Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00064: Permutations —reverse⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
[1,0] => [1] => [1] => [.,.]
[1,0,1,0] => [2,1] => [1,2] => [.,[.,.]]
[1,1,0,0] => [1,2] => [2,1] => [[.,.],.]
[1,0,1,0,1,0] => [3,2,1] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,1,0,0] => [2,3,1] => [1,3,2] => [.,[[.,.],.]]
[1,1,0,0,1,0] => [3,1,2] => [2,1,3] => [[.,.],[.,.]]
[1,1,0,1,0,0] => [2,1,3] => [3,1,2] => [[.,[.,.]],.]
[1,1,1,0,0,0] => [1,2,3] => [3,2,1] => [[[.,.],.],.]
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [1,2,4,3] => [.,[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [1,3,2,4] => [.,[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [1,4,2,3] => [.,[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,4,3,2] => [.,[[[.,.],.],.]]
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,1,4,3] => [[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [3,1,2,4] => [[.,[.,.]],[.,.]]
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [4,1,2,3] => [[.,[.,[.,.]]],.]
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [4,1,3,2] => [[.,[[.,.],.]],.]
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [4,2,1,3] => [[[.,.],[.,.]],.]
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [4,3,1,2] => [[[.,[.,.]],.],.]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [4,3,2,1] => [[[[.,.],.],.],.]
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [1,5,3,2,4] => [.,[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [1,5,4,2,3] => [.,[[[.,[.,.]],.],.]]
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [3,1,2,5,4] => [[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [5,1,2,4,3] => [[.,[.,[[.,.],.]]],.]
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [4,1,3,2,5] => [[.,[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [5,1,3,2,4] => [[.,[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [5,1,4,2,3] => [[.,[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [5,1,4,3,2] => [[.,[[[.,.],.],.]],.]
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [4,2,1,3,5] => [[[.,.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [5,2,1,3,4] => [[[.,.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [5,2,1,4,3] => [[[.,.],[[.,.],.]],.]
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [4,3,1,2,5] => [[[.,[.,.]],.],[.,.]]
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [5,3,1,2,4] => [[[.,[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [5,4,1,3,2] => [[[.,[[.,.],.]],.],.]
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [5,3,2,1,4] => [[[[.,.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [5,4,2,1,3] => [[[[.,.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [5,4,3,1,2] => [[[[.,[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [1,2,6,3,5,4] => [.,[.,[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,2,6,5,3,4] => [.,[.,[[[.,[.,.]],.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [1,5,2,4,3,6] => [.,[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [1,6,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [1,6,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [1,6,2,5,4,3] => [.,[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [1,5,3,2,4,6] => [.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [1,6,3,2,4,5] => [.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [1,6,3,2,5,4] => [.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [1,5,4,2,3,6] => [.,[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,6,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [1,6,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [1,6,5,2,4,3] => [.,[[[.,[[.,.],.]],.],.]]
>>> Load all 2110 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [1,6,4,3,2,5] => [.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [1,6,5,3,2,4] => [.,[[[[.,.],[.,.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [1,6,5,4,2,3] => [.,[[[[.,[.,.]],.],.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [2,1,3,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [2,1,6,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [2,1,6,3,5,4] => [[.,.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [2,1,6,4,3,5] => [[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [2,1,6,5,3,4] => [[.,.],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [3,1,2,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [3,1,2,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [3,1,2,6,5,4] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [4,1,2,3,6,5] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [6,1,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [5,1,2,4,3,6] => [[.,[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [6,1,2,4,3,5] => [[.,[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [6,1,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [6,1,2,5,4,3] => [[.,[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [4,1,3,2,5,6] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [4,1,3,2,6,5] => [[.,[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [5,1,3,2,4,6] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [6,1,3,2,4,5] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [6,1,3,2,5,4] => [[.,[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [5,1,4,2,3,6] => [[.,[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [6,1,4,2,3,5] => [[.,[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [6,1,5,2,3,4] => [[.,[[.,[.,[.,.]]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [6,1,5,2,4,3] => [[.,[[.,[[.,.],.]],.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [5,1,4,3,2,6] => [[.,[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [6,1,4,3,2,5] => [[.,[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [6,1,5,3,2,4] => [[.,[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [6,1,5,4,2,3] => [[.,[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => [[.,[[[[.,.],.],.],.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => [[[.,.],.],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [4,2,1,3,6,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [6,2,1,3,5,4] => [[[.,.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [6,2,1,4,3,5] => [[[.,.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [6,2,1,5,3,4] => [[[.,.],[[.,[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [6,2,1,5,4,3] => [[[.,.],[[[.,.],.],.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [4,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [4,3,1,2,6,5] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [6,3,1,2,5,4] => [[[.,[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [6,5,1,2,4,3] => [[[.,[.,[[.,.],.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [5,4,1,3,2,6] => [[[.,[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [6,4,1,3,2,5] => [[[.,[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [6,5,1,3,2,4] => [[[.,[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [6,5,1,4,2,3] => [[[.,[[.,[.,.]],.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => [[[.,[[[.,.],.],.]],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [6,3,2,1,5,4] => [[[[.,.],.],[[.,.],.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [6,5,2,1,4,3] => [[[[.,.],[[.,.],.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [1,2,3,7,5,4,6] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [1,2,3,7,6,4,5] => [.,[.,[.,[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [1,2,5,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [1,2,5,3,4,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [1,2,6,3,4,5,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [1,2,7,3,4,6,5] => [.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [1,2,6,3,5,4,7] => [.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [1,2,7,3,5,4,6] => [.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [1,2,7,3,6,4,5] => [.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [1,2,7,3,6,5,4] => [.,[.,[[.,[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [1,2,6,4,3,5,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [1,2,7,4,3,5,6] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [1,2,7,4,3,6,5] => [.,[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [1,2,6,5,3,4,7] => [.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [1,2,7,5,3,4,6] => [.,[.,[[[.,[.,.]],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [1,2,7,6,3,4,5] => [.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [1,2,7,6,3,5,4] => [.,[.,[[[.,[[.,.],.]],.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [1,2,7,5,4,3,6] => [.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [1,2,7,6,4,3,5] => [.,[.,[[[[.,.],[.,.]],.],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [1,2,7,6,5,3,4] => [.,[.,[[[[.,[.,.]],.],.],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [1,3,2,6,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [1,3,2,7,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [1,3,2,7,4,6,5] => [.,[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [1,3,2,7,5,4,6] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [1,3,2,7,6,4,5] => [.,[[.,.],[[[.,[.,.]],.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [1,4,2,3,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [1,4,2,3,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [1,4,2,3,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [1,4,2,3,7,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [1,4,2,3,7,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [1,5,2,3,4,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [1,5,2,3,4,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [1,6,2,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [1,7,2,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [1,7,2,3,4,6,5] => [.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [1,6,2,3,5,4,7] => [.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [1,7,2,3,5,4,6] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [1,7,2,3,6,4,5] => [.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [1,7,2,3,6,5,4] => [.,[[.,[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [1,5,2,4,3,6,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [1,5,2,4,3,7,6] => [.,[[.,[[.,.],.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [1,6,2,4,3,5,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [1,7,2,4,3,5,6] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [1,7,2,4,3,6,5] => [.,[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [1,6,2,5,3,4,7] => [.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [1,7,2,5,3,4,6] => [.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [1,7,2,6,3,4,5] => [.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [1,7,2,6,3,5,4] => [.,[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [1,6,2,5,4,3,7] => [.,[[.,[[[.,.],.],.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [1,7,2,5,4,3,6] => [.,[[.,[[[.,.],.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [1,7,2,6,4,3,5] => [.,[[.,[[[.,.],[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [1,7,2,6,5,3,4] => [.,[[.,[[[.,[.,.]],.],.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [1,7,2,6,5,4,3] => [.,[[.,[[[[.,.],.],.],.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [1,4,3,2,7,5,6] => [.,[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [1,5,3,2,4,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [1,5,3,2,4,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [1,6,3,2,4,5,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [1,7,3,2,4,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [1,7,3,2,4,6,5] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [1,6,3,2,5,4,7] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [1,7,3,2,5,4,6] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [1,7,3,2,6,4,5] => [.,[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [1,7,3,2,6,5,4] => [.,[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [1,5,4,2,3,6,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [1,5,4,2,3,7,6] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [1,6,4,2,3,5,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [1,7,4,2,3,5,6] => [.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [1,7,4,2,3,6,5] => [.,[[[.,[.,.]],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [1,6,5,2,3,4,7] => [.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [1,7,5,2,3,4,6] => [.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [1,7,6,2,3,4,5] => [.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [1,7,6,2,3,5,4] => [.,[[[.,[.,[[.,.],.]]],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [1,6,5,2,4,3,7] => [.,[[[.,[[.,.],.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [1,7,5,2,4,3,6] => [.,[[[.,[[.,.],.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [1,7,6,2,4,3,5] => [.,[[[.,[[.,.],[.,.]]],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [1,7,6,2,5,3,4] => [.,[[[.,[[.,[.,.]],.]],.],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [1,7,6,2,5,4,3] => [.,[[[.,[[[.,.],.],.]],.],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [1,6,4,3,2,5,7] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [1,7,4,3,2,5,6] => [.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [1,7,4,3,2,6,5] => [.