Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
[1,0] => [1] => [1] => [.,.]
[1,0,1,0] => [1,2] => [1,2] => [.,[.,.]]
[1,1,0,0] => [2,1] => [2,1] => [[.,.],.]
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [.,[[.,.],.]]
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [[.,.],[.,.]]
[1,1,0,1,0,0] => [2,3,1] => [3,1,2] => [[.,[.,.]],.]
[1,1,1,0,0,0] => [3,2,1] => [3,2,1] => [[[.,.],.],.]
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,2,3] => [.,[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,4,3,2] => [.,[[[.,.],.],.]]
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1,2,4] => [[.,[.,.]],[.,.]]
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,1,2,3] => [[.,[.,[.,.]]],.]
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,3,1,2] => [[[.,[.,.]],.],.]
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [4,1,3,2] => [[.,[[.,.],.]],.]
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [4,2,1,3] => [[[.,.],[.,.]],.]
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [[[[.,.],.],.],.]
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,5,4,2,3] => [.,[[[.,[.,.]],.],.]]
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [1,5,3,2,4] => [.,[[[.,.],[.,.]],.]]
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,1,2,5,4] => [[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.]
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,3,1,2,5] => [[[.,[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [5,1,2,4,3] => [[.,[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [5,3,1,2,4] => [[[.,[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,4,3,1,2] => [[[[.,[.,.]],.],.],.]
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [4,1,3,2,5] => [[.,[[.,.],.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [5,1,3,2,4] => [[.,[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [5,4,1,3,2] => [[[.,[[.,.],.]],.],.]
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [4,2,1,3,5] => [[[.,.],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [5,1,4,2,3] => [[.,[[.,[.,.]],.]],.]
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [5,2,1,3,4] => [[[.,.],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [5,4,2,1,3] => [[[[.,.],[.,.]],.],.]
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [5,1,4,3,2] => [[.,[[[.,.],.],.]],.]
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [5,2,1,4,3] => [[[.,.],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [5,3,2,1,4] => [[[[.,.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,6,5,3,4] => [.,[.,[[[.,[.,.]],.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,6,3,5,4] => [.,[.,[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,6,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,5,4,2,3,6] => [.,[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [1,6,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,6,5,4,2,3] => [.,[[[[.,[.,.]],.],.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,5,2,4,3,6] => [.,[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,6,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,6,5,2,4,3] => [.,[[[.,[[.,.],.]],.],.]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [1,5,3,2,4,6] => [.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [1,6,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [1,6,3,2,4,5] => [.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [1,6,5,3,2,4] => [.,[[[[.,.],[.,.]],.],.]]
>>> Load all 1012 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,6,2,5,4,3] => [.,[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [1,6,3,2,5,4] => [.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [1,6,4,3,2,5] => [.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,6,5,3,4] => [[.,.],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,6,3,5,4] => [[.,.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [2,1,6,4,3,5] => [[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,1,2,6,5,4] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [6,1,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [4,3,1,2,6,5] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [5,1,2,4,3,6] => [[.,[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [6,1,2,4,3,5] => [[.,[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [6,5,1,2,4,3] => [[[.,[.,[[.,.],.]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [6,1,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [6,1,2,5,4,3] => [[.,[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [6,3,1,2,5,4] => [[[.,[.,.]],[[.,.],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1,6,4,5] => [[[.,.],.],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,1,3,2,5,6] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [4,1,3,2,6,5] => [[.,[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [5,1,3,2,4,6] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [6,1,3,2,4,5] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [6,5,1,3,2,4] => [[[.,[[.,.],[.,.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [5,4,1,3,2,6] => [[[.,[[.,.],.]],.],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [6,1,3,2,5,4] => [[.,[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [6,4,1,3,2,5] => [[[.,[[.,.],.]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [4,2,1,3,6,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [5,1,4,2,3,6] => [[.,[[.,[.,.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [6,1,4,2,3,5] => [[.,[[.,[.,.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [6,5,1,4,2,3] => [[[.,[[.,[.,.]],.]],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [6,1,5,2,3,4] => [[.,[[.,[.,[.,.]]],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [5,4,2,1,3,6] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [6,1,5,4,2,3] => [[.,[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [6,2,1,3,5,4] => [[[.,.],[.,[[.,.],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [5,1,4,3,2,6] => [[.,[[[.,.],.],.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [6,1,4,3,2,5] => [[.,[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [6,5,1,4,3,2] => [[[.,[[[.,.],.],.]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [5,2,1,4,3,6] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [6,1,5,2,4,3] => [[.,[[.,[[.,.],.]],.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [6,2,1,4,3,5] => [[[.,.],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [6,5,2,1,4,3] => [[[[.,.],[[.,.],.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [5,3,2,1,4,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [6,1,5,3,2,4] => [[.,[[[.,.],[.,.]],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [6,2,1,5,3,4] => [[[.,.],[[.,[.,.]],.]],.]
