Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00073: Permutations —major-index to inversion-number bijection⟶ 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] => [2,3,1] => [[.,.],[.,.]]
[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] => [2,3,4,1] => [[.,.],[.,[.,.]]]
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,3,1,4] => [[.,.],[.,[.,.]]]
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,4,1,3] => [[.,.],[[.,.],.]]
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [3,4,2,1] => [[[.,.],.],[.,.]]
[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] => [3,2,4,1] => [[[.,.],.],[.,.]]
[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] => [4,2,3,1] => [[[.,.],[.,.]],.]
[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] => [4,2,1,3] => [[[.,.],[.,.]],.]
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [4,3,1,2] => [[[.,[.,.]],.],.]
[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] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [2,3,5,1,4] => [[.,.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [2,4,1,3,5] => [[.,.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,5,1,3,4] => [[.,.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,5,2,4,1] => [[[.,.],.],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [3,4,2,1,5] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [3,5,2,1,4] => [[[.,.],.],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [3,5,4,1,2] => [[.,[.,.]],[[.,.],.]]
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]]
[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] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,2,5,1,4] => [[[.,.],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]]
[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] => [4,2,3,5,1] => [[[.,.],[.,.]],[.,.]]
[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] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [5,2,3,1,4] => [[[.,.],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [5,2,4,1,3] => [[[.,.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,3,4,2,1] => [[[[.,.],.],[.,.]],.]
[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] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]]
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [4,2,1,3,5] => [[[.,.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [5,2,1,3,4] => [[[.,.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [4,3,1,2,5] => [[[.,[.,.]],.],[.,.]]
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [5,3,1,2,4] => [[[.,[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [5,4,2,3,1] => [[[[.,.],[.,.]],.],.]
[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] => [5,3,2,1,4] => [[[[.,.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [5,4,2,1,3] => [[[[.,.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [5,4,3,1,2] => [[[[.,[.,.]],.],.],.]
[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] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [2,3,6,1,4,5] => [[.,.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [3,4,6,2,5,1] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,4,6,2,1,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [3,4,6,5,1,2] => [[.,[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,4,2,6,1,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,5,2,4,6,1] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [3,6,2,4,5,1] => [[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [3,5,2,4,1,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [3,6,2,4,1,5] => [[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [3,6,2,5,1,4] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [4,6,3,5,2,1] => [[[[.,.],.],.],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [3,5,2,1,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [3,6,2,1,4,5] => [[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [4,6,3,2,5,1] => [[[[.,.],.],.],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [3,5,4,1,2,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [3,6,4,1,2,5] => [[.,[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [3,6,5,1,2,4] => [[.,[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [4,6,5,2,3,1] => [[[.,.],[.,.]],[[.,.],.]]
>>> Load all 1729 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [4,6,3,2,1,5] => [[[[.,.],.],.],[[.,.],.]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [4,6,5,2,1,3] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [4,6,5,3,1,2] => [[[.,[.,.]],.],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]]
[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] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [3,2,4,6,1,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [3,2,5,1,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [3,2,6,1,4,5] => [[[.,.],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [4,3,6,2,5,1] => [[[[.,.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [4,3,6,2,1,5] => [[[[.,.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [4,3,6,5,1,2] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]]
[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] => [4,2,3,5,6,1] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [4,2,3,5,1,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [4,2,3,6,1,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [5,3,4,6,2,1] => [[[[.,.],.],[.,.]],[.,.]]
[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] => [5,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[.,.]]
[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] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [6,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [6,2,3,5,1,4] => [[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [5,3,4,2,6,1] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [5,2,3,1,4,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [6,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [5,2,4,1,3,6] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [6,2,4,1,3,5] => [[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [6,2,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [6,3,5,2,4,1] => [[[[.,.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,3,4,2,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [6,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [6,3,5,2,1,4] => [[[[.,.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [6,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.]
[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] => [4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [4,3,2,6,1,5] => [[[[.,.],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [5,3,2,4,6,1] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [6,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [6,3,2,5,1,4] => [[[[.,.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [5,4,2,3,6,1] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [6,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [5,4,2,3,1,6] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [6,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [6,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [6,5,2,4,1,3] => [[[[.,.],[[.,.],.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.]
[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] => [5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [5,3,2,1,4,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [5,4,2,1,3,6] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [6,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [6,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],.]
[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] => [6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.]
[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] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [2,3,4,5,7,1,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [3,4,5,6,7,2,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [3,4,5,6,2,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [2,3,4,6,1,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [2,3,4,7,1,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [3,4,5,7,2,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [3,4,5,6,2,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [3,4,5,7,2,1,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [3,4,5,7,6,1,2] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [3,4,5,2,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [3,4,5,2,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [3,4,5,2,7,1,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [4,5,6,3,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [2,3,5,1,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [3,4,6,2,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [2,3,6,1,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [2,3,7,1,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [3,4,7,2,5,6,1] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [3,4,6,2,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [3,4,7,2,5,1,6] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [3,4,7,2,6,1,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [4,5,7,3,6,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [3,4,5,2,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [4,5,6,3,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [3,4,6,2,1,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [3,4,7,2,1,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [4,5,7,3,2,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [3,4,6,5,1,2,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [3,4,7,5,1,2,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [3,4,7,6,1,2,5] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [4,5,7,6,2,3,1] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [4,5,6,3,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [4,5,7,3,2,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [4,5,7,6,2,1,3] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [4,5,7,6,3,1,2] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [5,6,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [3,4,2,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [3,4,2,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [3,4,2,5,7,1,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [4,5,3,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [3,4,2,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [4,5,3,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [3,4,2,6,1,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [3,4,2,7,1,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [4,5,3,7,2,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [4,5,3,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [4,5,3,7,2,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [4,5,3,7,6,1,2] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [5,6,4,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [3,5,2,4,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [3,5,2,4,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [3,5,2,4,7,1,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [4,6,3,5,7,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [2,5,1,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [3,6,2,4,5,7,1] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [2,6,1,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [2,7,1,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [3,7,2,4,5,6,1] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [3,6,2,4,5,1,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [3,7,2,4,5,1,6] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [3,7,2,4,6,1,5] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [4,7,3,5,6,2,1] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [3,5,2,4,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [4,6,3,5,2,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [3,6,2,4,1,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [3,7,2,4,1,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [4,7,3,5,2,6,1] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [3,6,2,5,1,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [3,7,2,5,1,4,6] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [3,7,2,6,1,4,5] => [[[.,.],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [4,7,3,6,2,5,1] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [4,6,3,5,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [4,7,3,5,2,1,6] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [4,7,3,6,2,1,5] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [4,7,3,6,5,1,2] => [[[.,[.,.]],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [5,7,4,6,3,2,1] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [3,4,2,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [4,5,3,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [4,5,3,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [4,5,3,2,7,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [5,6,4,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [3,5,2,1,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [4,6,3,2,5,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [3,6,2,1,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [3,7,2,1,4,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [4,7,3,2,5,6,1] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [4,6,3,2,5,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [4,7,3,2,5,1,6] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [4,7,3,2,6,1,5] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [5,7,4,3,6,2,1] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [3,5,4,1,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [4,6,5,2,3,7,1] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [3,6,4,1,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [3,7,4,1,2,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [4,7,5,2,3,6,1] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [3,6,5,1,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [3,7,5,1,2,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [3,7,6,1,2,4,5] => [[.,[.,.]],[[[.,[.,.]],.],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [4,7,6,2,3,5,1] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [4,6,5,2,3,1,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [4,7,5,2,3,1,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [4,7,6,2,3,1,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [4,7,6,2,5,1,3] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [5,7,6,3,4,2,1] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [4,5,3,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [5,6,4,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [4,6,3,2,1,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [4,7,3,2,1,5,6] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [5,7,4,3,2,6,1] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [4,6,5,2,1,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [4,7,5,2,1,3,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [4,7,6,2,1,3,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [5,7,6,3,2,4,1] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [4,6,5,3,1,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [4,7,5,3,1,2,6] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [4,7,6,3,1,2,5] => [[[.,[.,.]],.],[[[.,.],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [4,7,6,5,1,2,3] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [5,7,6,4,2,3,1] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [5,6,4,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [5,7,4,3,2,1,6] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [5,7,6,3,2,1,4] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [5,7,6,4,2,1,3] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [5,7,6,4,3,1,2] => [[[[.,[.,.]],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [6,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]]