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [1,6,5,3,2,4,7] => [.,[[[[.,.],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [1,7,5,3,2,4,6] => [.,[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [1,7,6,3,2,4,5] => [.,[[[[.,.],[.,[.,.]]],.],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [1,7,6,3,2,5,4] => [.,[[[[.,.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [1,6,5,4,2,3,7] => [.,[[[[.,[.,.]],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [1,7,5,4,2,3,6] => [.,[[[[.,[.,.]],.],[.,.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [1,7,6,4,2,3,5] => [.,[[[[.,[.,.]],[.,.]],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [1,7,6,5,2,3,4] => [.,[[[[.,[.,[.,.]]],.],.],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [1,7,6,5,2,4,3] => [.,[[[[.,[[.,.],.]],.],.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,7,5,4,3,2,6] => [.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [1,7,6,4,3,2,5] => [.,[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [1,7,6,5,3,2,4] => [.,[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [1,7,6,5,4,2,3] => [.,[[[[[.,[.,.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [2,1,3,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [2,1,3,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [2,1,3,7,4,6,5] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [2,1,3,7,5,4,6] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [2,1,3,7,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [2,1,5,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [2,1,5,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [2,1,6,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [2,1,7,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [2,1,7,3,4,6,5] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [2,1,6,3,5,4,7] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [2,1,7,3,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [2,1,7,3,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [2,1,7,3,6,5,4] => [[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [2,1,6,4,3,5,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [2,1,7,4,3,5,6] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [2,1,7,4,3,6,5] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [2,1,6,5,3,4,7] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [2,1,7,5,3,4,6] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [2,1,7,6,3,4,5] => [[.,.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [2,1,7,6,3,5,4] => [[.,.],[[[.,[[.,.],.]],.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [2,1,7,5,4,3,6] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [2,1,7,6,4,3,5] => [[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [2,1,7,6,5,3,4] => [[.,.],[[[[.,[.,.]],.],.],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [3,1,2,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [3,1,2,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [3,1,2,4,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [3,1,2,4,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [3,1,2,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [3,1,2,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [3,1,2,6,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [3,1,2,7,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [3,1,2,7,4,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [3,1,2,6,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [3,1,2,7,5,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [3,1,2,7,6,4,5] => [[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [3,1,2,7,6,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [4,1,2,3,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [4,1,2,3,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [4,1,2,3,7,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [4,1,2,3,7,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [5,1,2,3,4,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [7,1,2,3,4,6,5] => [[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [6,1,2,3,5,4,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [7,1,2,3,5,4,6] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [7,1,2,3,6,4,5] => [[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [7,1,2,3,6,5,4] => [[.,[.,[.,[[[.,.],.],.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [5,1,2,4,3,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [5,1,2,4,3,7,6] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [6,1,2,4,3,5,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [7,1,2,4,3,5,6] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [7,1,2,4,3,6,5] => [[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [6,1,2,5,3,4,7] => [[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [7,1,2,5,3,4,6] => [[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [7,1,2,6,3,4,5] => [[.,[.,[[.,[.,[.,.]]],.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [7,1,2,6,3,5,4] => [[.,[.,[[.,[[.,.],.]],.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [6,1,2,5,4,3,7] => [[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [7,1,2,5,4,3,6] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [7,1,2,6,4,3,5] => [[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [7,1,2,6,5,3,4] => [[.,[.,[[[.,[.,.]],.],.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [7,1,2,6,5,4,3] => [[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [4,1,3,2,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [4,1,3,2,5,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [4,1,3,2,6,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [4,1,3,2,7,5,6] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [4,1,3,2,7,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [5,1,3,2,4,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [5,1,3,2,4,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [6,1,3,2,4,5,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [7,1,3,2,4,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [7,1,3,2,4,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [6,1,3,2,5,4,7] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [7,1,3,2,5,4,6] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [7,1,3,2,6,4,5] => [[.,[[.,.],[[.,[.,.]],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [7,1,3,2,6,5,4] => [[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [5,1,4,2,3,6,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [5,1,4,2,3,7,6] => [[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [6,1,4,2,3,5,7] => [[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [7,1,4,2,3,5,6] => [[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [7,1,4,2,3,6,5] => [[.,[[.,[.,.]],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [6,1,5,2,3,4,7] => [[.,[[.,[.,[.,.]]],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [7,1,5,2,3,4,6] => [[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [7,1,6,2,3,4,5] => [[.,[[.,[.,[.,[.,.]]]],.]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [7,1,6,2,3,5,4] => [[.,[[.,[.,[[.,.],.]]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [6,1,5,2,4,3,7] => [[.,[[.,[[.,.],.]],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [7,1,5,2,4,3,6] => [[.,[[.,[[.,.],.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [7,1,6,2,4,3,5] => [[.,[[.,[[.,.],[.,.]]],.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [7,1,6,2,5,3,4] => [[.,[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [7,1,6,2,5,4,3] => [[.,[[.,[[[.,.],.],.]],.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [5,1,4,3,2,6,7] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [5,1,4,3,2,7,6] => [[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [6,1,4,3,2,5,7] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [7,1,4,3,2,5,6] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [7,1,4,3,2,6,5] => [[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [6,1,5,3,2,4,7] => [[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [7,1,5,3,2,4,6] => [[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [7,1,6,3,2,4,5] => [[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [7,1,6,3,2,5,4] => [[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [6,1,5,4,2,3,7] => [[.,[[[.,[.,.]],.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [7,1,5,4,2,3,6] => [[.,[[[.,[.,.]],.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [7,1,6,4,2,3,5] => [[.,[[[.,[.,.]],[.,.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [7,1,6,5,2,3,4] => [[.,[[[.,[.,[.,.]]],.],.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [7,1,6,5,2,4,3] => [[.,[[[.,[[.,.],.]],.],.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [6,1,5,4,3,2,7] => [[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [7,1,5,4,3,2,6] => [[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [7,1,6,4,3,2,5] => [[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [7,1,6,5,3,2,4] => [[.,[[[[.,.],[.,.]],.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [7,1,6,5,4,2,3] => [[.,[[[[.,[.,.]],.],.],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [7,1,6,5,4,3,2] => [[.,[[[[[.,.],.],.],.],.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [3,2,1,4,7,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [3,2,1,6,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [3,2,1,7,4,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [3,2,1,7,4,6,5] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [3,2,1,7,5,4,6] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [3,2,1,7,6,4,5] => [[[.,.],.],[[[.,[.,.]],.],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [4,2,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [4,2,1,3,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [4,2,1,3,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [4,2,1,3,7,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [4,2,1,3,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [5,2,1,3,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [5,2,1,3,4,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [6,2,1,3,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [7,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [7,2,1,3,4,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [6,2,1,3,5,4,7] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [7,2,1,3,5,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [7,2,1,3,6,4,5] => [[[.,.],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [7,2,1,3,6,5,4] => [[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [5,2,1,4,3,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [5,2,1,4,3,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [6,2,1,4,3,5,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [7,2,1,4,3,5,6] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [7,2,1,4,3,6,5] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [6,2,1,5,3,4,7] => [[[.,.],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [7,2,1,5,3,4,6] => [[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [7,2,1,6,3,4,5] => [[[.,.],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [7,2,1,6,3,5,4] => [[[.,.],[[.,[[.,.],.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [6,2,1,5,4,3,7] => [[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [7,2,1,5,4,3,6] => [[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [7,2,1,6,4,3,5] => [[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [7,2,1,6,5,3,4] => [[[.,.],[[[.,[.,.]],.],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [7,2,1,6,5,4,3] => [[[.,.],[[[[.,.],.],.],.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [4,3,1,2,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [4,3,1,2,5,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [4,3,1,2,6,5,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [4,3,1,2,7,5,6] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [4,3,1,2,7,6,5] => [[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [5,3,1,2,4,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [5,3,1,2,4,7,6] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [6,3,1,2,4,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [7,3,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [7,3,1,2,4,6,5] => [[[.,[.,.]],[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [6,3,1,2,5,4,7] => [[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [7,3,1,2,5,4,6] => [[[.,[.,.]],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [7,3,1,2,6,4,5] => [[[.,[.,.]],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [7,3,1,2,6,5,4] => [[[.,[.,.]],[[[.,.],.],.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [5,4,1,2,3,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [5,4,1,2,3,7,6] => [[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [6,4,1,2,3,5,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [7,4,1,2,3,5,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [7,4,1,2,3,6,5] => [[[.,[.,[.,.]]],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [6,5,1,2,3,4,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [7,5,1,2,3,4,6] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [7,6,1,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [7,6,1,2,3,5,4] => [[[.,[.,[.,[[.,.],.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [6,5,1,2,4,3,7] => [[[.,[.,[[.,.],.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [7,5,1,2,4,3,6] => [[[.,[.,[[.,.],.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [7,6,1,2,4,3,5] => [[[.,[.,[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [7,6,1,2,5,3,4] => [[[.,[.,[[.,[.,.]],.]]],.],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [7,6,1,2,5,4,3] => [[[.,[.,[[[.,.],.],.