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [6,1,5,4,3,2] => [[.,[[[[.,.],.],.],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [6,2,1,5,4,3] => [[[.,.],[[[.,.],.],.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [6,3,2,1,5,4] => [[[[.,.],.],[[.,.],.]],.]
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,7,6,4,5] => [.,[.,[.,[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [1,2,3,7,5,4,6] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,7,6,3,4,5] => [.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,6,5,3,4,7] => [.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,7,3,4,6,5] => [.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [1,2,7,5,3,4,6] => [.,[.,[[[.,[.,.]],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,7,6,5,3,4] => [.,[.,[[[[.,[.,.]],.],.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,6,3,5,4,7] => [.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,7,3,5,4,6] => [.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,7,6,3,5,4] => [.,[.,[[[.,[[.,.],.]],.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [1,2,6,4,3,5,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [1,2,7,3,6,4,5] => [.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [1,2,7,4,3,5,6] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [1,2,7,6,4,3,5] => [.,[.,[[[[.,.],[.,.]],.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,7,3,6,5,4] => [.,[.,[[.,[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [1,2,7,4,3,6,5] => [.,[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [1,2,7,5,4,3,6] => [.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,3,2,7,6,4,5] => [.,[[.,.],[[[.,[.,.]],.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,3,2,7,4,6,5] => [.,[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [1,3,2,7,5,4,6] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,4,2,3,7,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,7,6,2,3,4,5] => [.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,6,5,2,3,4,7] => [.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,7,2,3,4,6,5] => [.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [1,7,5,2,3,4,6] => [.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,7,6,5,2,3,4] => [.,[[[[.,[.,[.,.]]],.],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,5,4,2,3,6,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,5,4,2,3,7,6] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,6,2,3,5,4,7] => [.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,7,2,3,5,4,6] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,7,6,2,3,5,4] => [.,[[[.,[.,[[.,.],.]]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [1,6,4,2,3,5,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [1,7,2,3,6,4,5] => [.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [1,7,4,2,3,5,6] => [.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [1,7,6,4,2,3,5] => [.,[[[[.,[.,.]],[.,.]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,6,5,4,2,3,7] => [.,[[[[.,[.,.]],.],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,7,2,3,6,5,4] => [.,[[.,[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [1,7,4,2,3,6,5] => [.,[[[.,[.,.]],[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [1,7,5,4,2,3,6] => [.,[[[[.,[.,.]],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,7,6,5,4,2,3] => [.,[[[[[.,[.,.]],.],.],.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,4,3,2,7,5,6] => [.,[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,5,2,4,3,6,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,5,2,4,3,7,6] => [.,[[.,[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,6,2,4,3,5,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,7,2,4,3,5,6] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,7,6,2,4,3,5] => [.,[[[.,[[.,.],[.,.]]],.],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,6,5,2,4,3,7] => [.,[[[.,[[.,.],.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,7,2,4,3,6,5] => [.,[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [1,7,5,2,4,3,6] => [.,[[[.,[[.,.],.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,7,6,5,2,4,3] => [.,[[[[.,[[.,.],.]],.],.],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [1,5,3,2,4,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [1,5,3,2,4,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [1,6,2,5,3,4,7] => [.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [1,7,2,5,3,4,6] => [.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [1,7,6,2,5,3,4] => [.,[[[.,[[.,[.,.]],.]],.],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [1,6,3,2,4,5,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [1,7,2,6,3,4,5] => [.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [1,7,3,2,4,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [1,7,6,3,2,4,5] => [.,[[[[.,.],[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [1,6,5,3,2,4,7] => [.,[[[[.,.],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [1,7,2,6,5,3,4] => [.,[[.,[[[.,[.,.]],.],.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [1,7,3,2,4,6,5] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [1,7,5,3,2,4,6] => [.,[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [1,7,6,5,3,2,4] => [.,[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,6,2,5,4,3,7] => [.,[[.,[[[.,.],.],.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,7,2,5,4,3,6] => [.,[[.,[[[.,.],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,7,6,2,5,4,3] => [.,[[[.,[[[.,.],.],.]],.],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [1,6,3,2,5,4,7] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [1,7,2,6,3,5,4] => [.,[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [1,7,3,2,5,4,6] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [1,7,6,3,2,5,4] => [.,[[[[.,.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [1,6,4,3,2,5,7] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [1,7,2,6,4,3,5] => [.,[[.,[[[.,.],[.,.]],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [1,7,3,2,6,4,5] => [.,[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [1,7,4,3,2,5,6] => [.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [1,7,6,4,3,2,5] => [.,[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,7,2,6,5,4,3] => [.,[[.,[[[[.,.],.],.],.]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [1,7,3,2,6,5,4] => [.,[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [1,7,4,3,2,6,5] => [.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [1,7,5,4,3,2,6] => [.