[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] => [3,2,4,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [3,2,4,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [3,2,4,5,7,1,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [4,3,5,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [3,2,4,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [4,3,5,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [3,2,4,6,1,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [3,2,4,7,1,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [4,3,5,7,2,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [4,3,5,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [4,3,5,7,2,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [4,3,5,7,6,1,2] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [5,4,6,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [3,2,4,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [4,3,5,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [4,3,5,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [4,3,5,2,7,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [5,4,6,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [3,2,5,1,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [4,3,6,2,5,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [3,2,6,1,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [3,2,7,1,4,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [4,3,7,2,5,6,1] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [4,3,6,2,5,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [4,3,7,2,5,1,6] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [4,3,7,2,6,1,5] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [5,4,7,3,6,2,1] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [4,3,5,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [5,4,6,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [4,3,6,2,1,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [4,3,7,2,1,5,6] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [5,4,7,3,2,6,1] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [4,3,6,5,1,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [4,3,7,5,1,2,6] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [4,3,7,6,1,2,5] => [[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [5,4,7,6,2,3,1] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [5,4,6,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [5,4,7,3,2,1,6] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [5,4,7,6,2,1,3] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [5,4,7,6,3,1,2] => [[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [6,5,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]]
[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] => [4,2,3,5,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [4,2,3,5,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [4,2,3,5,7,1,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [5,3,4,6,7,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [4,2,3,5,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [5,3,4,6,2,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [4,2,3,6,1,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [4,2,3,7,1,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [5,3,4,7,2,6,1] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [5,3,4,6,2,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [5,3,4,7,2,1,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [5,3,4,7,6,1,2] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [6,4,5,7,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]]
[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] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [5,2,3,4,7,1,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [6,3,4,5,7,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[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] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[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] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [7,2,3,4,6,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [7,3,4,5,6,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [6,3,4,5,2,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [7,3,4,5,2,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [6,2,3,5,1,4,7] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [7,2,3,5,1,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [7,2,3,6,1,4,5] => [[[.,.],[.,[[.,[.,.]],.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [7,3,4,6,2,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,3,4,5,2,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [7,3,4,5,2,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [7,3,4,6,2,1,5] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [7,3,4,6,5,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,4,5,6,3,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [5,3,4,2,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [5,3,4,2,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [5,3,4,2,7,1,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [6,4,5,3,7,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [5,2,3,1,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [6,3,4,2,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [6,2,3,1,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [7,2,3,1,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [7,3,4,2,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [6,3,4,2,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [7,3,4,2,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [7,3,4,2,6,1,5] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [7,4,5,3,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [5,2,4,1,3,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [6,3,5,2,4,7,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [6,2,4,1,3,5,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [7,2,4,1,3,5,6] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [7,3,5,2,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [6,2,5,1,3,4,7] => [[[.,.],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [7,2,5,1,3,4,6] => [[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [7,2,6,1,3,4,5] => [[[.,.],[[.,[.,[.,.]]],.]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [7,3,6,2,4,5,1] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [6,3,5,2,4,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [7,3,5,2,4,1,6] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [7,3,6,2,4,1,5] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [7,3,6,2,5,1,4] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [7,4,6,3,5,2,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,3,4,2,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [6,4,5,3,2,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [6,3,4,2,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [7,3,4,2,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [7,4,5,3,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [6,3,5,2,1,4,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [7,3,5,2,1,4,6] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [7,3,6,2,1,4,5] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [7,4,6,3,2,5,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [6,3,5,4,1,2,7] => [[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [7,3,5,4,1,2,6] => [[[.,[.,.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [7,3,6,4,1,2,5] => [[[.,[.,.]],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [7,3,6,5,1,2,4] => [[[.,[.,.]],[[[.,.],.],.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [7,4,6,5,2,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,4,5,3,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [7,4,5,3,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [7,4,6,3,2,1,5] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [7,4,6,5,2,1,3] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [7,4,6,5,3,1,2] => [[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,5,6,4,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[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] => [4,3,2,5,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [4,3,2,5,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [4,3,2,5,7,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [5,4,3,6,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [4,3,2,5,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [5,4,3,6,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [4,3,2,6,1,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [4,3,2,7,1,5,6] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [5,4,3,7,2,6,1] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [5,4,3,6,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [5,4,3,7,2,1,6] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [5,4,3,7,6,1,2] => [[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [4,2,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [5,3,2,4,7,1,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [6,4,3,5,7,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [5,2,1,3,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [6,2,1,3,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [7,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [7,3,2,4,6,1,5] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [7,4,3,5,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [6,4,3,5,2,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [6,3,2,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [7,3,2,4,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [7,4,3,5,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [6,3,2,5,1,4,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [7,3,2,5,1,4,6] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [7,3,2,6,1,4,5] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [7,4,3,6,2,5,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,4,3,5,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [7,4,3,5,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [7,4,3,6,2,1,5] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [7,4,3,6,5,1,2] => [[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,5,4,6,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [4,3,1,2,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [5,4,2,3,6,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [5,4,2,3,6,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [5,4,2,3,7,1,6] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [6,5,3,4,7,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [5,3,1,2,4,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [6,4,2,3,5,7,1] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [6,3,1,2,4,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [7,3,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [7,4,2,3,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [6,4,2,3,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [7,4,2,3,5,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [7,4,2,3,6,1,5] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [5,4,1,2,3,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [6,5,2,3,4,7,1] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [6,4,1,2,3,5,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [7,4,1,2,3,5,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [7,5,2,3,4,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [6,5,1,2,3,4,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [7,5,1,2,3,4,6] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [7,6,1,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [7,6,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [6,5,2,3,4,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [7,5,2,3,4,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [7,6,2,3,4,1,5] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [7,6,2,3,5,1,4] => [[[[.,.],[.,[[.,.],.]]],.],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [5,4,2,3,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [6,4,2,3,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [7,4,2,3,1,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [6,5,2,3,1,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [7,5,2,3,1,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [7,6,2,3,1,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [7,6,3,4,2,5,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [6,5,2,4,1,3,7] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [7,5,2,4,1,3,6] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [7,6,2,4,1,3,5] => [[[[.,.],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [7,6,2,5,1,3,4] => [[[[.,.],[[.,[.,.]],.]],.],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [7,6,3,5,2,4,1] => [[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [7,6,3,4,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [7,6,3,5,2,1,4] => [[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [7,6,3,5,4,1,2] => [[[[.,[.,.]],[[.,.],.]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[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] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [5,4,3,2,7,1,6] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [6,5,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [5,3,2,1,4,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [6,3,2,1,4,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [7,3,2,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [7,4,3,2,6,1,5] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [5,4,2,1,3,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [6,5,3,2,4,7,1] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [6,4,2,1,3,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [7,4,2,1,3,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [7,5,3,2,4,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [6,5,2,1,3,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [7,5,2,1,3,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [7,6,2,1,3,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [7,6,3,2,4,5,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [6,5,3,2,4,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [7,5,3,2,4,1,6] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [7,6,3,2,4,1,5] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [7,6,3,2,5,1,4] => [[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [5,4,3,1,2,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [6,5,4,2,3,7,1] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [6,4,3,1,2,5,7] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [7,4,3,1,2,5,6] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [7,5,4,2,3,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [6,5,3,1,2,4,7] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [7,5,3,1,2,4,6] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [7,6,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [7,6,4,2,3,5,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [6,5,4,1,2,3,7] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [7,5,4,1,2,3,6] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [7,6,4,1,2,3,5] => [[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [7,6,5,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [7,6,5,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [6,5,4,2,3,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [7,5,4,2,3,1,6] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [7,6,4,2,3,1,5] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [7,6,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [7,6,5,2,4,1,3] => [[[[[.,.],[[.,.],.]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[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] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [6,5,3,2,1,4,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [7,5,3,2,1,4,6] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [7,6,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [7,6,4,3,2,5,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [6,5,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [7,5,4,2,1,3,6] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [7,6,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [7,6,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [7,6,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [6,5,4,3,1,2,7] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [7,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [7,6,4,3,1,2,5] => [[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [7,6,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [7,6,5,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [7,6,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],.]
