,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,5,1,6,2,7,8,4] => [5,6,3,8,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => [5,6,3,7,1,2,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,5,1,6,7,2,8,4] => [5,7,3,8,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,5,1,6,7,8,2,4] => [5,8,3,2,1,6,7,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,5,1,6,7,2,4,8] => [5,7,3,2,1,6,4,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [5,6,3,2,1,4,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,5,1,6,8,2,4,7] => [5,8,3,2,1,6,4,7] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,5,1,6,2,4,7,8] => [5,6,3,2,1,4,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,5,6,1,2,7,8,4] => [6,1,3,8,5,2,7,4] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,5,6,1,2,7,4,8] => [6,1,3,7,5,2,4,8] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => [6,7,3,8,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,5,6,1,7,8,2,4] => [6,8,3,2,5,1,7,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,5,6,1,7,2,4,8] => [6,7,3,2,5,1,4,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,5,6,7,1,8,2,4] => [7,8,3,2,5,6,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,1,2,4] => [8,1,3,2,5,6,7,4] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [7,1,3,2,5,6,4,8] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,5,6,1,2,4,8,7] => [6,1,3,2,5,4,8,7] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,5,6,1,2,8,4,7] => [6,1,3,8,5,2,4,7] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [6,8,3,2,5,1,4,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [8,1,3,2,5,6,4,7] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [5,1,3,2,4,7,6,8] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,7,8,4,6] => [5,1,3,8,2,4,7,6] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6,8] => [5,1,3,7,2,4,6,8] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [5,7,3,8,1,4,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,7,8,2,4,6] => [5,8,3,2,1,4,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6,8] => [5,7,3,2,1,4,6,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,7,1,2,4,8,6] => [7,1,3,2,5,8,4,6] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [8,1,3,2,5,4,7,6] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6,8] => [7,1,3,2,5,4,6,8] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,5,1,2,4,6,8,7] => [5,1,3,2,4,6,8,7] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,5,1,2,4,8,6,7] => [5,1,3,2,4,8,6,7] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,5,1,2,8,4,6,7] => [5,1,3,8,2,4,6,7] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,5,8,1,2,4,6,7] => [8,1,3,2,5,4,6,7] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,4,6,7,8,5] => [3,1,2,4,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => [3,1,2,4,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,1,2,4,6,8,5,7] => [3,1,2,4,8,6,5,7] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,2,6,4,7,8,5] => [3,1,2,6,8,4,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => [3,1,2,7,8,6,4,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,2,6,7,8,4,5] => [3,1,2,8,4,6,7,5] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,6,4,5,8,7] => [3,1,2,6,4,5,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [3,1,2,6,4,8,5,7] => [3,1,2,6,8,4,5,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [3,6,1,7,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [3,1,6,7,2,8,4,5] => [3,7,1,8,4,6,2,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => [3,7,1,2,4,6,5,8] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [3,6,1,2,4,5,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [3,1,6,2,4,8,5,7] => [3,6,1,2,8,4,5,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [3,1,6,2,8,4,5,7] => [3,6,1,8,4,2,5,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => [3,8,1,2,4,6,5,7] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,6,2,4,5,7,8] => [3,6,1,2,4,5,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,6,1,2,4,7,8,5] => [6,1,3,2,8,4,7,5] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [3,6,1,2,7,8,4,5] => [6,1,3,8,4,2,7,5] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [3,6,1,2,7,4,5,8] => [6,1,3,7,4,2,5,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => [6,7,3,2,8,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [6,7,3,8,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => [6,8,3,2,4,1,7,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,6,1,7,2,4,5,8] => [6,7,3,2,4,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,6,7,1,2,4,8,5] => [7,1,3,2,8,6,4,5] => [[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [3,6,7,1,2,8,4,5] => [7,1,3,8,4,6,2,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [3,6,7,1,8,2,4,5] => [7,8,3,2,4,6,1,5] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [8,1,3,2,4,6,7,5] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,6,8,1,2,4,5,7] => [8,1,3,2,4,6,5,7] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => [3,1,2,4,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,4,7,5,8,6] => [3,1,2,4,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,2,4,7,8,5,6] => [3,1,2,4,8,5,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => [3,1,2,4,7,5,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,7,4,5,8,6] => [3,1,2,7,4,8,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,2,7,8,4,5,6] => [3,1,2,8,4,5,7,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,2,7,4,5,6,8] => [3,1,2,7,4,5,6,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,7,2,4,5,8,6] => [3,7,1,2,4,8,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => [3,8,1,2,4,5,7,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6,8] => [3,7,1,2,4,5,6,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,7,1,2,4,5,8,6] => [7,1,3,2,4,8,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [3,7,1,2,4,8,5,6] => [7,1,3,2,8,5,4,6] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [3,7,1,2,8,4,5,6] => [7,1,3,8,4,5,2,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [8,1,3,2,4,5,7,6] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6,8] => [7,1,3,2,4,5,6,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [3,1,2,4,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => [3,1,2,4,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [3,1,2,4,8,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,2,8,4,5,6,7] => [3,1,2,8,4,5,6,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [3,8,1,2,4,5,6,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [8,1,3,2,4,5,6,7] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,6,8,3,7] => [1,2,8,4,5,6,3,7] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,3,7,8] => [1,2,6,4,5,3,7,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,5,3,7,8,6] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,7,3,8,6] => [1,2,7,4,5,8,3,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,7,8,3,6] => [1,2,8,4,5,3,7,6] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,4,5,