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [2,1,3,7,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [2,1,3,7,4,6,5] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [2,1,3,7,5,4,6] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [2,1,7,6,3,4,5] => [[.,.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [2,1,6,5,3,4,7] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [2,1,7,3,4,6,5] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [2,1,7,5,3,4,6] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [2,1,7,6,5,3,4] => [[.,.],[[[[.,[.,.]],.],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [2,1,6,3,5,4,7] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [2,1,7,3,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [2,1,7,6,3,5,4] => [[.,.],[[[.,[[.,.],.]],.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [2,1,6,4,3,5,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [2,1,7,3,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [2,1,7,4,3,5,6] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [2,1,7,6,4,3,5] => [[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [2,1,7,3,6,5,4] => [[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [2,1,7,4,3,6,5] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [2,1,7,5,4,3,6] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [3,1,2,4,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,1,2,7,6,4,5] => [[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [3,1,2,6,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,1,2,7,4,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [3,1,2,7,5,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,1,2,7,6,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,1,2,3,7,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [7,6,1,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,5,1,2,3,4,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [7,1,2,3,4,6,5] => [[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [7,5,1,2,3,4,6] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [7,6,5,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,4,1,2,3,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [5,4,1,2,3,7,6] => [[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [6,1,2,3,5,4,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [7,1,2,3,5,4,6] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [7,6,1,2,3,5,4] => [[[.,[.,[.,[[.,.],.]]]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [6,4,1,2,3,5,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [7,1,2,3,6,4,5] => [[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [7,4,1,2,3,5,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [7,6,4,1,2,3,5] => [[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,5,4,1,2,3,7] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [7,1,2,3,6,5,4] => [[.,[.,[.,[[[.,.],.],.]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [7,4,1,2,3,6,5] => [[[.,[.,[.,.]]],[[.,.],.]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [7,5,4,1,2,3,6] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,6,5,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,3,1,2,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [4,3,1,2,5,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [4,3,1,2,6,5,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [4,3,1,2,7,5,6] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [4,3,1,2,7,6,5] => [[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [5,1,2,4,3,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [5,1,2,4,3,7,6] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [6,1,2,4,3,5,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [7,1,2,4,3,5,6] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [7,6,1,2,4,3,5] => [[[.,[.,[[.,.],[.,.]]]],.],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [6,5,1,2,4,3,7] => [[[.,[.,[[.,.],.]]],.],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [7,1,2,4,3,6,5] => [[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [7,5,1,2,4,3,6] => [[[.,[.,[[.,.],.]]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [7,6,5,1,2,4,3] => [[[[.,[.,[[.,.],.]]],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [5,3,1,2,4,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [5,3,1,2,4,7,6] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [6,1,2,5,3,4,7] => [[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [7,1,2,5,3,4,6] => [[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [7,6,1,2,5,3,4] => [[[.,[.,[[.,[.,.]],.]]],.],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [6,3,1,2,4,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [7,1,2,6,3,4,5] => [[.,[.,[[.,[.,[.,.]]],.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [7,3,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [7,6,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [6,5,3,1,2,4,7] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [7,1,2,6,5,3,4] => [[.,[.,[[[.,[.,.]],.],.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [7,3,1,2,4,6,5] => [[[.,[.,.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [7,5,3,1,2,4,6] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [7,6,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,4,3,1,2,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [5,4,3,1,2,7,6] => [[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [6,1,2,5,4,3,7] => [[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [7,1,2,5,4,3,6] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [7,6,1,2,5,4,3] => [[[.,[.,[[[.,.],.],.]]],.],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [6,3,1,2,5,4,7] => [[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [7,1,2,6,3,5,4] => [[.,[.,[[.,[[.,.],.]],.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [7,3,1,2,5,4,6] => [[[.,[.,.