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [5,4,1,3,2,6,7] => [[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [5,4,1,3,2,7,6] => [[[.,[[.,.],.]],.],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [6,4,1,3,2,5,7] => [[[.,[[.,.],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [7,4,1,3,2,5,6] => [[[.,[[.,.],.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [7,4,1,3,2,6,5] => [[[.,[[.,.],.]],[[.,.],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [6,5,1,3,2,4,7] => [[[.,[[.,.],[.,.]]],.],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [7,5,1,3,2,4,6] => [[[.,[[.,.],[.,.]]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [7,6,1,3,2,4,5] => [[[.,[[.,.],[.,[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [7,6,1,3,2,5,4] => [[[.,[[.,.],[[.,.],.]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [6,5,1,4,2,3,7] => [[[.,[[.,[.,.]],.]],.],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [7,5,1,4,2,3,6] => [[[.,[[.,[.,.]],.]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [7,6,1,4,2,3,5] => [[[.,[[.,[.,.]],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [7,6,1,5,2,3,4] => [[[.,[[.,[.,[.,.]]],.]],.],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [7,6,1,5,2,4,3] => [[[.,[[.,[[.,.],.]],.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [6,5,1,4,3,2,7] => [[[.,[[[.,.],.],.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [7,5,1,4,3,2,6] => [[[.,[[[.,.],.],.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [7,6,1,4,3,2,5] => [[[.,[[[.,.],.],[.,.]]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [7,6,1,5,3,2,4] => [[[.,[[[.,.],[.,.]],.]],.],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [7,6,1,5,4,2,3] => [[[.,[[[.,[.,.]],.],.]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [7,6,1,5,4,3,2] => [[[.,[[[[.,.],.],.],.]],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [4,3,2,1,7,5,6] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [5,3,2,1,4,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [5,3,2,1,4,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [6,3,2,1,4,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [7,3,2,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [7,3,2,1,4,6,5] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [6,3,2,1,5,4,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [7,3,2,1,5,4,6] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [7,3,2,1,6,4,5] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [7,3,2,1,6,5,4] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [5,4,2,1,3,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [5,4,2,1,3,7,6] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [6,4,2,1,3,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [7,4,2,1,3,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [7,4,2,1,3,6,5] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [6,5,2,1,3,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [7,5,2,1,3,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [7,6,2,1,3,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [7,6,2,1,3,5,4] => [[[[.,.],[.,[[.,.],.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [6,5,2,1,4,3,7] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [7,5,2,1,4,3,6] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [7,6,2,1,4,3,5] => [[[[.,.],[[.,.],[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [7,6,2,1,5,3,4] => [[[[.,.],[[.,[.,.]],.]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [7,6,2,1,5,4,3] => [[[[.,.],[[[.,.],.],.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [5,4,3,1,2,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [5,4,3,1,2,7,6] => [[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [6,4,3,1,2,5,7] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [7,4,3,1,2,5,6] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [7,4,3,1,2,6,5] => [[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [6,5,3,1,2,4,7] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [7,5,3,1,2,4,6] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [7,6,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [7,6,3,1,2,5,4] => [[[[.,[.,.]],[[.,.],.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [6,5,4,1,2,3,7] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [7,5,4,1,2,3,6] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [7,6,4,1,2,3,5] => [[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [7,6,5,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [7,6,5,1,2,4,3] => [[[[.,[.,[[.,.],.]]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [6,5,4,1,3,2,7] => [[[[.,[[.,.],.]],.],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [7,5,4,1,3,2,6] => [[[[.,[[.,.],.]],.],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [7,6,4,1,3,2,5] => [[[[.,[[.,.],.]],[.,.]],.],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [7,6,5,1,3,2,4] => [[[[.,[[.,.],[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [7,6,5,1,4,2,3] => [[[[.,[[.,[.,.]],.]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [7,6,5,1,4,3,2] => [[[[.,[[[.,.],.],.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [7,4,3,2,1,6,5] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [6,5,3,2,1,4,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [7,5,3,2,1,4,6] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [7,6,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [7,6,3,2,1,5,4] => [[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [6,5,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [7,5,4,2,1,3,6] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [7,6,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [7,6,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [7,6,5,2,1,4,3] => [[[[[.,.],[[.,.],.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [6,5,4,3,1,2,7] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [7,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [7,6,4,3,1,2,5] => [[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [7,6,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [7,6,5,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [7,6,5,4,1,3,2] => [[[[[.,[[.,.],.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [7,6,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [7,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [1,2,3,4,7,5,6,8] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [1,2,3,4,8,5,7,6] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [1,2,3,4,8,6,5,7] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [1,2,3,4,8,7,5,6] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [1,2,3,4,8,7,6,5] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => [1,2,3,5,4,8,6,7] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,2,1] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => [1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,3,2,1] => [1,2,3,6,4,5,8,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [1,2,3,7,4,5,6,8] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [1,2,3,8,4,5,7,6] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => [1,2,3,7,4,6,5,8] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [1,2,3,8,4,6,5,7] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [1,2,3,8,4,7,5,6] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [1,2,3,8,4,7,6,5] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,2,1] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => [1,2,3,7,5,4,6,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [1,2,3,8,5,4,6,7] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [1,2,3,8,5,4,7,6] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,2,1] => [1,2,3,7,6,4,5,8] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [1,2,3,8,6,4,5,7] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [1,2,3,8,7,4,5,6] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [1,2,3,8,7,4,6,5] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [1,2,3,7,6,5,4,8] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [1,2,3,8,6,5,4,7] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [1,2,3,8,7,5,4,6] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [1,2,3,8,7,6,4,5] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [1,2,3,8,7,6,5,4] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [1,2,4,3,5,8,6,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,2,1] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,2,1] => [1,2,4,3,7,5,6,8] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [1,2,4,3,8,5,6,7] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => [1,2,4,3,8,5,7,6] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [1,2,4,3,8,7,5,6] => [.,[.,[[.,.],[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [1,2,4,3,8,7,6,5] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [1,2,5,3,4,6,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => [1,2,5,3,4,6,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => [1,2,5,3,4,7,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [1,2,5,3,4,8,6,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [1,2,5,3,4,8,7,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [1,2,6,3,4,5,7,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [1,2,6,3,4,5,8,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [1,2,7,3,4,5,6,8] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [1,2,8,3,4,5,7,6] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,7,2,1] => [1,2,7,3,4,6,5,8] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => [1,2,8,3,4,6,5,7] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [1,2,8,3,4,7,6,5] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => [1,2,6,3,5,4,7,8] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,7,2,1] => [1,2,7,3,5,4,6,8] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,2,1] => [1,2,8,3,5,4,6,7] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [1,2,8,3,5,4,7,6] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,2,1] => [1,2,7,3,6,4,5,8] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => [1,2,8,3,6,4,5,7] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [1,2,8,3,7,4,5,6] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,2,1] => [1,2,8,3,7,4,6,5] => [.,[.,[[.,[[.,[[.,.],.]],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => [1,2,8,3,6,5,4,7] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [1,2,8,3,7,5,4,6] => [.,[.,[[.,[[[.,.],[.,.]],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [1,2,8,3,7,6,4,5] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [1,2,8,3,7,6,5,4] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [1,2,5,4,3,8,6,7] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => [1,2,6,4,3,5,7,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,7,2,1] => [1,2,7,4,3,5,6,8] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [1,2,8,4,3,5,6,7] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,8,2,1] => [1,2,8,4,3,5,7,6] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,2,1] => [1,2,8,4,3,6,5,7] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,8,2,1] => [1,2,8,4,3,7,5,6] => [.,[.,[[[.,.],[[.,[.,.]],.]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,2,1] => [1,2,8,4,3,7,6,5] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [1,2,6,5,3,4,7,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [1,2,7,5,3,4,6,8] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [1,2,8,5,3,4,6,7] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [1,2,7,6,3,4,5,8] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [1,2,8,7,3,4,5,6] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,2,1] => [1,2,8,7,3,4,6,5] => [.,[.,[[[.,[.,[[.,.],.]]],.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,8,2,1] => [1,2,8,7,3,5,4,6] => [.,[.,[[[.,[[.,.],[.,.]]],.],.]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,2,1] => [1,2,8,7,3,6,5,4] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [1,2,6,5,4,3,7,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [1,2,8,5,4,3,6,7] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [1,2,7,6,4,3,5,8] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [1,2,8,6,4,3,5,7] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,2,1] => [1,2,8,7,4,3,6,5] => [.,[.,[[[[.,.],[[.,.],.]],.],.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [1,2,8,7,6,3,4,5] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,2,1] => [1,2,8,7,6,3,5,4] => [.,[.,[[[[.,[[.,.],.]],.],.],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [1,2,7,6,5,4,3,8] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [1,2,8,6,5,4,3,7] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [1,2,8,7,5,4,3,6] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [1,2,8,7,6,4,3,5] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [1,2,8,7,6,5,3,4] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [1,2,8,7,6,5,4,3] => [.