3,6,8,7] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,4,5,3,8,6,7] => [1,2,5,4,3,8,6,7] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,6,7,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,6,3,7,8,5] => [1,2,6,4,8,3,7,5] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,6,3,7,5,8] => [1,2,6,4,7,3,5,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,6,7,3,8,5] => [1,2,7,4,8,6,3,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,6,7,8,3,5] => [1,2,8,4,3,6,7,5] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,8,3,5,7] => [1,2,8,4,3,6,5,7] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [1,2,6,4,3,5,7,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,3,7,5,8,6] => [1,2,4,3,7,8,5,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,4,3,7,8,5,6] => [1,2,4,3,8,5,7,6] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,4,3,7,5,6,8] => [1,2,4,3,7,5,6,8] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,4,7,3,8,5,6] => [1,2,7,4,8,5,3,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,4,7,8,3,5,6] => [1,2,8,4,3,5,7,6] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [1,2,7,4,3,5,6,8] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => [1,2,4,3,5,8,6,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [1,2,4,3,8,5,6,7] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [1,2,8,4,3,5,6,7] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [1,4,8,2,5,6,7,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,4,2,5,6,7,3,8] => [1,4,7,2,5,6,3,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,4,2,5,6,8,3,7] => [1,4,8,2,5,6,3,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,4,2,5,6,3,7,8] => [1,4,6,2,5,3,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [1,4,5,2,3,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => [1,4,7,2,5,8,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6,8] => [1,4,7,2,5,3,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,4,5,2,3,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => [1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [1,5,8,4,2,6,7,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,5,2,6,7,3,8] => [1,5,7,4,2,6,3,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,5,2,6,8,3,7] => [1,5,8,4,2,6,3,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,5,6,4,2,3,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,4,5,6,2,7,8,3] => [1,6,8,4,5,2,7,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,4,5,6,2,7,3,8] => [1,6,7,4,5,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,2,8,3] => [1,7,8,4,5,6,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,2,3] => [1,8,2,4,5,6,7,3] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,2,3,8] => [1,7,2,4,5,6,3,8] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,4,5,6,2,8,3,7] => [1,6,8,4,5,2,3,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => [1,6,2,4,5,3,7,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,4,5,2,3,7,8,6] => [1,5,2,4,3,8,7,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6,8] => [1,5,2,4,3,7,6,8] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => [1,5,7,4,2,8,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6,8] => [1,5,7,4,2,3,6,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [1,7,2,4,5,8,3,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,4,5,7,2,8,3,6] => [1,7,8,4,5,3,2,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => [1,7,2,4,5,3,6,8] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,5,2,3,8,6,7] => [1,5,2,4,3,8,6,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [1,5,8,4,2,3,6,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,2,3,6,7,8] => [1,5,2,4,3,6,7,8] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => [1,4,2,3,6,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,8,5,7] => [1,4,2,3,8,6,5,7] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,6,5,7,8] => [1,4,2,3,6,5,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,6,3,7,8,5] => [1,4,6,2,8,3,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => [1,4,6,2,7,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,6,7,3,8,5] => [1,4,7,2,8,6,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => [1,4,8,2,3,6,7,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,6,7,3,5,8] => [1,4,7,2,3,6,5,8] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,8,7] => [1,4,6,2,3,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,4,6,2,8,3,5,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,8,3,5,7] => [1,4,8,2,3,6,5,7] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => [1,4,6,2,3,5,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,4,6,2,3,7,8,5] => [1,6,2,4,8,3,7,5] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,4,6,2,3,7,5,8] => [1,6,2,4,7,3,5,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => [1,6,7,4,8,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,6,2,7,8,3,5] => [1,6,8,4,3,2,7,5] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,7,3,5,8] => [1,6,7,4,3,2,5,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,4,6,7,2,3,8,5] => [1,7,2,4,8,6,3,5] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => [1,7,8,4,3,6,2,5] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [1,7,2,4,3,6,5,8] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,8,7] => [1,6,2,4,3,5,8,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,8,5,7] => [1,6,2,4,8,3,5,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => [1,6,8,4,3,2,5,7] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [1,8,2,4,3,6,5,7] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,6,2,3,5,7,8] => [1,6,2,4,3,5,7,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,4,2,3,5,7,8,6] => [1,4,2,3,5,8,7,6] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => [1,4,2,3,5,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,4,2,3,7,5,8,6] => [1,4,2,3,7,8,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,3,7,8,5,6] => [1,4,2,3,8,5,7,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => [1,4,2,3,7,5,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,4,2,7,3,5,8,6] => [1,4,7,2,3,8,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => [1,4,7,2,8,5,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => [1,4,8,2,3,5,7,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => [1,4,7,2,3,5,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,4,7,2,3,5,8,6] => [1,7,2,4,3,8,5,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => [1,7,8,4,3,5,2,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6,8] => [1,7,2,4,3,5,6,8] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,4,2,3,5,6,8,7] => [1,4,2,3,5,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,4,2,3,5,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [1,4,2,3,8,5,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [1,4,8,2,3,5,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [1,8,2,4,3,5,6,7] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => [4,1,8,2,5,6,7,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [4,1,6,2,5,3,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,5,3,7,8,6] => [4,1,5,2,3,8,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,8] => [4,1,5,2,3,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,5,7,3,8,6] => [4,1,7,2,5,8,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,5,7,8,3,6] => [4,1,8,2,5,3,7,6] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,5,3,8,6,7] => [4,1,5,2,3,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,5,3,6,7,8] => [4,1,5,2,3,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [4,5,8,1,2,6,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,5,2,6,7,3,8] => [4,5,7,1,2,6,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [4,5,6,1,2,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => [4,5,8,1,2,6,3,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,1,5,2,6,3,7,8] => [4,5,6,1,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,1,5,6,2,7,3,8] => [4,6,7,1,5,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,5,6,7,2,8,3] => [4,7,8,1,5,6,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,2,3] => [4,8,2,1,5,6,7,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,5,6,2,3,8,7] => [4,6,2,1,5,3,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,5,6,8,2,3,7] => [4,8,2,1,5,6,3,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,1,5,6,2,3,7,8] => [4,6,2,1,5,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [4,5,2,1,3,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6,8] => [4,5,2,1,3,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [4,5,7,1,2,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [4,5,8,1,2,3,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,5,7,2,8,3,6] => [4,7,8,1,5,3,2,6] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6,8] => [4,7,2,1,5,3,6,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,1,5,2,3,8,6,7] => [4,5,2,1,3,8,6,7] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,1,5,2,8,3,6,7] => [4,5,8,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,5,2,3,6,7,8] => [4,5,2,1,3,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [5,1,7,4,2,6,3,8] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [5,1,6,4,2,3,8,7] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,5,1,2,6,8,3,7] => [5,1,8,4,2,6,3,7] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,5,1,6,2,7,8,3] => [5,6,8,4,1,2,7,3] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => [5,6,7,4,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,5,1,6,7,2,8,3] => [5,7,8,4,1,6,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,5,1,6,7,8,2,3] => [5,8,2,4,1,6,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [4,5,1,6,7,2,3,8] => [5,7,2,4,1,6,3,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [4,5,1,6,2,3,8,7] => [5,6,2,4,1,3,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [4,5,1,6,2,8,3,7] => [5,6,8,4,1,2,3,7] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [4,5,1,6,8,2,3,7] => [5,8,2,4,1,6,3,7] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,1,6,2,3,7,8] => [5,6,2,4,1,3,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,1,2,7,8,3] => [6,1,8,4,5,2,7,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,1,2,7,3,8] => [6,1,7,4,5,2,3,8] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,1,7,2,8,3] => [6,7,8,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,6,1,7,8,2,3] => [6,8,2,4,5,1,7,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => [7,8,2,4,5,6,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => [8,1,2,4,5,6,7,3] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [7,1,2,4,5,6,3,8] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [6,1,2,4,5,3,8,7] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,6,1,2,8,3,7] => [6,1,8,4,5,2,3,7] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [6,8,2,4,5,1,3,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [8,1,2,4,5,6,3,7] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [4,5,1,2,7,8,3,6] => [5,1,8,4,2,3,7,6] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6,8] => [5,1,7,4,2,3,6,8] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [4,5,1,7,2,8,3,6] => [5,7,8,4,1,3,2,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [4,5,1,7,8,2,3,6] => [5,8,2,4,1,3,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6,8] => [5,7,2,4,1,3,6,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [7,1,8,4,5,3,2,6] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [8,1,2,4,5,3,7,6] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,5,1,2,3,6,8,7] => [5,1,2,4,3,6,8,7] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,5,1,2,8,3,6,7] => [5,1,8,4,2,3,6,7] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,5,1,8,2,3,6,7] => [5,8,2,4,1,3,6,7] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [8,1,2,4,5,3,6,7] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [5,1,2,4,3,6,7,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [4,1,2,3,8,6,7,5] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,6,7,5,8] => [4,1,2,3,7,6,5,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [4,1,2,3,6,5,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,8,5,7] => [4,1,2,3,8,6,5,7] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [4,1,2,3,6,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,6,3,7,8,5] => [4,1,6,2,8,3,7,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5,8] => [4,1,6,2,7,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,8,7] => [4,1,6,2,3,5,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => [4,1,6,2,8,3,5,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,8,3,5,7] => [4,1,8,2,3,6,5,7] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,6,3,5,7,8] => [4,1,6,2,3,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [4,6,2,1,8,3,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,6,2,3,7,5,8] => [4,6,2,1,7,3,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [4,6,7,1,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,6,2,7,3,5,8] => [4,6,7,1,3,2,5,8] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,6,7,2,8,3,5] => [4,7,8,1,3,6,2,5] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,6,7,8,2,3,5] => [4,8,2,1,3,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,6,7,2,3,5,8] => [4,7,2,1,3,6,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,8,7] => [4,6,2,1,3,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,8,2,3,5,7] => [4,8,2,1,3,6,5,7] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,6,2,3,5,7,8] => [4,6,2,1,3,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [4,6,1,2,3,7,8,5] => [6,1,2,4,8,3,7,5] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [6,1,2,4,7,3,5,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,6,1,2,7,3,8,5] => [6,1,7,4,8,2,3,5] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [4,6,1,7,2,8,3,5] => [6,7,8,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => [6,7,2,4,3,1,5,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [4,6,7,1,2,8,3,5] => [7,1,8,4,3,6,2,5] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [7,8,2,4,3,6,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,8,7] => [6,1,2,4,3,5,8,7] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,8,5,7] => [6,1,2,4,8,3,5,7] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,8,3,5,7] => [6,1,8,4,3,2,5,7] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => [6,8,2,4,3,1,5,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [8,1,2,4,3,6,5,7] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [4,6,1,2,3,5,7,8] => [6,1,2,4,3,5,7,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [4,1,2,3,5,8,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [4,1,2,3,5,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => [4,1,2,3,7,8,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,3,7,8,5,6] => [4,1,2,3,8,5,7,6] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [4,1,2,3,7,5,6,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,7,3,5,8,6] => [4,1,7,2,3,8,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [4,1,2,7,3,8,5,6] => [4,1,7,2,8,5,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => [4,1,8,2,3,5,7,6] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,1,2,7,3,5,6,8] => [4,1,7,2,3,5,6,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [4,1,7,2,3,8,5,6] => [4,7,2,1,8,5,3,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,1,7,8,2,3,5,6] => [4,8,2,1,3,5,7,6] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [4,7,1,2,8,3,5,6] => [7,1,8,4,3,5,2,6] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => [7,8,2,4,3,5,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,7,8,1,2,3,5,6] => [8,1,2,4,3,5,7,6] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6,8] => [7,1,2,4,3,5,6,8] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [4,1,2,3,5,6,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [4,1,2,3,5,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [4,1,2,3,8,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,8,3,5,6,7] => [4,1,8,2,3,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [4,8,2,1,3,5,6,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [8,1,2,4,3,5,6,7] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,8,4,7] => [1,2,3,8,5,6,4,7] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,2,3,5,7,4,8,6] => [1,2,3,7,5,8,4,6] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,3,5,7,8,4,6] => [1,2,3,8,5,4,7,6] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6,8] => [1,2,3,7,5,4,6,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,8,6,7] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,5,8,4,6,7] => [1,2,3,8,5,4,6,7] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [1,2,5,8,3,6,7,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,2,5,3,6,7,4,8] => [1,2,5,7,3,6,4,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,5,3,6,4,8,7] => [1,2,5,6,3,4,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,2,5,3,6,8,4,7] => [1,2,5,8,3,6,4,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => [1,2,5,6,3,4,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [1,2,6,8,5,3,7,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,8] => [1,2,6,7,5,3,4,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [1,2,7,8,5,6,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,6,7,8,3,4] => [1,2,8,3,5,6,7,4] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,5,6,3,8,4,7] => [1,2,6,8,5,3,4,7] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,2,5,6,8,3,4,7] => [1,2,8,3,5,6,4,7] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,2,6,3,5,4,7,8] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,7,8,6] => [1,2,5,3,4,8,7,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6,8] => [1,2,5,3,4,7,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,2,5,3,7,4,8,6] => [1,2,5,7,3,8,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,2,5,3,7,8,4,6] => [1,2,5,8,3,4,7,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6,8] => [1,2,5,7,3,4,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,2,5,7,3,4,8,6] => [1,2,7,3,5,8,4,6] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,2,5,7,3,8,4,6] => [1,2,7,8,5,4,3,6] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,2,5,7,8,3,4,6] => [1,2,8,3,5,4,7,6] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [1,2,7,3,5,4,6,8] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,2,5,3,4,6,8,7] => [1,2,5,3,4,6,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4,8,6,7] => [1,2,5,3,4,8,6,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [1,2,5,8,3,4,6,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [1,2,8,3,5,4,6,7] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,5,3,4,6,7,8] => [1,2,5,3,4,6,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,5,2,3,6,7,4,8] => [1,5,2,7,3,6,4,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,5,2,3,6,4,8,7] => [1,5,2,6,3,4,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,5,2,3,6,8,4,7] => [1,5,2,8,3,6,4,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,2,3,6,4,7,8] => [1,5,2,6,3,4,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => [1,5,6,8,2,3,7,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [1,5,6,7,2,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,5,2,6,7,3,8,4] => [1,5,7,8,2,6,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,7,8,3,4] => [1,5,8,3,2,6,7,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,2,6,7,3,4,8] => [1,5,7,3,2,6,4,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => [1,5,6,8,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => [1,5,6,3,2,4,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,5,6,2,3,7,8,4] => [1,6,2,8,5,3,7,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,5,6,2,3,7,4,8] => [1,6,2,7,5,3,4,8] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,5,6,2,7,3,8,4] => [1,6,7,8,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,5,6,2,7,8,3,4] => [1,6,8,3,5,2,7,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,5,6,7,2,3,8,4] => [1,7,2,8,5,6,3,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,6,7,2,8,3,4] => [1,7,8,3,5,6,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => [1,8,2,3,5,6,7,4] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => [1,6,2,8,5,3,4,7] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => [1,6,8,3,5,2,4,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => [1,8,2,3,5,6,4,7] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => [1,5,2,3,4,8,7,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [1,5,2,3,4,7,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,7,4,8,6] => [1,5,2,7,3,8,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,7,8,4,6] => [1,5,2,8,3,4,7,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6,8] => [1,5,2,7,3,4,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,5,2,7,3,4,8,6] => [1,5,7,3,2,8,4,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,5,7,8,2,4,3,6] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,5,2,7,8,3,4,6] => [1,5,8,3,2,4,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => [1,5,7,3,2,4,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,5,7,2,3,4,8,6] => [1,7,2,3,5,8,4,6] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,2,3,8,4,6] => [1,7,2,8,5,4,3,6] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [1,7,8,3,5,4,2,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6,8] => [1,7,2,3,5,4,6,8] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,5,2,3,4,6,8,7] => [1,5,2,3,4,6,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,5,2,3,4,8,6,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,5,2,3,8,4,6,7] => [1,5,2,8,3,4,6,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [1,5,8,3,2,4,6,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [1,8,2,3,5,4,6,7] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [5,1,2,8,3,6,7,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,6,7,4,8] => [5,1,2,7,3,6,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,1,2,3,6,4,8,7] => [5,1,2,6,3,4,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,6,4,7,8] => [5,1,2,6,3,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,1,2,6,7,8,3,4] => [5,1,8,3,2,6,7,4] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,3,4,8,7] => [5,1,6,3,2,4,8,7] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,1,2,6,8,3,4,7] => [5,1,8,3,2,6,4,7] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,2,6,3,4,7,8] => [5,1,6,3,2,4,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [5,6,2,8,1,3,7,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,1,6,2,3,7,4,8] => [5,6,2,7,1,3,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [5,1,6,2,7,8,3,4] => [5,6,8,3,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,1,6,2,7,3,4,8] => [5,6,7,3,1,2,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,6,7,2,3,8,4] => [5,7,2,8,1,6,3,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [5,1,6,7,2,8,3,4] => [5,7,8,3,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,2,3,4] => [5,8,2,3,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,1,6,7,2,3,4,8] => [5,7,2,3,1,6,4,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => [5,6,2,8,1,3,4,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,1,6,8,2,3,4,7] => [5,8,2,3,1,6,4,7] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => [6,1,2,8,5,3,7,4] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => [6,1,7,8,5,2,3,4] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => [6,1,8,3,5,2,7,4] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => [6,7,2,8,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [5,6,1,7,2,8,3,4] => [6,7,8,3,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,6,1,7,8,2,3,4] => [6,8,2,3,5,1,7,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => [7,1,2,8,5,6,3,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [5,6,7,1,2,8,3,4] => [7,1,8,3,5,6,2,4] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [7,8,2,3,5,6,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => [7,1,2,3,5,6,4,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => [6,1,2,8,5,3,4,7] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,6,1,8,2,3,4,7] => [6,8,2,3,5,1,4,7] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [8,1,2,3,5,6,4,7] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,1,2,3,4,7,8] => [6,1,2,3,5,4,7,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [5,1,2,3,4,8,7,6] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,7,4,8,6] => [5,1,2,7,3,8,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6,8] => [5,1,2,7,3,4,6,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => [5,1,7,3,2,8,4,6] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,7,3,8,4,6] => [5,1,7,8,2,4,3,6] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,7,8,3,4,6] => [5,1,8,3,2,4,7,6] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6,8] => [5,1,7,3,2,4,6,8] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [5,1,7,2,3,8,4,6] => [5,7,2,8,1,4,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => [5,7,8,3,1,4,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,7,1,2,3,4,8,6] => [7,1,2,3,5,8,4,6] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => [7,1,8,3,5,4,2,6] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,7,1,8,2,3,4,6] => [7,8,2,3,5,4,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [8,1,2,3,5,4,7,6] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6,8] => [7,1,2,3,5,4,6,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [5,1,2,3,4,6,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => [5,1,2,3,4,8,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,8,4,6,7] => [5,1,2,8,3,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => [5,1,8,3,2,4,6,7] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [5,8,2,3,1,4,6,7] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [8,1,2,3,5,4,6,7] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,6,8,5,7] => [1,2,3,4,8,6,5,7] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [1,2,3,6,8,4,7,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => [1,2,3,6,7,4,5,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => [1,2,3,7,8,6,4,5] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,2,3,6,7,8,4,5] => [1,2,3,8,4,6,7,5] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,6,7,4,5,8] => [1,2,3,7,4,6,5,8] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,6,4,5,8,7] => [1,2,3,6,4,5,8,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => [1,2,3,6,8,4,5,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,6,8,4,5,7] => [1,2,3,8,4,6,5,7] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [1,2,6,3,8,4,7,5] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,2,6,3,4,7,5,8] => [1,2,6,3,7,4,5,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,2,6,3,7,4,8,5] => [1,2,6,7,8,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,2,6,3,7,8,4,5] => [1,2,6,8,4,3,7,5] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,2,6,3,7,4,5,8] => [1,2,6,7,4,3,5,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,2,6,7,3,4,8,5] => [1,2,7,3,8,6,4,5] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,2,6,7,3,8,4,5] => [1,2,7,8,4,6,3,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,7,8,3,4,5] => [1,2,8,3,4,6,7,5] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => [1,2,7,3,4,6,5,8] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,8,7] => [1,2,6,3,4,5,8,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,2,6,3,4,8,5,7] => [1,2,6,3,8,4,5,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [1,2,6,8,4,3,5,7] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [1,2,8,3,4,6,5,7] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,3,4,5,7,8] => [1,2,6,3,4,5,7,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [1,6,2,3,7,4,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,6,2,3,7,4,8,5] => [1,6,2,7,8,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,3,7,8,4,5] => [1,6,2,8,4,3,7,5] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => [1,6,7,8,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