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [7,6,3,1,2,5,4] => [[[[.,[.,.]],[[.,.],.]],.],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [6,4,3,1,2,5,7] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [7,1,2,6,4,3,5] => [[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [7,3,1,2,6,4,5] => [[[.,[.,.]],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [7,4,3,1,2,5,6] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [7,6,4,3,1,2,5] => [[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,5,4,3,1,2,7] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [7,1,2,6,5,4,3] => [[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [7,3,1,2,6,5,4] => [[[.,[.,.]],[[[.,.],.],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [7,4,3,1,2,6,5] => [[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [7,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [3,2,1,4,7,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [3,2,1,6,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [3,2,1,7,4,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,2,1,7,6,4,5] => [[[.,.],.],[[[.,[.,.]],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,2,1,7,4,6,5] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [3,2,1,7,5,4,6] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [4,1,3,2,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [4,1,3,2,5,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [4,1,3,2,6,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [4,1,3,2,7,5,6] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [4,1,3,2,7,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [5,1,3,2,4,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [5,1,3,2,4,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [6,1,3,2,4,5,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [7,1,3,2,4,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [7,6,1,3,2,4,5] => [[[.,[[.,.],[.,[.,.]]]],.],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [6,5,1,3,2,4,7] => [[[.,[[.,.],[.,.]]],.],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [7,1,3,2,4,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [7,5,1,3,2,4,6] => [[[.,[[.,.],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [7,6,5,1,3,2,4] => [[[[.,[[.,.],[.,.]]],.],.],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [5,4,1,3,2,6,7] => [[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [5,4,1,3,2,7,6] => [[[.,[[.,.],.]],.],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [6,1,3,2,5,4,7] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [7,1,3,2,5,4,6] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [7,6,1,3,2,5,4] => [[[.,[[.,.],[[.,.],.]]],.],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [6,4,1,3,2,5,7] => [[[.,[[.,.],.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [7,1,3,2,6,4,5] => [[.,[[.,.],[[.,[.,.]],.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [7,4,1,3,2,5,6] => [[[.,[[.,.],.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [7,6,4,1,3,2,5] => [[[[.,[[.,.],.]],[.,.]],.],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,5,4,1,3,2,7] => [[[[.,[[.,.],.]],.],.],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [7,1,3,2,6,5,4] => [[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [7,4,1,3,2,6,5] => [[[.,[[.,.],.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [7,5,4,1,3,2,6] => [[[[.,[[.,.],.]],.],[.,.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,6,5,4,1,3,2] => [[[[[.,[[.,.],.]],.],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [4,2,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [4,2,1,3,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [4,2,1,3,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [4,2,1,3,7,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [4,2,1,3,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [5,1,4,2,3,6,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [5,1,4,2,3,7,6] => [[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [6,1,4,2,3,5,7] => [[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [7,1,4,2,3,5,6] => [[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [7,6,1,4,2,3,5] => [[[.,[[.,[.,.]],[.,.]]],.],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [6,5,1,4,2,3,7] => [[[.,[[.,[.,.]],.]],.],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [7,1,4,2,3,6,5] => [[.,[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [7,5,1,4,2,3,6] => [[[.,[[.,[.,.]],.]],[.,.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [7,6,5,1,4,2,3] => [[[[.,[[.,[.,.]],.]],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [5,2,1,3,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [5,2,1,3,4,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [6,1,5,2,3,4,7] => [[.,[[.,[.,[.,.]]],.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [7,1,5,2,3,4,6] => [[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [7,6,1,5,2,3,4] => [[[.,[[.,[.,[.,.]]],.]],.],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [6,2,1,3,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [7,1,6,2,3,4,5] => [[.,[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [7,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [7,6,2,1,3,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [6,5,2,1,3,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [7,1,6,5,2,3,4] => [[.,[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [7,2,1,3,4,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [7,5,2,1,3,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [7,6,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [5,4,2,1,3,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [5,4,2,1,3,7,6] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [6,1,5,4,2,3,7] => [[.,[[[.,[.,.]],.],.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [7,1,5,4,2,3,6] => [[.,[[[.,[.,.]],.],[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [7,6,1,5,4,2,3] => [[[.,[[[.,[.,.]],.],.]],.],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [6,2,1,3,5,4,7] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [7,1,6,2,3,5,4] => [[.,[[.,[.,[[.,.],.]]],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [7,2,1,3,5,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [7,6,2,1,3,5,4] => [[[[.,.],[.,[[.,.],.]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [6,4,2,1,3,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [7,1,6,4,2,3,5] => [[.,[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [7,2,1,3,6,4,5] => [[[.,.],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [7,4,2,1,3,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [7,6,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [6,5,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [7,1,6,5,4,2,3] => [[.,[[[[.,[.,.]],.],.],.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [7,2,1,3,6,5,4] => [[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [7,4,2,1,3,6,5] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [7,5,4,2,1,3,6] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [7,6,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [4,3,2,1,7,5,6] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [5,1,4,3,2,6,7] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [5,1,4,3,2,7,6] => [[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [6,1,4,3,2,5,7] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [7,1,4,3,2,5,6] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [7,6,1,4,3,2,5] => [[[.,[[[.,.],.],[.,.]]