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [1,3,2,4,5,8,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,3,1] => [1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,3,1] => [1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [1,3,2,4,8,5,6,7] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [1,3,2,4,8,5,7,6] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => [1,3,2,4,8,6,5,7] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [1,3,2,4,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [1,3,2,5,4,8,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [1,3,2,6,4,5,7,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => [1,3,2,7,4,5,6,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => [1,3,2,8,4,5,6,7] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,3,1] => [1,3,2,8,4,5,7,6] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [1,3,2,7,4,6,5,8] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [1,3,2,8,4,6,5,7] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [1,3,2,8,4,7,5,6] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [1,3,2,7,5,4,6,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,3,1] => [1,3,2,8,5,4,6,7] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [1,3,2,8,5,4,7,6] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,2,3,1] => [1,3,2,7,6,4,5,8] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,3,1] => [1,3,2,8,6,4,5,7] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,2,3,1] => [1,3,2,8,7,4,5,6] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,2,3,1] => [1,3,2,8,7,4,6,5] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [1,3,2,7,6,5,4,8] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,3,1] => [1,3,2,8,6,5,4,7] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,2,3,1] => [1,3,2,8,7,5,4,6] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,3,1] => [1,3,2,8,7,6,4,5] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [1,3,2,8,7,6,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [1,4,2,3,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => [1,4,2,3,5,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [1,4,2,3,5,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [1,4,2,3,5,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [1,4,2,3,5,8,7,6] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [1,4,2,3,6,5,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,4,1] => [1,4,2,3,6,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [1,4,2,3,7,5,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [1,4,2,3,8,5,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [1,4,2,3,8,5,7,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,4,1] => [1,4,2,3,8,6,5,7] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,4,1] => [1,4,2,3,8,7,5,6] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [1,4,2,3,8,7,6,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [1,5,2,3,4,6,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => [1,5,2,3,4,6,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,5,1] => [1,5,2,3,4,7,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [1,5,2,3,4,8,6,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => [1,5,2,3,4,8,7,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [1,6,2,3,4,5,7,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [1,6,2,3,4,5,8,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [1,7,2,3,4,5,6,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [1,8,2,3,4,5,6,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [1,8,2,3,4,5,7,6] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => [1,7,2,3,4,6,5,8] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,8,1] => [1,8,2,3,4,6,5,7] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [1,8,2,3,4,7,5,6] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,8,1] => [1,8,2,3,4,7,6,5] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => [1,7,2,3,5,4,6,8] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [1,8,2,3,5,4,6,7] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [1,7,2,3,6,4,5,8] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,8,1] => [1,8,2,3,6,4,5,7] => [.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [1,8,2,3,6,5,4,7] => [.,[[.,[.,[[[.,.],.],[.,.]]]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [1,8,2,3,7,5,4,6] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,8,1] => [1,8,2,3,7,6,4,5] => [.,[[.,[.,[[[.,[.,.]],.],.]]],.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [1,8,2,3,7,6,5,4] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [1,5,2,4,3,6,7,8] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [1,5,2,4,3,6,8,7] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [1,5,2,4,3,7,6,8] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [1,5,2,4,3,8,6,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [1,5,2,4,3,8,7,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [1,6,2,4,3,5,7,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [1,6,2,4,3,5,8,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,7,1] => [1,7,2,4,3,5,6,8] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [1,8,2,4,3,5,6,7] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [1,7,2,4,3,6,5,8] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [1,8,2,4,3,6,5,7] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [1,8,2,4,3,7,5,6] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,8,1] => [1,8,2,4,3,7,6,5] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [1,6,2,5,3,4,7,8] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => [1,6,2,5,3,4,8,7] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [1,7,2,5,3,4,6,8] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [1,8,2,5,3,4,6,7] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,8,1] => [1,8,2,5,3,4,7,6] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => [1,7,2,6,3,4,5,8] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [1,8,2,6,3,4,5,7] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [1,8,2,7,3,4,5,6] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,8,1] => [1,8,2,7,3,4,6,5] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [1,7,2,6,3,5,4,8] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [1,8,2,6,3,5,4,7] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [1,8,2,7,3,5,4,6] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [1,8,2,7,3,6,4,5] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [1,8,2,7,3,6,5,4] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [1,7,2,5,4,3,6,8] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,2,7,1] => [1,7,2,6,4,3,5,8] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [1,8,2,6,4,3,5,7] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [1,8,2,7,4,3,5,6] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => [1,8,2,7,4,3,6,5] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,6,2,8,1] => [1,8,2,6,5,3,4,7] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [1,8,2,7,5,3,4,6] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => [1,8,2,7,6,3,4,5] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [1,8,2,7,6,3,5,4] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => [1,7,2,6,5,4,3,8] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [1,8,2,7,5,4,3,6] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,2,8,1] => [1,8,2,7,6,4,3,5] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [1,8,2,7,6,5,4,3] => [.,[[.,[[[[[.,.],.],.],.],.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => [1,4,3,2,5,8,6,7] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [1,4,3,2,8,5,6,7] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [1,4,3,2,8,7,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,5,1] => [1,5,3,2,4,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,3,5,1] => [1,5,3,2,4,6,8,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,5,1] => [1,5,3,2,4,7,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,5,1] => [1,5,3,2,4,8,6,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [1,5,3,2,4,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => [1,6,3,2,4,5,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [1,7,3,2,4,5,6,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [1,8,3,2,4,5,6,7] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => [1,8,3,2,4,5,7,6] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => [1,7,3,2,4,6,5,8] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [1,8,3,2,4,7,5,6] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,6,1] => [1,6,3,2,5,4,7,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,7,1] => [1,7,3,2,5,4,6,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => [1,8,3,2,5,4,6,7] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [1,8,3,2,5,4,7,6] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => [1,8,3,2,6,4,5,7] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [1,8,3,2,7,5,4,6] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [1,8,3,2,7,6,4,5] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [1,8,3,2,7,6,5,4] => [.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [1,5,4,2,3,6,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [1,5,4,2,3,6,8,7] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [1,5,4,2,3,7,6,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,4,5,1] => [1,5,4,2,3,8,6,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [1,5,4,2,3,8,7,6] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [1,6,4,2,3,5,7,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,4,6,1] => [1,6,4,2,3,5,8,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [1,7,4,2,3,5,6,8] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [1,8,4,2,3,5,6,7] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [1,8,4,2,3,5,7,6] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,4,8,1] => [1,8,4,2,3,6,5,7] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => [1,8,4,2,3,7,5,6] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,8,1] => [1,8,4,2,3,7,6,5] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [1,6,5,2,3,4,8,7] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => [1,7,5,2,3,4,6,8] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [1,8,5,2,3,4,7,6] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [1,7,6,2,3,4,5,8] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [1,8,6,2,3,4,5,7] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [1,8,7,2,3,4,5,6] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,8,1] => [1,8,7,2,3,4,6,5] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,2,7,8,1] => [1,8,7,2,3,5,4,6] => [.,[[[.,[.,[[.,.],[.,.]]]],.],.]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => [1,8,7,2,3,6,4,5] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [1,8,7,2,3,6,5,4] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [1,7,6,2,4,3,5,8] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,8,1] => [1,8,6,2,4,3,5,7] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [1,8,6,2,5,3,4,7] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,7,8,1] => [1,8,7,2,5,3,4,6] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => [1,8,7,2,6,3,4,5] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,8,1] => [1,8,7,2,6,3,5,4] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [1,8,7,2,5,4,3,6] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [1,8,7,2,6,5,3,4] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [1,8,7,2,6,5,4,3] => [.,[[[.,[[[[.,.],.],.],.]],.],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [1,5,4,3,2,6,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [1,5,4,3,2,7,6,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [1,5,4,3,2,8,7,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,3,4,6,1] => [1,6,4,3,2,5,7,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,7,1] => [1,7,4,3,2,5,6,8] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [1,8,4,3,2,5,6,7] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,8,1] => [1,8,4,3,2,5,7,6] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,8,1] => [1,8,4,3,2,7,5,6] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => [1,8,4,3,2,7,6,5] => [.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,3,5,6,1] => [1,6,5,3,2,4,7,8] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => [1,6,5,3,2,4,8,7] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [1,7,5,3,2,4,6,8] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [1,8,5,3,2,4,6,7] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,8,1] => [1,8,5,3,2,4,7,6] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => [1,7,6,3,2,4,5,8] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [1,8,6,3,2,4,5,7] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => [1,8,7,3,2,4,5,6] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => [1,8,7,3,2,4,6,5] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => [1,7,6,3,2,5,4,8] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => [1,8,6,3,2,5,4,7] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [1,8,7,3,2,5,4,6] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,8,1] => [1,8,7,3,2,6,4,5] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [1,6,5,4,2,3,8,7] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [1,8,5,4,2,3,6,7] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [1,8,5,4,2,3,7,6] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,7,1] => [1,7,6,4,2,3,5,8] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [1,8,6,4,2,3,5,7] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => [1,8,7,4,2,3,5,6] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,7,8,1] => [1,8,7,4,2,3,6,5] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,7,8,1] => [1,8,7,5,2,3,4,6] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [1,8,7,6,2,3,4,5] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [1,7,6,5,2,4,3,8] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [1,8,7,6,2,4,3,5] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [1,8,7,6,2,5,4,3] => [.,[[[[.,[[[.,.],.],.]],.],.