,6,2,7,8,3,4,5] => [1,6,8,3,4,2,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => [1,6,7,3,4,2,5,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,6,7,2,3,4,8,5] => [1,7,2,3,8,6,4,5] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,7,2,3,8,4,5] => [1,7,2,8,4,6,3,5] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,8,2,3,4,6,7,5] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => [1,7,2,3,4,6,5,8] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,8,7] => [1,6,2,3,4,5,8,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [1,6,2,3,8,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,6,2,3,8,4,5,7] => [1,6,2,8,4,3,5,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => [1,6,8,3,4,2,5,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [1,8,2,3,4,6,5,7] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [6,1,2,3,8,4,7,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => [6,1,2,3,7,4,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,3,7,4,8,5] => [6,1,2,7,8,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,1,2,3,7,8,4,5] => [6,1,2,8,4,3,7,5] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,7,3,4,8,5] => [6,1,7,3,8,2,4,5] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,1,2,7,3,8,4,5] => [6,1,7,8,4,2,3,5] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,1,2,7,8,3,4,5] => [6,1,8,3,4,2,7,5] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [6,1,2,7,3,4,5,8] => [6,1,7,3,4,2,5,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,7,2,3,4,8,5] => [6,7,2,3,8,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,1,7,2,3,8,4,5] => [6,7,2,8,4,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,1,7,2,8,3,4,5] => [6,7,8,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => [6,8,2,3,4,1,7,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [6,1,7,2,3,4,5,8] => [6,7,2,3,4,1,5,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,7,1,2,8,3,4,5] => [7,1,8,3,4,6,2,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,1,8,2,3,4,5] => [7,8,2,3,4,6,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [8,1,2,3,4,6,7,5] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => [7,1,2,3,4,6,5,8] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [6,1,2,3,4,5,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,8,5,7] => [6,1,2,3,8,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,8,4,5,7] => [6,1,2,8,4,3,5,7] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => [6,1,8,3,4,2,5,7] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [6,8,2,3,4,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [8,1,2,3,4,6,5,7] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [1,2,3,4,8,5,7,6] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => [1,2,3,4,7,5,6,8] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [1,2,3,7,4,8,5,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [1,2,3,7,8,5,4,6] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,3,7,8,4,5,6] => [1,2,3,8,4,5,7,6] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6,8] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [1,2,7,3,4,8,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,2,7,3,4,8,5,6] => [1,2,7,3,8,5,4,6] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [1,2,7,8,4,5,3,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,2,8,3,4,5,7,6] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6,8] => [1,2,7,3,4,5,6,8] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [1,7,2,3,4,8,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [1,7,2,3,8,5,4,6] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => [1,7,2,8,4,5,3,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => [1,7,8,3,4,5,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [1,8,2,3,4,5,7,6] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [7,1,2,3,4,8,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [7,1,2,3,8,5,4,6] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,1,2,3,8,4,5,6] => [7,1,2,8,4,5,3,6] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => [7,1,8,3,4,5,2,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [7,8,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [8,1,2,3,4,5,7,6] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [8,1,2,3,4,5,9,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [9,2,1,3,4,5,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [9,1,2,3,4,5,6,10,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => [1,8,2,3,4,5,9,6,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [7,1,2,3,4,5,6,9,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => [2,1,9,3,4,5,6,7,8] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7,9] => [8,2,1,3,4,5,6,7,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => [10,2,1,3,4,5,6,7,8,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,11,9] => [10,1,2,3,4,5,6,7,11,8,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => [8,1,2,3,4,5,6,7,10,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => [2,1,10,3,4,5,6,7,8,9] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8,10] => [9,2,1,3,4,5,6,7,8,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,11,1,3,4,5,6,7,8,9,10] => [11,2,1,3,4,5,6,7,8,9,10] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [1,2,3,8,4,5,6,9,7] => [1,2,3,8,4,5,9,6,7] => [.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,9,8] => [1,7,2,3,4,5,6,9,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7,9] => [2,1,8,3,4,5,6,7,9] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,9,10,1,3,4,5,6,7,8] => [10,2,1,3,4,5,6,7,9,8] => [[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,12,1,3,4,5,6,7,8,9,10,11] => [12,2,1,3,4,5,6,7,8,9,10,11] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [1,2,3,9,4,5,6,7,10,8] => [1,2,3,9,4,5,6,10,7,8] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [1,2,3,4,8,5,6,9,7] => [1,2,3,4,8,5,9,6,7] => [.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,1,3,4,5,9,6,7,8] => [2,1,3,4,5,9,6,7,8] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7] => [1,2,3,4,5,8,9,6,7] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,9,8] => [3,1,2,4,5,6,7,9,8] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,9,7,8] => [2,1,3,4,5,6,9,7,8] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [1,2,3,4,5,9,6,7,10,8] => [1,2,3,4,5,9,6,10,7,8] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,9,2,4,5,6,7,8] => [1,9,3,2,4,5,6,7,8] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,6,9,7,10,8] => [1,2,3,4,5,6,9,10,7,8] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,8,9,6] => [7,1,2,3,4,9,5,8,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,7,10,8,9] => [2,1,3,4,5,6,7,10,8,9] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,9,1,4,5,6,7,8] => [9,2,3,1,4,5,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,8,9,7] => [6,1,2,3,4,5,9,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[] => [] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,1,2] => [9,1,3,4,5,6,7,8,2] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,1,2,4,5,6,9,7,8] => [3,1,2,4,5,6,9,7,8] => [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => [3,1,2,9,4,5,6,7,8] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,9,2,4,5,6,7,8] => [3,9,1,2,4,5,6,7,8] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,9,1,2,4,5,6,7,8] => [9,1,3,2,4,5,6,7,8] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [4,1,2,3,5,9,6,7,8] => [4,1,2,3,5,9,6,7,8] => [[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => [4,1,2,3,9,5,6,7,8] => [[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,1,6,2,7,3,9,4,8] => [5,6,7,9,1,2,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5,1,2,3,4,9,6,7,8] => [5,1,2,3,4,9,6,7,8] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [5,9,1,2,3,4,6,7,8] => [9,1,2,3,5,4,6,7,8] => [[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7,9] => [8,1,2,3,4,6,5,7,9] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,9,7,8] => [6,1,2,3,4,5,9,7,8] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,7,9,2,3,4,5,6,8] => [1,9,2,3,4,5,7,6,8] => [.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8,9] => [1,7,2,3,4,5,6,8,9] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [7,1,8,2,9,3,4,5,6] => [7,8,9,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => [9,1,2,3,4,5,7,8,6] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6,9] => [8,1,2,3,4,5,7,6,9] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [7,9,1,2,3,4,5,6,8] => [9,1,2,3,4,5,7,6,8] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9] => [7,1,2,3,4,5,6,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,8,9,6,7] => [1,2,3,4,5,9,6,8,7] => [.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [1,2,3,4,8,9,5,6,7] => [1,2,3,4,9,5,6,8,7] => [.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => [1,9,2,3,4,5,6,8,7] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7,9] => [1,8,2,3,4,5,6,7,9] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [8,1,2,3,9,4,5,6,7] => [8,1,2,9,4,5,6,3,7] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [8,1,9,2,3,4,5,6,7] => [8,9,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [9,1,2,3,4,5,6,8,7] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,9,7,8] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,9,6,7,8] => [1,2,3,4,5,9,6,7,8] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [1,2,3,4,9,5,6,7,8] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [1,2,3,9,4,5,6,7,8] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => [1,2,9,3,4,5,6,7,8] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [1,9,2,3,4,5,6,7,8] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => [9,2,3,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,10,1,9] => [10,2,3,4,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,1,2] => [10,1,3,4,5,6,7,8,9,2] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,9,11,1,10] => [11,2,3,4,5,6,7,8,9,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,9,1,7,8] => [9,2,3,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [11,1,3,4,5,6,7,8,9,10,2] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => [10,2,3,4,5,6,7,1,8,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,9,1,6,7,8] => [9,2,3,4,5,1,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,10,1,7,8,9] => [10,2,3,4,5,6,1,7,8,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,9,1,5,6,7,8] => [9,2,3,4,1,5,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,10,1,6,7,8,9] => [10,2,3,4,5,1,6,7,8,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,5,6,1,2,3,9,10,7,8] => [6,1,2,4,5,3,10,7,9,8] => [[.,[.,[[.,.],[.,.]]]],[[.,[[.,.],.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8] => [7,2,3,4,5,6,1,9,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8] => [3,2,1,5,4,7,6,9,8] => [[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,5,4,6,7,8,9] => [3,2,1,5,4,6,7,8,9] => [[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,4,5,6,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,7,8,9] => [2,1,4,3,6,5,7,8,9] => [[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,2] => [1,9,3,4,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[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] => [1,3,2,5,4,7,6,9,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,8,7] => [.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,1,5,4,7,6,9,8,10] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,8,7,9,10] => [2,1,4,3,6,5,8,7,9,10] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,3,4,5,6,7,8,9,2] => [.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,9,8] => [.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3] => [.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4] => [.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5] => [.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,6,5,8,7,10,9] => [.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6] => [.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7] => [.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,2] => [3,9,1,4,5,6,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,6,1,7,8,9,2] => [6,9,3,4,5,1,7,8,2] => [[[.,[.,.]],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,1,8,9,2] => [7,9,3,4,5,6,1,8,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,1,9,2] => [8,9,3,4,5,6,7,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [3,10,1,4,5,6,7,8,9,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,8,1,9,10,2] => [8,10,3,4,5,6,7,1,9,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,1,10,2] => [9,10,3,4,5,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [1,10,2,3,4,5,6,7,8,9] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [9,1,2,3,4,5,6,8,7,10] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [1,10,2,3,4,5,6,7,9,8] => [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [1,11,2,3,4,5,6,7,8,9,10] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,8,2,9] => [3,8,1,4,5,6,7,2,9] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,10,8,9] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [1,2,3,4,5,6,7,8,11,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,4,7,5,8,9,6] => [1,2,3,4,7,9,5,8,6] => [.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,3,6,4,7,8,9,5] => [1,2,3,6,9,4,7,8,5] => [.,[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,9,4] => [1,2,5,9,3,6,7,8,4] => [.,[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,9,3] => [1,4,9,2,5,6,7,8,3] => [.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [10,1,2,3,4,5,6,7,8,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,1,6,2,7,8,9] => [5,6,3,4,1,2,7,8,9] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,1,4,8,9,2,5,6,7] => [3,9,1,4,2,5,6,8,7] => [[.,[.,.]],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,6,8,7,9] => [4,1,2,3,5,6,8,7,9] => [[.,[.,[.,.]]