[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] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [7,6,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [7,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],.]
[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] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [3,4,5,6,7,8,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [3,4,5,6,7,2,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [2,3,4,5,7,1,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [2,3,4,5,8,1,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [3,4,5,6,8,2,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [3,4,5,6,7,2,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [3,4,5,6,8,7,1,2] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [4,5,6,7,8,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [3,4,5,6,2,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [3,4,5,6,2,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [3,4,5,6,2,8,1,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [4,5,6,7,3,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [2,3,4,6,1,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [3,4,5,7,2,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [2,3,4,7,1,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [2,3,4,8,1,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [3,4,5,8,2,6,7,1] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [3,4,5,8,2,7,1,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [4,5,6,8,3,7,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [3,4,5,6,2,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [4,5,6,7,3,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [3,4,5,7,2,1,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [3,4,5,8,2,1,6,7] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [4,5,6,8,3,2,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [3,4,5,8,6,1,2,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [3,4,5,8,7,1,2,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [4,5,6,7,3,2,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [4,5,6,8,3,2,1,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [4,5,6,8,7,2,1,3] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [4,5,6,8,7,3,1,2] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [5,6,7,8,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [3,4,5,2,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [3,4,5,2,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [3,4,5,2,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [4,5,6,3,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [3,4,5,2,7,1,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [4,5,6,3,8,2,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [4,5,6,3,8,2,1,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [4,5,6,3,8,7,1,2] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [5,6,7,4,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [2,3,5,1,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [3,4,6,2,5,7,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [4,5,7,3,6,8,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [2,3,6,1,4,5,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [2,3,7,1,4,5,6,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [2,3,8,1,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [3,4,8,2,5,6,7,1] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [4,5,8,3,6,7,2,1] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [3,4,7,2,5,1,6,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [3,4,8,2,7,1,5,6] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [4,5,8,3,7,2,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,6,8,5,3] => [4,5,8,3,7,2,1,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [4,5,8,3,7,6,1,2] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [5,6,8,4,7,3,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [3,4,5,2,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [4,5,6,3,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [4,5,6,3,2,8,1,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [5,6,7,4,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [3,4,8,2,1,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [4,5,8,3,2,6,1,7] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,7,8,6,3] => [4,5,8,3,2,7,1,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [5,6,8,4,3,7,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [3,4,6,5,1,2,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,4,3,8] => [3,4,7,6,1,2,5,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [3,4,8,6,1,2,5,7] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [3,4,8,7,1,2,5,6] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [4,5,8,7,2,3,6,1] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [4,5,8,7,2,3,1,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [4,5,6,3,2,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [4,5,8,3,2,1,6,7] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [5,6,8,4,3,2,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [4,5,8,7,6,1,2,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [5,6,7,4,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [5,6,8,4,3,2,1,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [5,6,8,7,3,2,1,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [5,6,8,7,4,2,1,3] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [5,6,8,7,4,3,1,2] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [6,7,8,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [3,4,2,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [3,4,2,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [3,4,2,5,6,8,1,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [3,4,2,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [4,5,3,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [4,5,3,6,8,2,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [5,6,4,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [3,4,2,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [4,5,3,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [4,5,3,6,2,8,1,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [3,4,2,7,1,5,6,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [3,4,2,8,1,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [4,5,3,7,2,6,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [4,5,3,8,2,6,1,7] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [4,5,3,8,2,7,1,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [5,6,4,8,3,7,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [4,5,3,8,2,1,6,7] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [4,5,3,8,6,1,2,7] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [4,5,3,8,7,1,2,6] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [5,6,4,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [5,6,4,8,3,2,1,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [5,6,4,8,7,2,1,3] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [6,7,5,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [2,4,1,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [3,5,2,4,6,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [3,5,2,4,6,8,1,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [4,6,3,5,7,8,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [4,6,3,5,7,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [3,5,2,4,7,1,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [3,5,2,4,8,1,6,7] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [4,6,3,5,8,2,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [4,6,3,5,8,2,1,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [4,6,3,5,8,7,1,2] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [5,7,4,6,8,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [2,5,1,3,4,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [4,7,3,5,6,8,2,1] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [2,6,1,3,4,5,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [2,7,1,3,4,5,6,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [2,8,1,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [3,8,2,4,5,6,7,1] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [4,8,3,5,6,7,2,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [3,7,2,4,5,1,6,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [3,8,2,4,7,1,5,6] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [3,5,2,4,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [4,6,3,5,2,7,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [4,6,3,5,2,7,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [4,6,3,5,2,8,1,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [4,7,3,5,2,6,1,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [4,8,3,5,2,6,1,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,4,7,8,6,2] => [4,8,3,5,2,7,1,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [3,7,2,5,1,4,6,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => [3,7,2,6,1,4,5,8] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => [3,8,2,6,1,4,5,7] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [3,8,2,7,1,4,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,7,4,2] => [4,8,3,7,2,5,6,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [4,7,3,6,2,5,1,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,6,4,8,2] => [4,8,3,6,2,5,1,7] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,6,8,4,2] => [4,8,3,7,2,5,1,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [4,8,3,7,2,6,1,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [5,8,4,7,3,6,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [4,7,3,5,2,1,6,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [5,8,4,6,3,2,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [4,8,3,6,2,1,5,7] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [4,8,3,7,2,1,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => [4,7,3,6,5,1,2,8] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [4,8,3,7,5,1,2,6] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [4,8,3,7,6,1,2,5] => [[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,7,5,4,2] => [5,8,4,7,6,2,3,1] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [5,7,4,6,3,2,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [5,8,4,7,6,3,1,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [6,8,5,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [3,4,2,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [4,5,3,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [4,5,3,2,7,1,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [4,5,3,2,8,1,6,7] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [5,6,4,3,8,2,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [5,6,4,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [6,7,5,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [3,5,2,1,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [5,7,4,3,6,8,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [3,8,2,1,4,5,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [4,7,3,2,5,6,1,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [5,8,4,3,6,7,2,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [4,6,3,2,5,1,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [4,7,3,2,5,1,6,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [5,8,4,3,6,2,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,3,6,7,5,8,2] => [4,8,3,2,6,1,5,7] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => [4,8,3,2,7,1,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,6,8,7,5,2] => [5,8,4,3,7,2,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [5,8,4,3,7,2,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [5,8,4,3,7,6,1,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [6,8,5,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => [3,5,4,1,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [3,6,4,1,2,5,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [5,8,6,3,4,7,2,1] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,3,7,2,8] => [3,7,5,1,2,4,6,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [3,7,6,1,2,4,5,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [3,8,6,1,2,4,5,7] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [3,8,7,1,2,4,5,6] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [5,8,7,3,4,6,2,1] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,5,7,3,2,8] => [4,7,6,2,3,1,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,5,7,3,8,2] => [4,8,6,2,3,1,5,7] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,5,8,7,3,2] => [5,8,7,3,4,2,6,1] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [4,8,7,2,5,1,3,6] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [4,8,7,2,6,1,3,5] => [[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [5,8,7,3,6,2,4,1] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [5,7,6,3,4,2,1,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [6,8,7,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [4,5,3,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [5,6,4,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [5,6,4,3,2,8,1,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [6,7,5,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [4,7,3,2,1,5,6,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [4,8,3,2,1,5,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [5,8,4,3,2,6,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [6,8,5,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,4,6,3,2,7,8] => [4,6,5,2,1,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,4,6,3,2,8,7] => [5,7,6,3,2,4,8,1] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [4,7,5,2,1,3,6,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [4,8,5,2,1,3,6,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [4,8,6,2,1,3,5,7] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [4,8,7,2,1,3,5,6] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,4,6,8,7,3,2] => [5,8,7,3,2,4,6,1] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,4,7,6,3,2,8] => [5,7,6,3,2,4,1,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,4,7,8,6,3,2] => [5,8,7,3,2,6,1,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,4,3,2,7,8] => [4,6,5,3,1,2,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,4,7,8,3,2] => [4,8,7,3,1,2,5,6] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => [4,8,6,5,1,2,3,7] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [4,8,7,6,1,2,3,5] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => [5,8,7,6,2,3,1,4] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [6,8,7,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [5,6,4,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [6,7,5,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [5,8,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [6,8,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => [5,8,7,3,2,1,4,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,6,5,4,8,7,3,2] => [6,8,7,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,5,7,4,3,2,8] => [5,7,6,4,2,1,3,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [5,8,6,4,2,1,3,7] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [5,8,7,6,2,1,3,4] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [6,8,7,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [5,8,7,6,3,1,2,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [5,8,7,6,4,1,2,3] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [6,7,5,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [6,8,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [6,8,7,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [6,8,7,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [6,8,7,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [6,8,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [7,8,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[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] => [3,2,4,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [3,2,4,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [3,2,4,5,6,8,1,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [4,3,5,6,7,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [3,2,4,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [4,3,5,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [3,2,4,5,8,1,6,7] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [4,3,5,6,8,7,1,2] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [5,4,6,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [3,2,4,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [4,3,5,6,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [4,3,5,6,2,8,1,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [5,4,6,7,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [4,3,5,7,2,6,8,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [3,2,4,8,1,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [4,3,5,8,7,1,2,6] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [5,4,6,8,7,3,1,2] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [6,5,7,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [3,2,4,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [4,3,5,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [4,3,5,2,6,8,1,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [4,3,5,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [5,4,6,3,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [4,3,5,2,7,1,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [4,3,5,2,8,1,6,7] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [5,4,6,3,8,2,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [5,4,6,3,8,2,1,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [5,4,6,3,8,7,1,2] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [6,5,7,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [3,2,5,1,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [4,3,6,2,5,7,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [5,4,7,3,6,8,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [4,3,7,2,5,6,8,1] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [3,2,8,1,4,5,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [4,3,8,2,5,6,7,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [4,3,8,2,5,7,1,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [4,3,6,2,5,1,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [5,4,7,3,6,2,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [5,4,8,3,6,2,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,5,3,8] => [4,3,7,2,6,1,5,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [4,3,8,2,6,1,5,7] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [4,3,8,2,7,1,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [5,4,8,3,7,2,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [5,4,8,3,6,2,1,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,7,6,8,5,3] => [5,4,8,3,7,2,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [5,4,8,3,7,6,1,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [6,5,8,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [4,3,5,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [5,4,6,3,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [5,4,6,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [6,5,7,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [5,4,7,3,2,6,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [4,3,7,2,1,5,6,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [4,3,8,2,1,5,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [5,4,8,3,2,6,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [5,4,8,3,2,6,1,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [5,4,8,3,2,7,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [6,5,8,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [4,3,6,5,1,2,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [5,4,7,6,2,3,8,1] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [4,3,8,5,1,2,6,7] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [5,4,8,6,2,3,7,1] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [4,3,8,6,1,2,5,7] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [4,3,8,7,1,2,5,6] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [5,4,8,6,2,3,1,7] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [5,4,8,7,2,3,1,6] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [5,4,8,7,2,6,1,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [6,5,8,7,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [6,5,7,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [6,5,8,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [5,4,8,6,2,1,3,7] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [5,4,8,7,2,1,3,6] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [6,5,8,7,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,5,4,3,8] => [5,4,7,6,3,1,2,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => [5,4,8,6,3,1,2,7] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [5,4,8,7,3,1,2,6] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [5,4,8,7,6,1,2,3] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,7,5,4,3] => [6,5,8,7,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [6,5,7,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [6,5,8,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [6,5,8,7,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [6,5,8,7,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [6,5,8,7,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [7,6,8,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [4,2,3,5,6,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [4,2,3,5,6,7,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [4,2,3,5,6,8,1,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [4,2,3,5,8,1,6,7] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [5,3,4,6,8,2,1,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [6,4,5,7,8,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [5,3,4,6,2,7,1,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [4,2,3,8,1,5,6,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [5,3,4,8,2,6,1,7] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [6,4,5,7,3,2,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [5,3,4,7,2,1,6,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [6,4,5,8,3,2,7,1] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [5,3,4,8,7,1,2,6] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [6,4,5,8,7,3,1,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [7,5,6,8,4,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[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] => [5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [5,2,3,4,6,8,1,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [6,3,4,5,7,8,2,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [6,3,4,5,7,2,8,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [5,2,3,4,7,1,6,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [5,2,3,4,8,1,6,7] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [6,3,4,5,8,2,7,1] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [6,3,4,5,8,2,1,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [6,3,4,5,8,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [7,4,5,6,8,3,2,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[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] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [6,2,3,4,5,7,1,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [6,2,3,4,5,8,1,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [7,3,4,5,6,8,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[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] => [7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[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] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [8,2,3,4,5,7,1,6] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [8,3,4,5,6,7,2,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [8,3,4,5,6,2,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [8,2,3,4,6,1,5,7] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [8,2,3,4,7,1,5,6] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [7,3,4,5,6,2,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [8,3,4,5,6,2,1,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [8,3,4,5,7,2,1,6] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [8,3,4,5,7,6,1,2] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [8,4,5,6,7,3,2,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [6,3,4,5,2,7,8,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [6,3,4,5,2,7,1,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [7,4,5,6,3,8,2,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,7,8,6,1] => [8,3,4,5,2,7,1,6] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [8,2,3,5,1,4,6,7] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [8,2,3,6,1,4,5,7] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [8,2,3,7,1,4,5,6] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [8,3,4,7,2,5,6,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [8,3,4,7,2,6,1,5] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,7,6,4,1] => [8,4,5,7,3,6,2,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [6,3,4,5,2,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [7,4,5,6,3,2,8,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [8,3,4,5,2,1,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,5,7,4,1,8] => [7,3,4,6,2,1,5,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [8,4,5,7,3,2,6,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => [8,3,4,7,6,1,2,5] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [7,4,5,6,3,2,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [8,4,5,6,3,2,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [8,5,6,7,4,3,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [6,4,5,3,7,2,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [6,4,5,3,8,2,7,1] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [6,4,5,3,8,2,1,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [6,4,5,3,8,7,1,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [7,5,6,4,8,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [5,2,3,1,4,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [7,2,3,1,4,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [8,2,3,1,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [8,3,4,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [8,3,4,2,5,6,1,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [7,4,5,3,6,2,8,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [8,4,5,3,6,2,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [8,4,5,3,7,2,6,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [8,4,5,3,6,2,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [8,5,6,4,7,3,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => [6,3,5,2,4,7,8,1] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [6,3,5,2,4,8,1,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [8,2,4,1,3,5,6,7] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => [8,3,5,2,4,7,1,6] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [8,3,6,2,4,5,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => [8,3,7,2,4,5,6,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => [8,3,7,2,4,6,1,5] => [[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => [6,3,5,2,4,1,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [7,4,6,3,5,2,8,1] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => [8,3,5,2,4,1,6,7] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [8,4,6,3,5,2,7,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [8,3,6,2,4,1,5,7] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [8,3,7,2,4,1,5,6] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [8,4,7,3,5,2,6,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [7,3,6,2,5,1,4,8] => [[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [8,3,6,2,5,1,4,7] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,5,8,3,1] => [8,3,7,2,5,1,4,6] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [8,3,7,2,6,1,4,5] => [[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [8,4,7,3,6,2,5,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,4,7,6,5,8,3,1] => [8,4,7,3,5,2,1,6] => [[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [8,4,7,3,6,5,1,2] => [[[[.,[.,.]],.],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [8,5,7,4,6,3,2,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [5,3,4,2,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [6,4,5,3,2,8,1,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [7,5,6,4,3,8,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [8,3,4,2,1,5,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [8,4,5,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [7,3,5,2,1,4,6,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,4,6,3,7,8,1] => [8,3,5,2,1,4,6,7] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [7,3,6,2,1,4,5,8] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [8,3,6,2,1,4,5,7] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => [8,3,7,2,1,4,5,6] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [8,4,7,3,2,5,1,6] => [[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [8,4,7,3,2,6,1,5] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => [8,5,7,4,3,6,2,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,4,7,8,3,1] => [8,3,7,4,1,2,5,6] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [8,4,7,5,2,3,6,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [8,3,6,5,1,2,4,7] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [8,3,7,5,1,2,4,6] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [8,3,7,6,1,2,4,5] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [7,5,6,4,3,2,8,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [8,4,5,3,2,1,6,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [8,5,6,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [8,4,7,3,2,1,5,6] => [[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [8,5,7,4,3,2,6,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,6,5,7,8,4,3,1] => [8,4,7,6,2,1,3,5] => [[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [8,4,7,6,3,1,2,5] => [[[[.,[.,.]],.],[[[.,.],.],.]],.]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [8,4,7,6,5,1,2,3] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [8,5,7,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [7,5,6,4,3,2,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [8,5,6,4,3,2,1,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [8,5,7,4,3,2,1,6] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => [8,5,7,6,4,2,1,3] => [[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [8,5,7,6,4,3,1,2] => [[[[[.,[.,.]],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [8,6,7,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [4,3,2,5,6,8,1,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [5,4,3,6,7,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [5,4,3,6,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [5,4,3,6,8,7,1,2] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [6,5,4,7,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [5,4,3,6,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [4,3,2,6,1,5,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => [4,3,2,7,1,5,6,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [4,3,2,8,1,5,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [5,4,3,8,2,6,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [5,4,3,7,2,6,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [5,4,3,8,2,7,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [6,5,4,8,3,7,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [5,4,3,6,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [6,5,4,7,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => [5,4,3,7,2,1,6,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [5,4,3,8,2,1,6,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [6,5,4,8,3,2,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,6,7,5,4,8] => [5,4,3,7,6,1,2,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [6,5,4,8,7,2,3,1] => [[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [6,5,4,7,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [6,5,4,8,3,2,1,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => [6,5,4,8,7,2,1,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [6,5,4,8,7,3,1,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [4,2,1,3,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [5,3,2,4,6,7,8,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [5,3,2,4,6,8,1,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [5,3,2,4,6,1,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [6,4,3,5,7,2,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [5,3,2,4,7,1,6,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [5,3,2,4,8,1,6,7] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [6,4,3,5,8,2,7,1] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [6,4,3,5,8,2,1,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [6,4,3,5,8,7,1,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [7,5,4,6,8,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [5,2,1,3,4,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [7,2,1,3,4,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [8,2,1,3,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [8,3,2,4,5,6,1,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => [8,3,2,4,5,7,1,6] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [8,4,3,5,6,2,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => [7,3,2,4,6,1,5,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [8,4,3,5,6,2,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [6,4,3,5,2,8,1,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [7,5,4,6,3,8,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [7,4,3,5,2,6,8,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [7,4,3,5,2,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [8,4,3,5,2,6,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [7,4,3,6,2,5,8,1] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => [8,3,2,5,1,4,6,7] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => [7,3,2,6,1,4,5,8] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [8,3,2,6,1,4,5,7] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [8,3,2,7,1,4,5,6] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [8,4,3,6,2,5,1,7] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [8,4,3,7,2,6,1,5] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [7,4,3,5,2,1,6,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [8,5,4,6,3,2,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,6,5,7,4,1,8] => [7,4,3,6,2,1,5,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [8,4,3,6,2,1,5,7] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [8,4,3,6,5,1,2,7] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,6,7,5,8,4,1] => [8,4,3,7,5,1,2,6] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [7,5,4,6,3,2,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [8,5,4,7,6,3,1,2] => [[[[[.,[.,.]],.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [8,6,5,7,4,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [4,3,1,2,5,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,2,1,5,6,8,7] => [5,4,2,3,6,7,8,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,2,1,5,8,7,6] => [6,5,3,4,7,8,2,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [6,5,3,4,7,2,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [5,4,2,3,8,1,6,7] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [6,5,3,4,8,2,7,1] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [6,5,3,4,8,2,1,7] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [6,5,3,4,8,7,1,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [7,6,4,5,8,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [5,3,1,2,4,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [6,4,2,3,5,7,1,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [6,4,2,3,5,8,1,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [7,5,3,4,6,8,2,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [7,3,1,2,4,5,6,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [8,3,1,2,4,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [8,4,2,3,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,2,5,7,6,1,8] => [7,4,2,3,5,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [8,4,2,3,5,7,1,6] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => [8,5,3,4,6,7,2,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [7,5,3,4,6,2,8,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [7,4,2,3,5,1,6,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [8,4,2,3,5,1,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [8,4,2,3,6,1,5,7] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [8,6,4,5,7,3,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [5,4,1,2,3,6,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,2,1,6,8,7] => [6,5,2,3,4,7,8,1] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,2,1,7,8,6] => [6,5,2,3,4,8,1,7] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [7,6,3,4,5,8,2,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [6,4,1,2,3,5,7,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [7,5,2,3,4,6,8,1] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [7,4,1,2,3,5,6,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [8,4,1,2,3,5,6,7] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [8,5,2,3,4,6,1,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,2,1,8,7] => [7,6,2,3,4,5,8,1] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [7,5,1,2,3,4,6,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [8,5,1,2,3,4,6,7] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [8,6,2,3,4,5,7,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [7,6,1,2,3,4,5,8] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [8,6,1,2,3,4,5,7] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [8,7,1,2,3,4,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [8,7,2,3,4,5,6,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [8,7,2,3,4,5,1,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [8,7,2,3,4,6,1,5] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => [7,6,3,4,5,2,8,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,5,2,7,1,8] => [7,5,2,3,4,1,6,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,5,2,7,8,1] => [8,5,2,3,4,1,6,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [8,6,2,3,4,1,5,7] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,5,7,8,2,1] => [8,7,2,3,4,1,5,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [8,6,2,3,5,1,4,7] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [8,7,2,3,6,1,4,5] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => [8,7,3,4,5,2,1,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [5,4,2,3,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [6,5,3,4,2,7,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [6,5,3,4,2,8,1,7] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [7,6,4,5,3,8,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => [8,4,2,3,1,5,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => [8,5,3,4,2,7,1,6] => [[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [7,5,2,3,1,4,6,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,4,6,7,8,2,1] => [8,7,2,3,1,4,5,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [8,7,3,4,2,5,1,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [7,6,3,5,2,4,8,1] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [8,6,2,4,1,3,5,7] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,4,7,8,2,1] => [8,7,2,4,1,3,5,6] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [8,6,2,5,1,3,4,7] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [8,7,2,5,1,3,4,6] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [8,7,2,6,1,3,4,5] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [7,6,3,5,2,4,1,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [8,6,3,5,2,4,1,7] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => [8,7,3,5,2,4,1,6] => [[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => [8,7,3,6,2,4,1,5] => [[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [8,7,3,6,2,5,1,4] => [[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [8,7,4,6,3,5,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [7,6,4,5,3,2,8,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,5,4,2,8,7,1] => [8,6,4,5,3,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,5,4,7,2,1,8] => [7,6,3,4,2,1,5,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [8,6,3,4,2,1,5,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,5,4,7,8,2,1] => [8,7,3,4,2,1,5,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [8,7,4,6,5,2,3,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [8,7,4,5,3,2,1,6] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [8,7,4,6,3,2,1,5] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [8,7,4,6,5,2,1,3] => [[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [8,7,4,6,5,3,1,2] => [[[[[.,[.,.]],.],[[.,.],.]],.],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [8,7,5,6,4,3,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [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] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [5,4,3,2,6,8,1,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [5,4,3,2,7,1,6,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [5,4,3,2,8,1,6,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [6,5,4,3,8,2,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [6,5,4,3,8,2,1,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [6,5,4,3,8,7,1,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [5,3,2,1,4,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [6,4,3,2,5,8,1,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [7,5,4,3,6,8,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [7,3,2,1,4,5,6,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,3,2,5,7,8,6,1] => [8,4,3,2,5,7,1,6] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [8,5,4,3,6,7,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [7,5,4,3,6,2,8,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [8,5,4,3,6,2,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [8,5,4,3,7,2,6,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [8,5,4,3,7,6,1,2] => [[[[[.,[.,.]],.],.],[[.,.],.]],.]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [8,6,5,4,7,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [5,4,2,1,3,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [6,5,3,2,4,7,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => [7,6,4,3,5,8,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [6,4,2,1,3,5,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [7,5,3,2,4,6,8,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [8,4,2,1,3,5,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [7,5,3,2,4,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [8,5,3,2,4,6,1,7] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => [8,6,4,3,5,7,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [7,6,3,2,4,5,8,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [8,5,2,1,3,4,6,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [8,7,2,1,3,4,5,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,3,5,7,6,2,1,8] => [7,6,3,2,4,5,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => [8,7,3,2,4,6,1,5] => [[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [7,6,4,3,5,2,8,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,3,6,5,7,2,1,8] => [7,6,3,2,4,1,5,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [8,6,3,2,4,1,5,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [8,7,3,2,4,1,5,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [8,7,4,3,5,2,6,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,6,7,5,2,8,1] => [8,6,3,2,5,1,4,7] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [8,7,3,2,6,1,4,5] => [[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [8,7,4,3,6,5,1,2] => [[[[[.,[.,.]],.],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [8,7,5,4,6,3,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [5,4,3,1,2,6,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => [6,5,4,2,3,7,8,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [7,6,5,3,4,8,2,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,5,3,2,6,1,7,8] => [6,4,3,1,2,5,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,3,2,6,1,8,7] => [7,5,4,2,3,6,8,1] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,5,3,2,6,8,7,1] => [8,5,4,2,3,6,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [7,6,4,2,3,5,8,1] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [7,5,3,1,2,4,6,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [8,6,4,2,3,5,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,5,3,7,6,2,1,8] => [7,6,4,2,3,5,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,3,7,6,2,8,1] => [8,6,4,2,3,5,1,7] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [8,7,4,2,3,6,1,5] => [[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [6,5,4,1,2,3,7,8] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [7,6,5,2,3,4,8,1] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [8,5,4,1,2,3,6,7] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [8,6,4,1,2,3,5,7] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,5,6,3,7,8,2,1] => [8,7,4,1,2,3,5,6] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [7,6,5,1,2,3,4,8] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [8,6,5,1,2,3,4,7] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [8,7,5,1,2,3,4,6] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [8,7,6,1,2,3,4,5] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [8,7,6,2,3,4,5,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => [7,6,5,2,3,4,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [8,7,6,2,3,4,1,5] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [8,7,6,3,4,5,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [7,6,5,3,4,2,8,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [8,6,5,3,4,2,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [8,6,4,2,3,1,5,7] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,5,7,3,2,1,8] => [7,6,5,2,3,1,4,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [8,6,5,2,3,1,4,7] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [8,7,6,2,3,1,4,5] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [8,7,6,3,4,2,5,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [8,6,5,2,4,1,3,7] => [[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [8,7,6,2,4,1,3,5] => [[[[[.,.],[[.,.],[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,5,3,2,1] => [8,7,6,2,5,1,3,4] => [[[[[.,.],[[.,[.,.]],.]],.],.],.]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [8,7,6,3,5,2,4,1] => [[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [7,6,5,3,4,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [8,6,5,3,4,2,1,7] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [8,7,5,3,4,2,1,6] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [8,7,6,3,4,2,1,5] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [8,7,6,3,5,2,1,4] => [[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [8,7,6,3,5,4,1,2] => [[[[[.,[.,.]],[[.,.],.]],.],.],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [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] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [6,5,4,3,2,8,1,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [6,4,3,2,1,5,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [7,5,4,3,2,6,8,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [7,4,3,2,1,5,6,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [8,4,3,2,1,5,6,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [8,5,4,3,2,6,1,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [8,5,4,3,2,7,1,6] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [8,6,5,4,3,7,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => [6,5,3,2,1,4,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [7,5,3,2,1,4,6,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => [8,5,3,2,1,4,6,7] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [8,6,4,3,2,5,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,4,3,6,7,2,1,8] => [7,6,3,2,1,4,5,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,4,3,6,7,2,8,1] => [8,6,3,2,1,4,5,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [8,7,3,2,1,4,5,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,4,3,6,8,7,2,1] => [8,7,4,3,2,5,6,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,4,3,7,6,2,1,8] => [7,6,4,3,2,5,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [8,7,4,3,2,6,1,5] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [6,5,4,2,1,3,7,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [7,6,5,3,2,4,8,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [8,5,4,2,1,3,6,7] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [8,6,5,3,2,4,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [7,6,4,2,1,3,5,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [8,6,4,2,1,3,5,7] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [7,6,5,2,1,3,4,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [8,7,5,2,1,3,4,6] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [8,7,6,2,1,3,4,5] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [7,6,5,3,2,4,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [8,7,5,3,2,4,1,6] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => [8,7,6,3,2,4,1,5] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => [8,7,6,3,2,5,1,4] => [[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [6,5,4,3,1,2,7,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [7,6,5,4,2,3,8,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,4,3,2,7,1,8] => [7,5,4,3,1,2,6,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [7,6,4,3,1,2,5,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [8,7,5,4,2,3,6,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [8,7,6,3,1,2,4,5] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [7,6,5,4,1,2,3,8] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,4,3,2,8,1] => [8,6,5,4,1,2,3,7] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [8,7,5,4,1,2,3,6] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [8,7,6,4,1,2,3,5] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [8,7,6,5,1,2,3,4] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [8,7,6,5,2,3,4,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [7,6,5,4,2,3,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [8,6,5,4,2,3,1,7] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [8,7,6,4,2,3,1,5] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [8,7,6,5,2,3,1,4] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [8,7,6,5,2,4,1,3] => [[[[[[.,.],[[.,.],.]],.],.],.],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [8,7,6,5,3,4,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [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] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [7,5,4,3,2,1,6,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [8,5,4,3,2,1,6,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [7,6,4,3,2,1,5,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [8,6,4,3,2,1,5,7] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [8,7,4,3,2,1,5,6] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [8,7,5,4,3,2,6,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [7,6,5,3,2,1,4,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [8,6,5,3,2,1,4,7] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [8,7,5,3,2,1,4,6] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [8,7,6,3,2,1,4,5] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,5,4,8,7,3,2,1] => [8,7,6,4,3,2,5,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [7,6,5,4,2,1,3,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [8,6,5,4,2,1,3,7] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [8,7,6,4,2,1,3,5] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [8,7,6,5,2,1,3,4] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [8,7,6,5,3,2,4,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [7,6,5,4,3,1,2,8] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [8,6,5,4,3,1,2,7] => [[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,5,4,3,8,2,1] => [8,7,5,4,3,1,2,6] => [[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [8,7,6,4,3,1,2,5] => [[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [8,7,6,5,3,1,2,4] => [[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [8,7,6,5,4,1,2,3] => [[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [8,7,6,5,4,2,3,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [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] => [8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [8,7,5,4,3,2,1,6] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [8,7,6,4,3,2,1,5] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [8,7,6,5,4,2,1,3] => [[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [8,7,6,5,4,3,1,2] => [[[[[[[.,[.,.]],.],.],.],.],.],.]