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [1,6,5,4,3,2,7,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [1,6,5,4,3,2,8,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [1,7,5,4,3,2,6,8] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [1,8,5,4,3,2,6,7] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [1,8,5,4,3,2,7,6] => [.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [1,8,7,4,3,2,5,6] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,7,8,1] => [1,8,7,4,3,2,6,5] => [.,[[[[[.,.],.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => [1,7,6,5,3,2,4,8] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,8,1] => [1,8,6,5,3,2,4,7] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,8,1] => [1,8,7,5,3,2,4,6] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [1,8,7,6,3,2,4,5] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [1,8,7,6,3,2,5,4] => [.,[[[[[.,.],[[.,.],.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [1,7,6,5,4,2,3,8] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [1,8,6,5,4,2,3,7] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [1,8,7,6,4,2,3,5] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [1,8,7,6,5,2,3,4] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [1,8,7,6,5,2,4,3] => [.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [1,7,6,5,4,3,2,8] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [1,8,6,5,4,3,2,7] => [.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => [1,8,7,5,4,3,2,6] => [.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [1,8,7,6,4,3,2,5] => [.,[[[[[[.,.],.],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [1,8,7,6,5,3,2,4] => [.,[[[[[[.,.],[.,.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [1,8,7,6,5,4,2,3] => [.,[[[[[[.,[.,.]],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [2,1,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [2,1,3,4,7,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [2,1,3,4,8,5,7,6] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => [2,1,3,4,8,6,5,7] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [2,1,3,4,8,7,5,6] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [2,1,3,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [2,1,3,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [2,1,3,6,4,5,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,3,1,2] => [2,1,3,6,4,5,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [2,1,3,8,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,1,2] => [2,1,3,8,4,5,7,6] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [2,1,3,8,4,6,5,7] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [2,1,3,8,4,7,5,6] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,1,2] => [2,1,3,8,4,7,6,5] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [2,1,3,8,5,4,6,7] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [2,1,3,8,5,4,7,6] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,1,2] => [2,1,3,8,6,4,5,7] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [2,1,3,8,7,4,5,6] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [2,1,3,8,7,4,6,5] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,1,2] => [2,1,3,8,6,5,4,7] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,1,2] => [2,1,3,8,7,5,4,6] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [2,1,3,8,7,6,4,5] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [2,1,3,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [2,1,4,3,5,8,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [2,1,4,3,8,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [2,1,4,3,8,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [2,1,4,3,8,6,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [2,1,4,3,8,7,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,1,2] => [2,1,5,3,4,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,1,2] => [2,1,5,3,4,6,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [2,1,6,3,4,5,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [2,1,7,3,4,5,6,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [2,1,8,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [2,1,8,3,4,7,6,5] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [2,1,6,3,5,4,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [2,1,8,3,5,4,7,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => [2,1,7,3,6,4,5,8] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => [2,1,8,3,6,4,5,7] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => [2,1,8,3,7,4,5,6] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [2,1,8,3,7,4,6,5] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,1,2] => [2,1,8,3,7,5,4,6] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => [2,1,8,3,7,6,4,5] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [2,1,8,3,7,6,5,4] => [[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [2,1,5,4,3,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,1,2] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,1,2] => [2,1,6,4,3,5,7,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [2,1,6,4,3,5,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,8,1,2] => [2,1,8,4,3,5,7,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,1,2] => [2,1,8,4,3,6,5,7] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,8,1,2] => [2,1,8,4,3,7,5,6] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,1,2] => [2,1,8,4,3,7,6,5] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [2,1,6,5,3,4,8,7] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => [2,1,8,5,3,4,6,7] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,8,1,2] => [2,1,8,5,3,4,7,6] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [2,1,7,6,3,4,5,8] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [2,1,8,7,3,4,5,6] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [2,1,8,7,3,4,6,5] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,1,2] => [2,1,8,6,3,5,4,7] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,8,1,2] => [2,1,8,7,3,5,4,6] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [2,1,8,7,3,6,4,5] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => [2,1,8,7,3,6,5,4] => [[.,.],[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [2,1,8,5,4,3,6,7] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,8,1,2] => [2,1,8,5,4,3,7,6] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [2,1,8,6,4,3,5,7] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,1,2] => [2,1,8,7,4,3,5,6] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [2,1,8,7,4,3,6,5] => [[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [2,1,7,6,5,3,4,8] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [2,1,8,7,5,3,4,6] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [2,1,8,7,6,3,4,5] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [2,1,8,7,6,3,5,4] => [[.,.],[[[[.,[[.,.],.]],.],.],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [2,1,7,6,5,4,3,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [2,1,8,6,5,4,3,7] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [2,1,8,7,5,4,3,6] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [2,1,8,7,6,4,3,5] => [[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [2,1,8,7,6,5,3,4] => [[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [3,1,2,4,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [3,1,2,4,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [3,1,2,4,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [3,1,2,4,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,1,3] => [3,1,2,4,7,5,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [3,1,2,4,8,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [3,1,2,4,8,5,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => [3,1,2,4,8,6,5,7] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => [3,1,2,4,8,7,5,6] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [3,1,2,4,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,2,1,3] => [3,1,2,5,4,6,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,1,3] => [3,1,2,5,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,2,1,3] => [3,1,2,6,4,5,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,1,3] => [3,1,2,7,4,5,6,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [3,1,2,8,4,5,6,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => [3,1,2,8,4,5,7,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [3,1,2,8,4,7,5,6] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,1,3] => [3,1,2,7,5,4,6,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,1,3] => [3,1,2,8,5,4,7,6] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,2,1,3] => [3,1,2,7,6,4,5,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,1,3] => [3,1,2,8,6,4,5,7] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,2,1,3] => [3,1,2,8,7,4,5,6] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,2,1,3] => [3,1,2,8,7,4,6,5] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => [3,1,2,8,6,5,4,7] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,2,1,3] => [3,1,2,8,7,5,4,6] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [3,1,2,8,7,6,4,5] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [3,1,2,8,7,6,5,4] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [4,1,2,3,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [4,1,2,3,5,6,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [4,1,2,3,5,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [4,1,2,3,5,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [4,1,2,3,5,8,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [4,1,2,3,6,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [4,1,2,3,6,5,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [4,1,2,3,7,5,6,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [4,1,2,3,8,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [4,1,2,3,8,5,7,6] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [4,1,2,3,7,6,5,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => [4,1,2,3,8,6,5,7] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [4,1,2,3,8,7,5,6] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [4,1,2,3,8,7,6,5] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [5,1,2,3,4,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [5,1,2,3,4,6,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [5,1,2,3,4,8,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [5,1,2,3,4,8,7,6] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [6,1,2,3,4,5,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [6,1,2,3,4,5,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [8,1,2,3,4,5,7,6] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [7,1,2,3,4,6,5,8] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [8,1,2,3,4,6,5,7] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [8,1,2,3,4,7,5,6] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [8,1,2,3,4,7,6,5] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [6,1,2,3,5,4,7,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => [7,1,2,3,5,4,6,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [8,1,2,3,5,4,6,7] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [8,1,2,3,5,4,7,6] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,1,7] => [7,1,2,3,6,4,5,8] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [8,1,2,3,6,4,5,7] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [8,1,2,3,7,4,5,6] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [7,1,2,3,6,5,4,8] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [8,1,2,3,6,5,4,7] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,1,8] => [8,1,2,3,7,5,4,6] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [8,1,2,3,7,6,5,4] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [5,1,2,4,3,6,7,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => [5,1,2,4,3,6,8,7] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [6,1,2,4,3,5,7,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,1,6] => [6,1,2,4,3,5,8,7] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [7,1,2,4,3,5,6,8] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [8,1,2,4,3,5,6,7] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => [8,1,2,4,3,5,7,6] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [8,1,2,4,3,6,5,7] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [8,1,2,4,3,7,6,5] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,1,6] => [6,1,2,5,3,4,7,8] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,1,7] => [7,1,2,5,3,4,6,8] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [8,1,2,5,3,4,6,7] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [8,1,2,5,3,4,7,6] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,1,7] => [7,1,2,6,3,4,5,8] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [8,1,2,6,3,4,5,7] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [8,1,2,7,3,4,5,6] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [8,1,2,7,3,4,6,5] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [7,1,2,6,3,5,4,8] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,1,8] => [8,1,2,7,3,5,4,6] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [8,1,2,7,3,6,4,5] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,1,8] => [8,1,2,7,3,6,5,4] => [[.,[.,[[.,[[[.,.],.],.]],.