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,7,6,8,9] => [5,1,2,3,4,7,6,8,9] => [[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [1,2,3,9,5,4,6,7,8] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,5,7,9,6,8] => [1,2,3,4,5,9,7,6,8] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [1,2,3,4,5,6,10,7,8,9] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,4,6,9,5,7,8] => [1,2,3,4,9,6,5,7,8] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [1,2,3,4,5,10,6,7,8,9] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [1,2,3,4,10,5,6,7,8,9] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [1,2,9,4,3,5,6,7,8] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [1,2,3,10,4,5,6,7,8,9] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [1,2,10,3,4,5,6,7,8,9] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,4,7,5,8,6,9] => [1,2,3,4,7,8,5,6,9] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [3,1,2,5,4,7,6,9,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,9,8] => [3,5,1,2,4,7,6,9,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7,9] => [3,5,1,6,2,4,8,7,9] => [[.,[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,9] => [3,4,1,2,6,5,8,7,9] => [[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8,10] => [3,1,2,5,4,7,6,9,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [3,4,1,2,6,5,8,7,10,9] => [[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8,10] => [1,9,2,3,4,5,6,7,8,10] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [6,7,8,9,10,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => [7,8,9,10,11,12,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [3,1,2,4,5,6,7,8,9,10,11] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,8,9,12,10,11] => [1,2,3,4,5,6,7,8,9,12,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,10,2,4,5,6,7,8,9] => [3,10,1,2,4,5,6,7,8,9] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => [3,1,2,4,5,6,7,8,9,10,11,12] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,11,2] => [3,11,1,4,5,6,7,8,9,10,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [10,1,2,3,4,6,7,8,9,5] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => [9,10,2,3,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,10,1,4,5,6,7,8,9] => [10,2,3,1,4,5,6,7,8,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,10,1,5,6,7,8,9] => [10,2,3,4,1,5,6,7,8,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,2,3,4,7,8,9,5] => [6,1,2,3,9,4,7,8,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [5,10,1,2,3,4,6,7,8,9] => [10,1,2,3,5,4,6,7,8,9] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => [10,1,2,3,4,5,6,7,9,8] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,8,1,9,7] => [8,2,3,4,5,6,9,1,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,7,9,1,10,8] => [9,2,3,4,5,6,7,10,1,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,10,1,11,2] => [10,11,3,4,5,6,7,8,9,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,9] => [4,1,2,3,6,5,8,7,9] => [[.,[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,1,9,3] => [8,2,9,4,5,6,7,1,3] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => [3,1,2,10,4,5,6,7,8,9] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => [5,1,2,3,4,10,6,7,8,9] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,10,1,11,9] => [10,2,3,4,5,6,7,8,11,1,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,9,1,10,3] => [9,2,10,4,5,6,7,8,1,3] => [[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,1,3,4,5,8,6,7,9] => [2,1,3,4,5,8,6,7,9] => [[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,9,8] => [1,4,5,2,3,7,6,9,8] => [.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,9] => [1,4,2,3,6,5,8,7,9] => [.,[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,10,9] => [1,4,2,3,6,5,8,7,10,9] => [.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [2,1,7,8,9,10,3,4,5,6] => [2,1,10,3,4,5,7,8,9,6] => [[.,.],[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [3,4,1,2,8,9,10,5,6,7] => [4,1,3,2,10,5,6,8,9,7] => [[.,[[.,.],.]],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,6,7,8,1,2,3,4,10,9] => [8,1,2,3,5,6,7,4,10,9] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,7,1,8,2,9,3] => [7,8,9,4,5,6,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,9,10,7] => [8,1,2,3,4,5,10,6,9,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,9,8] => [1,2,3,4,7,5,6,9,8] => [.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,7,8] => [2,1,4,3,6,5,9,7,8] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [1,3,2,5,4,7,6,10,8,9] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7,9] => [8,2,1,4,3,6,5,7,9] => [[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,6,2,7,3,8,4,9,5,10] => [1,6,7,8,9,2,3,4,5,10] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [12,1,2,3,4,5,6,7,8,9,10,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [4,2,5,1,3,7,6,9,8,10] => [[[.,.],[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,6,3,5,4,10,7,9,8,12,11] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,9,8] => [1,5,3,2,4,7,6,9,8] => [.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8] => [4,2,5,1,3,7,6,9,8] => [[[.,.],[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,8,5,9,7] => [4,1,6,2,8,3,9,5,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,6,2,7,3,8,4,9,5] => [1,6,7,8,9,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,7,3,8,4,9] => [5,6,7,8,1,2,3,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,9,8] => [3,1,2,7,5,4,6,9,8] => [[.,[.,.]],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [8,1,9,2,10,3,4,5,6,7] => [8,9,10,3,4,5,6,1,2,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,10,11,1,12,2] => [11,12,3,4,5,6,7,8,9,10,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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 σ is a pair i<j such that i<σ(j)<σ(i). The element σ(j) is then an invisible inversion bottom.
A descent view in a permutation π is an element π(j) such that π(i+1)<π(j)<π(i), and additionally the smallest element in the decreasing run containing π(i) is smaller than the smallest element in the decreasing run containing π(j).
This map is a bijection χ:Sn→Sn, such that
An invisible inversion of a permutation σ is a pair i<j such that i<σ(j)<σ(i). The element σ(j) is then an invisible inversion bottom.
A descent view in a permutation π is an element π(j) such that π(i+1)<π(j)<π(i), and additionally the smallest element in the decreasing run containing π(i) is smaller than the smallest element in the decreasing run containing π(j).
This map is a bijection χ:Sn→Sn, such that
- the multiset of descent views in π is the multiset of invisible inversion bottoms in χ(π),
- the set of left-to-right maxima of π is the set of maximal elements in the cycles of χ(π),
- the set of global ascent of π is the set of global ascent of χ(π),
- the set of maximal elements in the decreasing runs of π is the set of weak deficiency positions of χ(π), and
- the set of minimal elements in the decreasing runs of π is the set of weak deficiency values of χ(π).
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
searching the database
Sorry, this map was not found in the database.