[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] => [8,9,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [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] => [8,7,6,5,4,3,1,2,9] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[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] => [9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[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] => [9,8,7,6,5,4,3,1,2,10] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,6,8,5,4,3,2,1,9] => [8,7,6,5,4,2,1,3,9] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[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] => [8,7,6,5,4,2,3,1,9] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[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] => [10,11,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1,12] => [11,10,9,8,7,6,5,4,3,2,1,12] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [8,7,9,6,5,4,3,2,1,10] => [9,8,7,6,5,4,2,1,3,10] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,6,5,8,4,3,2,1,9] => [8,7,6,5,3,2,1,4,9] => [[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,5,4,3,2,1,9] => [8,7,6,5,4,1,2,3,9] => [[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [8,7,6,9,5,4,3,2,1,10] => [9,8,7,6,5,3,2,1,4,10] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],[.,.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,8,7,6,5,3,2,1,9] => [8,7,6,4,5,3,2,1,9] => [[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,9,8,7,6,4,3,2,1,10] => [9,8,7,6,4,5,3,2,1,10] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,6,5,4,3,8,2,1,9] => [8,7,5,4,3,2,1,6,9] => [[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [8,7,6,5,4,9,3,2,1,10] => [9,8,7,5,4,3,2,1,6,10] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => [8,6,5,4,3,2,1,7,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [8,6,7,5,4,3,2,1,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [8,7,6,5,4,3,2,9,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [8,7,9,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [7,9,6,8,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [8,7,6,5,4,3,9,2,1,10] => [9,8,6,5,4,3,2,1,7,10] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],[.,.]]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [7,8,6,5,4,3,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [6,7,5,4,3,2,1,9,8] => [8,7,6,5,4,2,3,9,1] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [7,8,9,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => [9,7,6,5,4,3,2,1,8,10] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[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] => [9,8,7,6,5,4,3,2,10,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[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] => [9,8,10,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [8,9,7,6,5,4,3,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [8,9,10,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[] => [] => [] => .
[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] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [9,2,3,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [9,3,4,5,6,7,8,2,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,1] => [9,2,3,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,5,8,7,6,9,1] => [9,3,4,5,6,7,2,1,8] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,1] => [9,2,3,4,5,1,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [9,6,7,8,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [9,2,3,1,4,5,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [9,6,7,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [9,7,8,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [9,2,1,3,4,5,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [9,3,1,2,4,5,6,7,8] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,9,1] => [9,4,1,2,3,5,6,7,8] => [[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,7,2,8,9,1] => [9,6,1,2,3,4,5,7,8] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,2,9,1] => [9,7,1,2,3,4,5,6,8] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [9,8,1,2,3,4,5,6,7] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [3,8,7,6,5,4,9,2,1] => [9,8,5,6,4,3,2,1,7] => [[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,6,3,7,8,9,2,1] => [9,8,4,1,2,3,5,6,7] => [[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [9,8,7,1,2,3,4,5,6] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,8,7,6,5,9,3,2,1] => [9,8,7,4,5,3,2,1,6] => [[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,9,8,7,6,5,3,2,1] => [9,8,7,5,6,4,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => [9,7,5,3,1,2,4,6,8] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [9,8,7,6,1,2,3,4,5] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,8,7,6,9,4,3,2,1] => [9,8,7,6,3,4,2,1,5] => [[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => [9,8,7,6,4,5,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => [9,5,4,3,2,1,6,7,8] => [[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [9,8,7,6,5,1,2,3,4] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,8,5,4,3,2,1] => [9,8,7,6,5,2,3,4,1] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,8,7,9,5,4,3,2,1] => [9,8,7,6,5,2,3,1,4] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,9,8,7,5,4,3,2,1] => [9,8,7,6,5,3,4,2,1] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => [9,6,5,4,3,2,1,7,8] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,6,5,4,3,2,9,8,1] => [9,7,6,5,4,3,2,8,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,6,8,9,5,4,3,2,1] => [9,8,7,6,5,2,1,3,4] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,6,9,8,5,4,3,2,1] => [9,8,7,6,5,3,2,4,1] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,6,5,4,3,2,9,1] => [9,7,6,5,4,3,1,2,8] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]
[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] => [9,8,7,6,5,4,1,2,3] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [9,8,7,6,5,4,2,3,1] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [9,7,6,5,4,3,2,1,8] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[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] => [9,8,6,5,4,3,2,1,7] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,7,6,5,4,9,3,2,1] => [9,8,7,5,4,3,2,1,6] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[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] => [9,8,7,6,4,3,2,1,5] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,7,6,9,5,4,3,2,1] => [9,8,7,6,5,3,2,1,4] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[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] => [9,8,7,6,5,4,2,1,3] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[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] => [9,8,7,6,5,4,3,1,2] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[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] => [2,3,4,5,6,7,8,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[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] => [2,3,4,5,6,7,9,1,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[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] => [2,3,4,5,6,9,1,7,8] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[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] => [2,3,4,5,9,1,6,7,8] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[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] => [2,3,4,9,1,5,6,7,8] => [[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[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] => [2,3,9,1,4,5,6,7,8] => [[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[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] => [2,9,1,3,4,5,6,7,8] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[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] => [2,3,4,5,6,7,8,9,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[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] => [3,4,5,6,7,8,9,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[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] => [2,3,4,5,6,7,8,10,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[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] => [2,3,4,5,6,7,10,1,8,9] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[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] => [2,3,4,5,6,10,1,7,8,9] => [[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[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] => [2,3,4,5,10,1,6,7,8,9] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[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] => [2,3,4,10,1,5,6,7,8,9] => [[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[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] => [2,3,10,1,4,5,6,7,8,9] => [[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[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] => [2,10,1,3,4,5,6,7,8,9] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[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] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [3,4,5,6,7,8,9,10,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [2,3,4,5,6,7,8,9,11,1,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [4,5,6,7,8,9,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [10,2,1,3,4,5,6,7,8,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [2,11,1,3,4,5,6,7,8,9,10] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [3,4,5,6,7,8,9,10,11,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [4,5,6,7,8,9,10,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,10,1] => [10,3,1,2,4,5,6,7,8,9] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => [11,2,1,3,4,5,6,7,8,9,10] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [2,12,1,3,4,5,6,7,8,9,10,11] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [5,6,7,8,9,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,9,10,1] => [10,4,1,2,3,5,6,7,8,9] => [[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,10,11,1] => [11,3,1,2,4,5,6,7,8,9,10] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [5,6,7,8,9,10,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,9,10,11,1] => [11,4,1,2,3,5,6,7,8,9,10] => [[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,6,7,2,8,9,10,1] => [10,6,1,2,3,4,5,7,8,9] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [6,7,8,9,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,7,8,2,9,10,1] => [10,7,1,2,3,4,5,6,8,9] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [6,7,8,9,10,