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => [6,1,2,5,4,3,8,7] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [8,1,2,5,4,3,6,7] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,2,1,7] => [7,1,2,6,4,3,5,8] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,1,8] => [8,1,2,7,4,3,6,5] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [7,1,2,6,5,3,4,8] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,6,2,1,8] => [8,1,2,6,5,3,4,7] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,1,8] => [8,1,2,7,5,3,4,6] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [8,1,2,7,6,3,4,5] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,1,8] => [8,1,2,7,6,3,5,4] => [[.,[.,[[[.,[[.,.],.]],.],.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [7,1,2,6,5,4,3,8] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => [8,1,2,6,5,4,3,7] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,1,8] => [8,1,2,7,5,4,3,6] => [[.,[.,[[[[.,.],.],[.,.]],.]]],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [8,1,2,7,6,5,4,3] => [[.,[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [4,1,3,2,5,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [4,1,3,2,5,7,6,8] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [4,1,3,2,6,5,8,7] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [4,1,3,2,8,5,6,7] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [4,1,3,2,8,5,7,6] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [4,1,3,2,8,6,5,7] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [4,1,3,2,8,7,6,5] => [[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,3,1,5] => [5,1,3,2,4,6,8,7] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,1,5] => [5,1,3,2,4,7,6,8] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => [5,1,3,2,4,8,6,7] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [7,1,3,2,4,5,6,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [8,1,3,2,4,5,6,7] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [8,1,3,2,4,5,7,6] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [8,1,3,2,4,6,5,7] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [8,1,3,2,4,7,6,5] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [6,1,3,2,5,4,8,7] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,1,7] => [7,1,3,2,5,4,6,8] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [8,1,3,2,5,4,6,7] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [8,1,3,2,5,4,7,6] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [8,1,3,2,7,4,6,5] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [8,1,3,2,6,5,4,7] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,1,8] => [8,1,3,2,7,5,4,6] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => [8,1,3,2,7,6,4,5] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [8,1,3,2,7,6,5,4] => [[.,[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [5,1,4,2,3,6,7,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,4,1,5] => [5,1,4,2,3,8,6,7] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [5,1,4,2,3,8,7,6] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [6,1,4,2,3,5,7,8] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,4,1,6] => [6,1,4,2,3,5,8,7] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [7,1,4,2,3,5,6,8] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [8,1,4,2,3,5,6,7] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,1,8] => [8,1,4,2,3,5,7,6] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,4,1,8] => [8,1,4,2,3,6,5,7] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [8,1,4,2,3,7,5,6] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [8,1,4,2,3,7,6,5] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [6,1,5,2,3,4,7,8] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [6,1,5,2,3,4,8,7] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [8,1,5,2,3,4,6,7] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [7,1,6,2,3,4,5,8] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [8,1,6,2,3,4,5,7] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [8,1,7,2,3,4,5,6] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [8,1,6,2,3,5,4,7] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => [8,1,7,2,3,6,4,5] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,1,8] => [8,1,7,2,3,6,5,4] => [[.,[[.,[.,[[[.,.],.],.]]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [6,1,5,2,4,3,8,7] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,5,1,7] => [7,1,5,2,4,3,6,8] => [[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [8,1,5,2,4,3,7,6] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [8,1,6,2,4,3,5,7] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,1,8] => [8,1,7,2,4,3,5,6] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [8,1,7,2,4,3,6,5] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [7,1,6,2,5,3,4,8] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [8,1,6,2,5,3,4,7] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,7,1,8] => [8,1,7,2,5,3,4,6] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [8,1,7,2,6,3,4,5] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [8,1,7,2,6,3,5,4] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,1,7] => [7,1,6,2,5,4,3,8] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [8,1,7,2,5,4,3,6] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [8,1,7,2,6,4,3,5] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [8,1,7,2,6,5,4,3] => [[.,[[.,[[[[.,.],.],.],.]],.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [5,1,4,3,2,6,7,8] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,1,5] => [5,1,4,3,2,6,8,7] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [5,1,4,3,2,8,7,6] => [[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [7,1,4,3,2,5,6,8] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [8,1,4,3,2,5,6,7] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [8,1,4,3,2,5,7,6] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [8,1,4,3,2,6,5,7] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [8,1,4,3,2,7,5,6] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [8,1,4,3,2,7,6,5] => [[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => [7,1,5,3,2,4,6,8] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [8,1,5,3,2,4,6,7] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [8,1,5,3,2,4,7,6] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,1,8] => [8,1,7,3,2,4,5,6] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [7,1,6,3,2,5,4,8] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [8,1,6,3,2,5,4,7] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,1,8] => [8,1,7,3,2,5,4,6] => [[.,[[[.,.],[[.,.],[.,.]]],.]],.]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,1,8] => [8,1,7,3,2,6,5,4] => [[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,1,6] => [6,1,5,4,2,3,8,7] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [7,1,5,4,2,3,6,8] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [8,1,5,4,2,3,6,7] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [7,1,6,4,2,3,5,8] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [8,1,6,4,2,3,5,7] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [8,1,7,4,2,3,5,6] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,7,1,8] => [8,1,7,4,2,3,6,5] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,1,8] => [8,1,6,5,2,3,4,7] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,7,1,8] => [8,1,7,5,2,3,4,6] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [8,1,7,6,2,3,4,5] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => [7,1,6,5,2,4,3,8] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,5,7,1,8] => [8,1,7,5,2,4,3,6] => [[.,[[[.,[[.,.],.]],[.,.]],.]],.]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,1,8] => [8,1,7,6,2,4,3,5] => [[.,[[[.,[[.,.],[.,.]]],.],.]],.]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => [8,1,7,6,2,5,4,3] => [[.,[[[.,[[[.,.],.],.]],.],.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [6,1,5,4,3,2,8,7] => [[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [8,1,5,4,3,2,6,7] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [8,1,5,4,3,2,7,6] => [[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,7,1,8] => [8,1,7,4,3,2,6,5] => [[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,1,7] => [7,1,6,5,3,2,4,8] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [8,1,7,5,3,2,4,6] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => [8,1,7,6,3,2,4,5] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [7,1,6,5,4,2,3,8] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => [8,1,7,5,4,2,3,6] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,1,8] => [8,1,7,6,4,2,3,5] => [[.,[[[[.,[.,.]],[.,.]],.],.]],.]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [8,1,7,6,5,2,3,4] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [8,1,7,6,5,2,4,3] => [[.,[[[[.,[[.,.],.]],.],.],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [7,1,6,5,4,3,2,8] => [[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [8,1,6,5,4,3,2,7] => [[.,[[[[[.,.],.],.],.],[.,.]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => [8,1,7,5,4,3,2,6] => [[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [8,1,7,6,4,3,2,5] => [[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [8,1,7,6,5,3,2,4] => [[.,[[[[[.,.],[.,.]],.],.],.]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [8,1,7,6,5,4,2,3] => [[.,[[[[[.,[.,.]],.],.],.],.]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [8,1,7,6,5,4,3,2] => [[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,1,2,3] => [3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => [3,2,1,4,8,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [3,2,1,4,8,5,7,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [3,2,1,4,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [3,2,1,5,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [3,2,1,6,4,5,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => [3,2,1,7,4,5,6,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [3,2,1,8,4,5,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => [3,2,1,8,4,5,7,6] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,1,2,3] => [3,2,1,7,4,6,5,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,1,2,3] => [3,2,1,8,4,6,5,7] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [3,2,1,8,4,7,5,6] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => [3,2,1,8,4,7,6,5] => [[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [3,2,1,6,5,4,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,1,2,3] => [3,2,1,7,5,4,6,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,1,2,3] => [3,2,1,8,5,4,6,7] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [3,2,1,8,5,4,7,6] => [[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => [3,2,1,7,6,4,5,8] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [3,2,1,8,6,4,5,7] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [3,2,1,8,7,4,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => [3,2,1,8,7,4,6,5] => [[[.,.],.],[[[.,[[.,.],.]],.],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [3,2,1,7,6,5,4,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,1,2,3] => [3,2,1,8,6,5,4,7] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,1,2,3] => [3,2,1,8,7,5,4,6] => [[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [3,2,1,8,7,6,4,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [3,2,1,8,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [4,2,1,3,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => [4,2,1,3,5,8,6,7] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,1,2,4] => [4,2,1,3,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [4,2,1,3,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [4,2,1,3,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [4,2,1,3,8,5,6,7] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [4,2,1,3,8,5,7,6] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [4,2,1,3,8,6,5,7] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => [4,2,1,3,8,7,5,6] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [4,2,1,3,8,7,6,5] => [[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [5,2,1,3,4,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [5,2,1,3,4,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [7,2,1,3,4,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [8,2,1,3,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [8,2,1,3,4,5,7,6] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [8,2,1,3,4,6,5,7] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,1,2,8] => [8,2,1,3,4,7,5,6] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [7,2,1,3,5,4,6,8] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,1,2,8] => [8,2,1,3,6,4,5,7] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,1,2,8] => [8,2,1,3,7,4,6,5] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => [8,2,1,3,6,5,4,7] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => [8,2,1,3,7,6,4,5] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [8,2,1,3,7,6,5,4] => [[[.,.],[.,[[[[.,.],.],.],.