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [6,5,1,4,3,2,7] => [[[.,[[[.,.],.],.]],.],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [7,1,4,3,2,6,5] => [[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [7,5,1,4,3,2,6] => [[[.,[[[.,.],.],.]],[.,.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [7,6,5,1,4,3,2] => [[[[.,[[[.,.],.],.]],.],.],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [5,2,1,4,3,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [5,2,1,4,3,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [6,1,5,2,4,3,7] => [[.,[[.,[[.,.],.]],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [7,1,5,2,4,3,6] => [[.,[[.,[[.,.],.]],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [7,6,1,5,2,4,3] => [[[.,[[.,[[.,.],.]],.]],.],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [6,2,1,4,3,5,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [7,1,6,2,4,3,5] => [[.,[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [7,2,1,4,3,5,6] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [7,6,2,1,4,3,5] => [[[[.,.],[[.,.],[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [6,5,2,1,4,3,7] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [7,1,6,5,2,4,3] => [[.,[[[.,[[.,.],.]],.],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [7,2,1,4,3,6,5] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [7,5,2,1,4,3,6] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [7,6,5,2,1,4,3] => [[[[[.,.],[[.,.],.]],.],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [5,3,2,1,4,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [5,3,2,1,4,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [6,1,5,3,2,4,7] => [[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [7,1,5,3,2,4,6] => [[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [7,6,1,5,3,2,4] => [[[.,[[[.,.],[.,.]],.]],.],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [6,2,1,5,3,4,7] => [[[.,.],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [7,1,6,2,5,3,4] => [[.,[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [7,2,1,5,3,4,6] => [[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [7,6,2,1,5,3,4] => [[[[.,.],[[.,[.,.]],.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [6,3,2,1,4,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [7,1,6,3,2,4,5] => [[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [7,2,1,6,3,4,5] => [[[.,.],[[.,[.,[.,.]]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [7,3,2,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [7,6,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [6,5,3,2,1,4,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [7,1,6,5,3,2,4] => [[.,[[[[.,.],[.,.]],.],.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [7,2,1,6,5,3,4] => [[[.,.],[[[.,[.,.]],.],.]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [7,3,2,1,4,6,5] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [7,5,3,2,1,4,6] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [6,1,5,4,3,2,7] => [[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [7,1,5,4,3,2,6] => [[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [7,6,1,5,4,3,2] => [[[.,[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [6,2,1,5,4,3,7] => [[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [7,1,6,2,5,4,3] => [[.,[[.,[[[.,.],.],.]],.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [7,2,1,5,4,3,6] => [[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [7,6,2,1,5,4,3] => [[[[.,.],[[[.,.],.],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [6,3,2,1,5,4,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [7,1,6,3,2,5,4] => [[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [7,2,1,6,3,5,4] => [[[.,.],[[.,[[.,.],.]],.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [7,3,2,1,5,4,6] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [7,6,3,2,1,5,4] => [[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [7,1,6,4,3,2,5] => [[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [7,2,1,6,4,3,5] => [[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [7,3,2,1,6,4,5] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [7,1,6,5,4,3,2] => [[.,[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [7,2,1,6,5,4,3] => [[[.,.],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [7,3,2,1,6,5,4] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [7,4,3,2,1,6,5] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,5,7,6] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [1,2,3,4,8,6,5,7] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [1,2,3,4,8,7,6,5] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [1,2,3,8,7,4,5,6] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [1,2,3,8,4,5,7,6] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [1,2,3,8,6,4,5,7] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [1,2,3,8,7,6,4,5] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [1,2,3,8,4,6,5,7] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [1,2,3,8,7,4,6,5] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [1,2,3,8,4,7,5,6] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [1,2,3,8,5,4,6,7] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [1,2,3,8,7,5,4,6] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [1,2,3,8,4,7,6,5] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [1,2,3,8,5,4,7,6] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [1,2,3,8,6,5,4,7] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [1,2,3,8,7,6,5,4] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,5,6,7] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [1,2,4,3,8,5,7,6] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [1,2,4,3,8,7,6,5] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [1,2,6,5,3,4,7,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [1,2,8,5,3,4,6,7] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [1,2,8,7,6,5,3,4] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [1,2,8,3,5,4,6,7] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [1,2,8,3,6,4,5,7] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [1,2,8,4,3,5,6,7] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [1,2,8,3,6,5,4,7] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [1,2