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,2,8,9,10,11,1] => [11,6,1,2,3,4,5,7,8,9,10] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,2,9,10,11,1] => [11,7,1,2,3,4,5,6,8,9,10] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [2,3,4,5,6,7,8,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [2,3,4,5,6,7,1,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [3,4,5,6,7,8,2,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [2,3,4,5,6,1,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [4,5,6,3,7,2,8,1,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [3,4,2,5,6,7,8,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [3,4,2,5,1,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [5,6,4,7,3,8,2,9,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [3,4,2,1,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => [7,8,6,5,4,3,2,9,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [3,2,4,5,6,7,8,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [3,2,4,5,6,7,8,1,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[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] => [5,4,6,3,7,2,8,1,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,9,8,7,6,5] => [7,6,8,5,9,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [7,6,8,5,4,3,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => [4,3,2,5,1,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [8,7,6,9,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,3,2,1,6,5,7,8,9] => [5,4,3,2,6,1,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [8,7,6,5,9,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => [6,5,4,3,2,7,1,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,4,3,2,1,8,7,6,9] => [7,6,5,4,3,8,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [8,7,6,5,4,9,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => [7,6,5,4,3,2,8,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [8,7,6,5,4,3,9,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [2,3,4,5,6,7,8,9,1,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [2,3,4,5,6,7,8,1,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [3,4,5,6,7,8,9,2,10,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [7,8,9,10,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [5,6,4,7,3,8,2,9,1,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [3,2,4,5,6,7,8,9,10,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[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] => [6,5,7,4,8,3,9,2,10,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[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] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [9,8,7,10,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [9,8,7,6,10,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,3,2,1,9,8,7,6,10] => [8,7,6,5,4,9,3,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [9,8,7,6,5,10,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,5,4,3,2,1,9,8,7,10] => [8,7,6,5,4,3,9,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[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] => [9,8,7,6,5,4,10,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => [8,7,6,5,4,3,2,9,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [9,8,7,6,5,4,3,10,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[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] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [6,1,2,3,4,5,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [7,1,2,3,4,5,6,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[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] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,4,6,5,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,5,7,6,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [8,1,2,3,4,5,6,7,9,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [3,2,4,5,6,7,9,1,8] => [[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,10,9,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,2,3,1] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,2,1,3] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => [4,2,3,5,6,7,9,1,8] => [[[.,.],[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [4,2,3,5,6,7,8,9,1] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9] => [4,3,1,2,5,6,7,8,9] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [10,8,9,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [10,8,7,6,5,4,3,2,1,9] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [11,9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,9,7,6,5,4,3,2,10,1] => [10,8,7,6,5,4,3,1,2,9] => [[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => [10,9,8,7,5,6,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,10,9,8,7,6,5,3,2,1] => [10,9,8,6,7,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [8,6,7,9,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,2,1,9,8,7,6,5] => [8,7,5,6,9,4,3,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,5,3,2,1,9,8,7,6] => [8,7,6,4,5,9,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [5,6,4,3,2,1,9,8,7] => [8,7,6,5,3,4,9,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => [2,3,5,1,4,6,7,8,9] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,10,1] => [10,2,3,4,5,1,6,7,8,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [8,2,1,3,4,5,6,7,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [3,9,2,4,5,6,7,8,1] => [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [8,2,3,4,5,6,7,9,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [3,2,9,1,4,5,6,7,8] => [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [8,3,4,5,6,7,9,2,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [10,3,4,5,6,7,8,9,2,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [10,9,8,1,2,3,4,5,6,7] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [10,9,7,6,5,4,3,2,1,8] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,8,7,6,5,4,10,3,2,1] => [10,9,8,6,5,4,3,2,1,7] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,8,7,6,5,10,4,3,2,1] => [10,9,8,7,5,4,3,2,1,6] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,8,7,6,10,5,4,3,2,1] => [10,9,8,7,6,4,3,2,1,5] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,8,7,10,6,5,4,3,2,1] => [10,9,8,7,6,5,3,2,1,4] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,10,1] => [10,2,3,4,5,6,1,7,8,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [6,4,5,7,3,8,2,9,1,10] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [10,9,1,2,3,4,5,6,7,8] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [11,2,3,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [11,10,1,2,3,4,5,6,7,8,9] => [[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,10,9,8,7,2,1] => [10,9,7,6,5,4,8,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => [9,7,5,3,1,2,4,6,8,10] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,11,10,9,8,7,6,5,4,3] => [10,9,11,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,11,10,9,8,7,6,5,4,3,1] => [11,9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [3,4,5,6,7,9,2,8,1] => [[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => [10,9,8,7,6,5,4,3,2,11,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [10,9,8,7,1,2,3,4,5,6] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9] => [6,5,4,3,1,2,7,8,9] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8,9] => [5,4,3,1,2,6,7,8,9] => [[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [4,2,3,9,1,5,6,7,8] => [[[.,.],[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,1,2,3] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [2,3,4,5,6,7,8,9,10,1,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [2,3,4,5,6,8,1,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8,9] => [5,3,1,2,4,6,7,8,9] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [10,9,8,7,6,1,2,3,4,5] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [10,9,8,7,6,5,1,2,3,4] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [10,1,2,3,4,5,6,7,8,9,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [2,8,1,3,4,5,6,7,9] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,7,6,5,4,3,2,10,9,1] => [10,8,7,6,5,4,3,2,9,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [9,2,3,4,5,6,7,8,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [7,2,3,4,5,6,9,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9,10] => [6,5,4,3,1,2,7,8,9,10] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [5,6,4,3,2,7,1,8,9] => [7,5,4,3,1,2,6,8,9] => [[[[[.,[.,.]],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10] => [7,6,5,4,3,1,2,8,9,10] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10,11] => [7,6,5,4,3,1,2,8,9,10,11] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1,10,11] => [9,8,7,6,5,4,3,2,1,10,11] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,9,10,2,11,1] => [11,9,1,2,3,4,5,6,7,8,10] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => [5,2,3,4,9,1,6,7,8] => [[[.,.],[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,6,5,4,3,9,8,2] => [7,9,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,2,1,7,8,9,6] => [6,5,4,3,2,9,1,7,8] => [[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,2,8,7,6,5,4,1,9] => [8,6,5,7,4,3,2,1,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => [10,7,6,5,4,3,2,1,8,9] => [[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [5,6,4,7,3,8,2,10,1,9] => [[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,10,1] => [10,8,6,4,2,1,3,5,7,9] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => [12,10,8,6,4,2,1,3,5,7,9,11] => [[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,11,10] => [10,2,3,4,5,6,7,8,9,11,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => [6,2,3,4,5,9,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,7,8,10,9,1] => [10,3,2,4,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,5,4,3,2,1,9,10,8] => [8,7,6,5,4,3,2,10,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,3,2,1,8,9,10,7] => [7,6,5,4,3,2,10,1,8,9] => [[[[[[[.,.],.],.],.],.],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [6,5,7,4,8,3,10,2,9,1] => [[[[[[.,.],.],.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7,9] => [4,6,3,5,7,2,8,1,9] => [[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,4,6,3,7,2,8,1,9] => [8,6,4,2,1,3,5,7,9] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,5,3,6,2,7,1,8,9] => [7,5,3,1,2,4,6,8,9] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]
Map
to 312-avoiding permutation
Description
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
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.