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [5,2,1,4,3,6,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,1,2,5] => [5,2,1,4,3,8,6,7] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [5,2,1,4,3,8,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [6,2,1,4,3,5,7,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,1,2,6] => [6,2,1,4,3,5,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [7,2,1,4,3,5,6,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,1,2,8] => [8,2,1,4,3,5,7,6] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [7,2,1,4,3,6,5,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,1,2,8] => [8,2,1,4,3,6,5,7] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [8,2,1,4,3,7,5,6] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,1,2,8] => [8,2,1,4,3,7,6,5] => [[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,1,2,6] => [6,2,1,5,3,4,8,7] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,1,2,8] => [8,2,1,6,3,4,5,7] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [8,2,1,7,3,4,5,6] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => [7,2,1,6,3,5,4,8] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => [8,2,1,7,3,5,4,6] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [6,2,1,5,4,3,7,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [6,2,1,5,4,3,8,7] => [[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [7,2,1,5,4,3,6,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [8,2,1,5,4,3,7,6] => [[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,1,2,8] => [8,2,1,6,4,3,5,7] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,1,2,8] => [8,2,1,7,4,3,5,6] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [8,2,1,7,4,3,6,5] => [[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,6,1,2,8] => [8,2,1,6,5,3,4,7] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,1,2,8] => [8,2,1,7,5,3,4,6] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,1,2,8] => [8,2,1,7,6,3,4,5] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,1,2,8] => [8,2,1,7,6,3,5,4] => [[[.,.],[[[.,[[.,.],.]],.],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [7,2,1,6,5,4,3,8] => [[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [8,2,1,7,5,4,3,6] => [[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,1,2,8] => [8,2,1,7,6,4,3,5] => [[[.,.],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => [8,2,1,7,6,5,3,4] => [[[.,.],[[[[.,[.,.]],.],.],.]],.]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [8,2,1,7,6,5,4,3] => [[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [4,3,1,2,5,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,1,3,4] => [4,3,1,2,5,7,6,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [4,3,1,2,6,5,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [4,3,1,2,6,5,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [4,3,1,2,8,5,6,7] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [4,3,1,2,8,5,7,6] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [4,3,1,2,8,6,5,7] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [4,3,1,2,8,7,5,6] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [4,3,1,2,8,7,6,5] => [[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [5,3,1,2,4,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => [5,3,1,2,4,6,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [5,3,1,2,4,7,6,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,1,3,5] => [5,3,1,2,4,8,6,7] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [5,3,1,2,4,8,7,6] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,1,3,6] => [6,3,1,2,4,5,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [6,3,1,2,4,5,8,7] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [7,3,1,2,4,5,6,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [8,3,1,2,4,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,1,3,8] => [8,3,1,2,4,5,7,6] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [7,3,1,2,4,6,5,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,1,3,8] => [8,3,1,2,4,6,5,7] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [8,3,1,2,4,7,5,6] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,1,3,8] => [8,3,1,2,4,7,6,5] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,1,3,6] => [6,3,1,2,5,4,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,1,3,7] => [7,3,1,2,5,4,6,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [8,3,1,2,5,4,6,7] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,1,3,8] => [8,3,1,2,5,4,7,6] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,2,1,3,7] => [7,3,1,2,6,4,5,8] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [8,3,1,2,6,4,5,7] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,1,3,8] => [8,3,1,2,7,4,5,6] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [8,3,1,2,6,5,4,7] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => [8,3,1,2,7,6,4,5] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [8,3,1,2,7,6,5,4] => [[[.,[.,.]],[[[[.,.],.],.],.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [5,4,1,2,3,6,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [5,4,1,2,3,8,6,7] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [5,4,1,2,3,8,7,6] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [6,4,1,2,3,5,7,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [7,4,1,2,3,5,6,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [8,4,1,2,3,5,6,7] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,1,4,8] => [8,4,1,2,3,7,5,6] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [6,5,1,2,3,4,8,7] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [7,5,1,2,3,4,6,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [8,5,1,2,3,4,6,7] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [7,6,1,2,3,4,5,8] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [8,6,1,2,3,4,5,7] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [8,7,1,2,3,4,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [8,7,1,2,3,4,6,5] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [7,6,1,2,3,5,4,8] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [8,6,1,2,3,5,4,7] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => [8,7,1,2,3,6,4,5] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [8,7,1,2,3,6,5,4] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [6,5,1,2,4,3,8,7] => [[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [8,5,1,2,4,3,6,7] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => [8,5,1,2,4,3,7,6] => [[[.,[.,[[.,.],.]]],[[.,.],.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,1,6,8] => [8,6,1,2,4,3,5,7] => [[[.,[.,[[.,.],[.,.]]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [8,7,1,2,4,3,5,6] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => [8,7,1,2,4,3,6,5] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [8,6,1,2,5,3,4,7] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,1,7,8] => [8,7,1,2,5,3,4,6] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => [8,7,1,2,6,3,4,5] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [7,6,1,2,5,4,3,8] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [8,6,1,2,5,4,3,7] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,1,7,8] => [8,7,1,2,5,4,3,6] => [[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,1,7,8] => [8,7,1,2,6,5,3,4] => [[[.,[.,[[[.,[.,.]],.],.]]],.],.]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [8,7,1,2,6,5,4,3] => [[[.,[.,[[[[.,.],.],.],.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [5,4,1,3,2,8,6,7] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [5,4,1,3,2,8,7,6] => [[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [7,4,1,3,2,5,6,8] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [8,4,1,3,2,5,6,7] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => [8,4,1,3,2,5,7,6] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [7,4,1,3,2,6,5,8] => [[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [8,4,1,3,2,6,5,7] => [[[.,[[.,.],.]],[[.,.],[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [8,4,1,3,2,7,6,5] => [[[.,[[.,.],.]],[[[.,.],.],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [7,5,1,3,2,4,6,8] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [8,5,1,3,2,4,6,7] => [[[.,[[.,.],[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,1,5,8] => [8,5,1,3,2,4,7,6] => [[[.,[[.,.],[.,.]]],[[.,.],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [8,6,1,3,2,4,5,7] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,1,7,8] => [8,7,1,3,2,4,5,6] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,1,7,8] => [8,7,1,3,2,4,6,5] => [[[.,[[.,.],[.,[[.,.],.]]]],.],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,1,7,8] => [8,7,1,3,2,5,4,6] => [[[.,[[.,.],[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [8,7,1,3,2,6,4,5] => [[[.,[[.,.],[[.,[.,.]],.]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [6,5,1,4,2,3,8,7] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [7,5,1,4,2,3,6,8] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [8,5,1,4,2,3,6,7] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => [8,5,1,4,2,3,7,6] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,1,6,7] => [7,6,1,4,2,3,5,8] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [8,6,1,4,2,3,5,7] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,1,7,8] => [8,7,1,4,2,3,5,6] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,1,6,8] => [8,6,1,5,2,3,4,7] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [8,7,1,5,2,3,4,6] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [8,7,1,6,2,3,4,5] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [8,7,1,6,2,3,5,4] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,1,6,7] => [7,6,1,5,2,4,3,8] => [[[.,[[.,[[.,.],.]],.]],.],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,3,4,2,5,1,6,8] => [8,6,1,5,2,4,3,7] => [[[.,[[.,[[.,.],.]],.]],[.,.]],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [8,7,1,6,2,5,3,4] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [8,7,1,6,2,5,4,3] => [[[.,[[.,[[[.,.],.],.]],.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [6,5,1,4,3,2,7,8] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [6,5,1,4,3,2,8,7] => [[[.,[[[.,.],.],.]],.],[[.,.],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [7,6,1,4,3,2,5,8] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [8,6,1,4,3,2,5,7] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [8,7,1,4,3,2,6,5] => [[[.,[[[.,.],.],[[.,.],.]]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [8,6,1,5,3,2,4,7] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,1,7,8] => [8,7,1,5,4,2,3,6] => [[[.,[[[.,[.,.]],.],[.,.]]],.],.]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => [8,7,1,6,4,2,3,5] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [8,7,1,6,5,2,3,4] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [8,7,1,6,5,2,4,3] => [[[.,[[[.,[[.,.],.]],.],.]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [8,6,1,5,4,3,2,7] => [[[.,[[[[.,.],.],.],.]],[.,.]],.]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [8,7,1,6,4,3,2,5] => [[[.,[[[[.,.],.],[.,.]],.]],.],.]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [8,7,1,6,5,3,2,4] => [[[.,[[[[.,.],[.,.]],.],.]],.],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [8,7,1,6,5,4,3,2] => [[[.,[[[[[.,.],.],.],.],.]],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [4,3,2,1,5,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [4,3,2,1,5,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [4,3,2,1,5,8,6,7] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [4,3,2,1,5,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [4,3,2,1,6,5,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [4,3,2,1,6,5,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [4,3,2,1,7,5,6,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [4,3,2,1,8,5,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [4,3,2,1,8,5,7,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [4,3,2,1,7,6,5,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [4,3,2,1,8,6,5,7] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [4,3,2,1,8,7,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [5,3,2,1,4,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => [5,3,2,1,4,6,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,1,2,3,5] => [5,3,2,1,4,7,6,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => [5,3,2,1,4,8,6,7] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [5,3,2,1,4,8,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [6,3,2,1,4,5,8,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [7,3,2,1,4,5,6,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,1,2,3,8] => [8,3,2,1,4,5,7,6] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [7,3,2,1,4,6,5,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,1,2,3,8] => [8,3,2,1,4,6,5,7] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,1,2,3,8] => [8,3,2,1,4,7,5,6] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [8,3,2,1,4,7,6,5] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => [6,3,2,1,5,4,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [6,3,2,1,5,4,8,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [7,3,2,1,5,4,6,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,1,2,3,8] => [8,3,2,1,5,4,6,7] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,1,2,3,8] => [8,3,2,1,5,4,7,6] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,1,2,3,7] => [7,3,2,1,6,4,5,8] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,1,2,3,8] => [8,3,2,1,6,4,5,7] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,1,2,3,8] => [8,3,2,1,7,4,5,6] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [8,3,2,1,7,4,6,5] => [[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [8,3,2,1,6,5,4,7] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [8,3,2,1,7,6,4,5] => [[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [8,3,2,1,7,6,5,4] => [[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [5,4,2,1,3,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [6,4,2,1,3,5,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [6,4,2,1,3,5,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,1,2,4,8] => [8,4,2,1,3,5,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,1,2,4,8] => [8,4,2,1,3,5,7,6] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,1,2,4,8] => [8,4,2,1,3,6,5,7] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,1,2,4,8] => [8,4,2,1,3,7,5,6] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [8,4,2,1,3,7,6,5] => [[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [8,5,2,1,3,4,6,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [8,7,2,1,3,4,5,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [8,7,2,1,3,4,6,5] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,1,2,6,8] => [8,6,2,1,3,5,4,7] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => [8,7,2,1,3,5,4,6] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [8,7,2,1,3,6,4,5] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,1,2,7,8] => [8,7,2,1,3,6,5,4] => [[[[.,.],[.,[[[.,.],.],.