,8,5,4,3,6,7] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,5,6,7] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [1,3,2,4,8,5,7,6] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [1,3,2,4,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [1,3,2,8,7,6,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [1,4,2,3,7,5,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [1,4,2,3,8,5,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [1,4,2,3,8,5,7,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [1,4,2,3,8,7,6,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [1,8,7,2,3,4,5,6] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [1,7,6,2,3,4,5,8] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [1,8,6,2,3,4,5,7] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [1,7,5,2,3,4,6,8] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,6,8,5,2] => [1,8,5,2,3,4,7,6] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [1,8,7,6,5,2,3,4] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [1,8,4,2,3,5,6,7] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [1,8,6,4,2,3,5,7] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [1,8,4,2,3,6,5,7] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [1,4,3,2,8,5,6,7] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [1,4,3,2,8,7,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [1,8,2,4,3,5,6,7] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [1,8,7,6,5,2,4,3] => [.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [1,8,2,5,3,4,6,7] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [1,8,6,5,3,2,4,7] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [1,8,7,6,5,3,2,4] => [.,[[[[[[.,.],[.,.]],.],.],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [1,8,4,3,2,5,6,7] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [1,8,7,6,4,3,2,5] => [.,[[[[[[.,.],.],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [1,8,7,2,6,5,4,3] => [.,[[[.,[[[[.,.],.],.],.]],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [1,8,5,4,3,2,6,7] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [1,8,7,5,4,3,2,6] => [.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [1,8,4,3,2,7,6,5] => [.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [1,8,5,4,3,2,7,6] => [.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [1,8,6,5,4,3,2,7] => [.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,5,7,6] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [2,1,3,4,8,6,5,7] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,1,3,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [2,1,3,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [2,1,4,3,8,7,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [2,1,4,3,8,6,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,6,3,4,5,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,1,8,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [2,1,8,7,6,3,4,5] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [2,1,6,5,3,4,8,7] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [2,1,8,7,3,4,6,5] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [2,1,8,7,6,5,3,4] => [[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,6,3,5,4,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [2,1,8,3,5,4,7,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [2,1,6,4,3,5,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [2,1,8,3,7,4,6,5] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [2,1,8,4,3,6,5,7] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [2,1,8,7,4,3,6,5] => [[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [2,1,8,4,3,7,5,6] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [2,1,8,5,4,3,6,7] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [2,1,8,4,3,7,6,5] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,1,2,4,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [3,1,2,4,8,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [3,1,2,4,8,5,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [3,1,2,4,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [3,1,2,5,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [3,1,2,7,4,5,6,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,1,2,8,7,6,5,4] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [4,1,2,3,5,6,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,1,2,3,5,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [4,1,2,3,5,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [4,1,2,3,5,8,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [4,1,2,3,6,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,1,2,3,6,5,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [4,1,2,3,7,5,6,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,1,2,3,8,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [4,1,2,3,8,7,5,6] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [4,1,2,3,7,6,5,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,1,2,3,8,5,7,6] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [4,1,2,3,8,6,5,7] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,1,2,3,8,7,6,5] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,1,2,3,4,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,1,2,3,4,8,7,6] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,1,2,3,4,5,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,1,2,3,4,5,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [8,7,1,2,3,4,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [7,6,1,2,3,4,5,8] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [8,1,2,3,4,7,6,5] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [8,7,6,5,1,2,3,4] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [5,4,1,2,3,8,7,6] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [8,1,2,3,5,4,7,6] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [8,4,1,2,3,5,6,7] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [8,7,4,1,2,3,5,6] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [6,5,4,1,2,3,8,7] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [4,3,1,2,6,5,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [4,3,1,2,8,5,6,7] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [4,3,1,2,8,7,5,6] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [4,3,1,2,8,5,7,6] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [4,3,1,2,8,6,5,7] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [4,3,1,2,8,7,6,5] => [[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [8,7,1,2,4,3,5,6] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [6,5,1,2,4,3,8,7] => [[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [8,1,2,4,3,6,5,7] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [8,7,1,2,4,3,6,5] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [8,1,2,4,3,7,6,5] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [8,7,6,5,1,2,4,3] => [[[[[.,[.,[[.,.],.]]],.],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [5,3,1,2,4,8,7,6] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => [8,6,1,2,5,3,4,7] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [8,7,5,3,1,2,4,6] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [8,7,6,5,3,1,2,4] => [[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [5,4,3,1,2,8,7,6] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [8,1,2,5,4,3,6,7] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [8,7,1,2,5,4,3,6] => [[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => [8,6,1,2,5,4,3,7] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [8,7,6,1,2,5,4,3] => [[[[.,[.,[[[.,.],.],.]]],.],.],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [8,1,2,7,3,5,4,6] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => [8,1,2,7,6,3,5,4] => [[.,[.,[[[.,[[.,.],.]],.],.]]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [8,7,5,4,3,1,2,6] => [[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [8,3,1,2,7,6,5,4] => [[[.,[.,.]],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [8,6,5,4,3,1,2,7] => [[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [3,2,1,4,8,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [3,2,1,4,8,5,7,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [3,2,1,4,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [3,2,1,8,4,5,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [3,2,1,8,7,4,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [3,2,1,8,4,5,7,6] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [3,2,1,8,6,4,5,7] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [3,2,1,8,7,6,4,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [3,2,1,8,4,6,5,7] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,2,1,8,7,4,6,5] => [[[.,.],.],[[[.,[[.,.],.]],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [3,2,1,8,4,7,5,6] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => [3,2,1,8,5,4,6,7] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [3,2,1,8,7,5,4,6] => [[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [3,2,1,8,4,7,6,5] => [[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => [3,2,1,8,5,4,7,6] => [[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [3,2,1,8,6,5,4,7] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [4,1,3,2,5,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [4,1,3,2,5,7,6,8] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [4,1,3,2,6,5,8,7] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [4,1,3,2,8,5,6,7] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [4,1,3,2,8,5,7,6] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [4,1,3,2,8,6,5,7] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [4,1,3,2,8,7,6,5] => [[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [7,1,3,2,4,5,6,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [8,1,3,2,4,5,6,7] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [8,1,3,2,4,5,7,6] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [8,1,3,2,4,7,6,5] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [8,7,6,5,1,3,2,4] => [[[[[.,[[.,.],[.,.]]],.],.],.],.]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [5,4,1,3,2,8,7,6] => [[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [6,1,3,2,5,4,8,7] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [8,1,3,2,5,4,7,6] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [8,1,3,2,7,4,6,5] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [7,5,4,1,3,2,6,8] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [7,6,5,4,1,3,2,8] => [[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [4,2,1,3,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [4,2,1,3,8,5,6,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [4,2,1,3,8,7,5,6] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [4,2,1,3,8,5,7,6] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [4,2,1,3,8,6,5,7] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [4,2,1,3,8,7,6,5] => [[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [5,1,4,2,3,8,7,6] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [8,1,4,2,3,5,6,7] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [8,6,1,4,2,3,5,7] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [8,1,4,2,3,7,5,6] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,2,7,6,5,8,1] => [8,1,4,2,3,7,6,5] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [8,7,6,5,1,4,2,3] => [[[[[.,[[.,[.,.]],.]],.],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [5,2,1,3,4,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [8,1,5,2,3,4,6,7] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [8,7,6,2,1,3,4,5] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [7,6,5,2,1,3,4,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [8,7,6,5,2,1,3,4] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => [7,1,5,4,2,3,6,8] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [8,4,2,1,3,5,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [8,7,4,2,1,3,5,6] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [8,7,6,4,2,1,3,5] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [6,5,4,2,1,3,8,7] => [[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [8,5,4,2,1,3,7,6] => [[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [4,3,2,1,5,8,6,7] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [4,3,2,1,5,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [4,3,2,1,7,5,6,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [4,3,2,1,8,5,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [4,3,2,1,8,7,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [4,3,2,1,7,6,5,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [4,3,2,1,8,5,7,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [4,3,2,1,8,6,5,7] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [5,1,4,3,2,8,7,6] => [[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [8,1,4,3,2,5,6,7] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [8,1,4,3,2,7,6,5] => [[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [8,7,6,5,1,4,3,2] => [[[[[.,[[[.,.],.],.]],.],.],.],.]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => [5,2,1,4,3,8,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [6,1,5,2,4,3,8,7] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [8,1,5,2,4,3,7,6] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [6,2,1,4,3,5,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [6,5,2,1,4,3,8,7] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [8,7,1,6,5,2,4,3] => [[[.,[[[.,[[.,.],.]],.],.]],.],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [8,1,7,2,4,3,6,5] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [8,7,2,1,4,3,6,5] => [[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [5,3,2,1,4,8,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [6,2,1,5,3,4,8,7] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [7,1,6,2,5,3,4,8] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [6,3,2,1,4,5,8,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [7,3,2,1,4,5,6,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [8,1,7,3,2,4,5,6] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [8,2,1,7,3,4,5,6] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [7,6,5,3,2,1,4,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [8,3,2,1,4,7,6,5] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [5,4,3,2,1,6,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [5,4,3,2,1,7,6,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [5,4,3,2,1,8,6,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [6,1,5,4,3,2,8,7] => [[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [8,1,5,4,3,2,6,7] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [8,1,5,4,3,2,7,6] => [[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [8,6,1,5,4,3,2,7] => [[[.,[[[[.,.],.],.],.]],[.,.]],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [8,7,6,1,5,4,3,2] => [[[[.,[[[[.,.],.],.],.]],.],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [6,2,1,5,4,3,8,7] => [[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [8,1,7,2,6,3,5,4] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [8,2,1,7,3,5,4,6] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [6,4,3,2,1,5,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [7,4,3,2,1,5,6,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [8,4,3,2,1,5,6,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [7,6,4,3,2,1,5,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [8,2,1,7,6,4,3,5] => [[[.,.],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [8,7,6,4,3,2,1,5] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [8,1,7,2,6,5,4,3] => [[.,[[.,[[[[.,.],.],.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [7,4,3,2,1,6,5,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [8,1,7,4,3,2,6,5] => [[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [8,3,2,1,7,4,6,5] => [[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [8,4,3,2,1,6,5,7] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [8,7,4,3,2,1,6,5] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [7,5,4,3,2,1,6,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [8,1,7,5,4,3,2,6] => [[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [8,5,4,3,2,1,6,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [8,1,7,6,5,4,3,2] => [[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [8,2,1,7,6,5,4,3] => [[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [8,3,2,1,7,6,5,4] => [[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [8,4,3,2,1,7,6,5] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [8,5,4,3,2,1,7,6] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,6,5,4,3,2,1,9] => [8,6,5,4,3,2,1,7,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [1,9,7,6,5,4,3,2,8] => [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,7,6,5,4,3,2,1,10] => [9,7,6,5,4,3,2,1,8,10] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,7,5,4,3,2,1,9] => [8,7,5,4,3,2,1,6,9] => [[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,7,9,6,5,4,3,2] => [1,9,6,5,4,3,2,8,7] => [.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => [1,9,8,6,5,4,3,2,7] => [.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [1,10,8,7,6,5,4,3,2,9] => [.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [1,11,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [9,1,3,2,4,5,6,7,8] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => [9,6,5,4,3,2,1,7,8] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [9,1,8,7,6,5,4,3,2] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1] => [9,2,1,8,7,6,5,4,3] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,7,6,5,9,4,3,2,1] => [9,4,3,2,1,8,7,6,5] => [[[[[.,.],.],.],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => [9,6,5,4,3,2,1,8,7] => [[[[[[[.,.],.],.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [9,7,6,5,4,3,2,1,8] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,7,8] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,6,7,8] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,5,6,7,8] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,4,5,6,7,8] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,3,4,5,6,7,8] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,8,9] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,9,6,8,7] => [.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,7,8,9] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,6,7,8,9] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,5,6,7,8,9] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,4,5,6,7,8,9] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,3,4,5,6,7,8,9] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [2,1,6,5,4,3,10,9,8,7] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [4,3,2,1,8,7,6,5,10,9] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [4,3,2,1,10,9,8,7,6,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [6,5,4,3,2,1,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [7,1,2,3,4,5,6,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => [10,7,6,5,4,3,2,1,9,8] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [10,1,9,8,7,6,5,4,3,2] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [10,8,7,6,5,4,3,2,1,9] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [10,2,1,9,8,7,6,5,4,3] => [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [3,1,2,5,4,7,6,9,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [3,1,2,5,4,7,6,9,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
Map
to 312-avoiding permutation
Description
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
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.