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [6,5,2,1,4,3,8,7] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,1,2,5,8] => [8,5,2,1,4,3,6,7] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => [8,5,2,1,4,3,7,6] => [[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,1,2,6,8] => [8,6,2,1,4,3,5,7] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,1,2,7,8] => [8,7,2,1,4,3,5,6] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [8,7,2,1,4,3,6,5] => [[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,1,2,6,8] => [8,6,2,1,5,3,4,7] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => [8,7,2,1,5,3,4,6] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [8,7,2,1,6,3,4,5] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,1,2,6,8] => [8,6,2,1,5,4,3,7] => [[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,1,2,7,8] => [8,7,2,1,5,4,3,6] => [[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [8,7,2,1,6,5,4,3] => [[[[.,.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [5,4,3,1,2,6,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [5,4,3,1,2,7,6,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,1,3,4,5] => [5,4,3,1,2,8,6,7] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [5,4,3,1,2,8,7,6] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [6,4,3,1,2,5,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [6,4,3,1,2,5,8,7] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [7,4,3,1,2,5,6,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => [8,4,3,1,2,5,7,6] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [7,4,3,1,2,6,5,8] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [8,4,3,1,2,6,5,7] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [8,4,3,1,2,7,6,5] => [[[[.,[.,.]],.],[[[.,.],.],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [6,5,3,1,2,4,8,7] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [7,5,3,1,2,4,6,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [8,5,3,1,2,4,6,7] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,1,3,5,8] => [8,5,3,1,2,4,7,6] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [8,7,3,1,2,4,6,5] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,1,3,6,7] => [7,6,3,1,2,5,4,8] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => [8,6,3,1,2,5,4,7] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [8,7,3,1,2,6,4,5] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [6,5,4,1,2,3,7,8] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [6,5,4,1,2,3,8,7] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [8,5,4,1,2,3,6,7] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [8,5,4,1,2,3,7,6] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [8,6,4,1,2,3,5,7] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => [8,7,4,1,2,3,5,6] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [8,7,4,1,2,3,6,5] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [7,6,5,1,2,3,4,8] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [8,6,5,1,2,3,4,7] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [8,7,5,1,2,3,4,6] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [8,7,6,1,2,3,4,5] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [8,7,6,1,2,3,5,4] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [7,6,5,1,2,4,3,8] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [7,3,4,2,1,5,6,8] => [8,6,5,1,2,4,3,7] => [[[[.,[.,[[.,.],.]]],.],[.,.]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => [8,7,5,1,2,4,3,6] => [[[[.,[.,[[.,.],.]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [8,7,6,1,2,4,3,5] => [[[[.,[.,[[.,.],[.,.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [8,7,6,1,2,5,3,4] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [8,7,6,1,2,5,4,3] => [[[[.,[.,[[[.,.],.],.]]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [6,5,4,1,3,2,8,7] => [[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,1,4,5,7] => [7,5,4,1,3,2,6,8] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => [8,5,4,1,3,2,6,7] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => [8,5,4,1,3,2,7,6] => [[[[.,[[.,.],.]],.],[[.,.],.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [8,6,4,1,3,2,5,7] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,1,4,7,8] => [8,7,4,1,3,2,6,5] => [[[[.,[[.,.],.]],[[.,.],.]],.],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [7,6,5,1,3,2,4,8] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,1,5,6,8] => [8,6,5,1,3,2,4,7] => [[[[.,[[.,.],[.,.]]],.],[.,.]],.]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [8,7,6,1,3,2,4,5] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [8,7,6,1,3,2,5,4] => [[[[.,[[.,.],[[.,.],.]]],.],.],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,1,5,6,7] => [7,6,5,1,4,2,3,8] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,1,5,7,8] => [8,7,5,1,4,2,3,6] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [8,7,6,1,4,2,3,5] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [8,7,6,1,5,2,3,4] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [8,7,6,1,5,2,4,3] => [[[[.,[[.,[[.,.],.]],.]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [7,6,5,1,4,3,2,8] => [[[[.,[[[.,.],.],.]],.],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => [8,6,5,1,4,3,2,7] => [[[[.,[[[.,.],.],.]],.],[.,.]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,1,5,7,8] => [8,7,5,1,4,3,2,6] => [[[[.,[[[.,.],.],.]],[.,.]],.],.]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [8,7,6,1,4,3,2,5] => [[[[.,[[[.,.],.],[.,.]]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [8,7,6,1,5,3,2,4] => [[[[.,[[[.,.],[.,.]],.]],.],.],.]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [8,7,6,1,5,4,2,3] => [[[[.,[[[.,[.,.]],.],.]],.],.],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [8,7,6,1,5,4,3,2] => [[[[.,[[[[.,.],.],.],.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [5,4,3,2,1,6,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [5,4,3,2,1,7,6,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [5,4,3,2,1,8,6,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [5,4,3,2,1,8,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [6,4,3,2,1,5,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [6,4,3,2,1,5,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [7,4,3,2,1,5,6,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [8,4,3,2,1,5,6,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [8,4,3,2,1,5,7,6] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [7,4,3,2,1,6,5,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [8,4,3,2,1,6,5,7] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [8,4,3,2,1,7,5,6] => [[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [8,4,3,2,1,7,6,5] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [6,5,3,2,1,4,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => [6,5,3,2,1,4,8,7] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [7,5,3,2,1,4,6,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [7,6,4,1,2,3,5,8] => [8,5,3,2,1,4,6,7] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,5,8] => [8,5,3,2,1,4,7,6] => [[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [7,6,3,2,1,4,5,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,5,4,1,2,3,6,8] => [8,6,3,2,1,4,5,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [8,7,3,2,1,4,5,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,6,4,1,2,3,7,8] => [8,7,3,2,1,4,6,5] => [[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => [7,6,3,2,1,5,4,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [8,6,3,2,1,5,4,7] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [6,4,5,1,2,3,7,8] => [8,7,3,2,1,5,4,6] => [[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,6,1,2,3,7,8] => [8,7,3,2,1,6,4,5] => [[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [8,7,3,2,1,6,5,4] => [[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [8,7,3,1,2,4,5,6] => [6,5,4,2,1,3,7,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [6,5,4,2,1,3,8,7] => [[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [7,6,3,1,2,4,5,8] => [8,5,4,2,1,3,6,7] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [8,5,4,2,1,3,7,6] => [[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [7,6,4,2,1,3,5,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [8,6,4,2,1,3,5,7] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [6,5,3,1,2,4,7,8] => [8,7,4,2,1,3,5,6] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,6,3,1,2,4,7,8] => [8,7,4,2,1,3,6,5] => [[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [8,4,3,1,2,5,6,7] => [7,6,5,2,1,3,4,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => [8,6,5,2,1,3,4,7] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [8,7,5,2,1,3,4,6] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [8,7,6,2,1,3,4,5] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [7,6,5,2,1,4,3,8] => [[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [8,6,5,2,1,4,3,7] => [[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => [8,7,6,2,1,4,3,5] => [[[[[.,.],[[.,.],[.,.]]],.],.],.]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [8,7,6,2,1,5,3,4] => [[[[[.,.],[[.,[.,.]],.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [6,5,4,3,1,2,7,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [6,5,4,3,1,2,8,7] => [[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [8,6,2,1,3,4,5,7] => [7,5,4,3,1,2,6,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [7,6,4,3,1,2,5,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,2,1,3,4,6,8] => [8,6,4,3,1,2,5,7] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [8,7,5,3,1,2,4,6] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [8,7,6,3,1,2,4,5] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [7,6,5,4,1,2,3,8] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [8,6,5,4,1,2,3,7] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,4,5,7,8] => [8,7,5,4,1,2,3,6] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [8,7,6,4,1,2,3,5] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [8,7,6,5,1,2,3,4] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [8,7,6,5,1,2,4,3] => [[[[[.,[.,[[.,.],.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [7,6,5,4,1,3,2,8] => [[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [8,6,5,4,1,3,2,7] => [[[[[.,[[.,.],.]],.],.],[.,.]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [8,7,5,4,1,3,2,6] => [[[[[.,[[.,.],.]],.],[.,.]],.],.]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [8,7,6,4,1,3,2,5] => [[[[[.,[[.,.],.]],[.,.]],.],.],.]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [8,7,6,5,1,3,2,4] => [[[[[.,[[.,.],[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [8,7,6,5,1,4,2,3] => [[[[[.,[[.,[.,.]],.]],.],.],.],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [8,7,6,5,1,4,3,2] => [[[[[.,[[[.,.],.],.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [7,5,4,3,2,1,6,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [8,5,4,3,2,1,6,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [8,5,4,3,2,1,7,6] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [7,6,4,3,2,1,5,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [8,6,4,3,2,1,5,7] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,2,3,4,7,8] => [8,7,4,3,2,1,5,6] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,6,1,2,3,4,7,8] => [8,7,4,3,2,1,6,5] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [7,6,5,3,2,1,4,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [8,6,5,3,2,1,4,7] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [8,7,5,3,2,1,4,6] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [8,7,6,3,2,1,4,5] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [8,7,6,3,2,1,5,4] => [[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [7,6,5,4,2,1,3,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [8,6,5,4,2,1,3,7] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [8,7,6,4,2,1,3,5] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [8,7,6,5,2,1,3,4] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [8,7,6,5,2,1,4,3] => [[[[[[.,.],[[.,.],.]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [7,6,5,4,3,1,2,8] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [8,6,5,4,3,1,2,7] => [[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,3,4,5,7,8] => [8,7,5,4,3,1,2,6] => [[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [8,7,6,4,3,1,2,5] => [[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [8,7,6,5,3,1,2,4] => [[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [8,7,6,5,4,1,2,3] => [[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [8,7,6,5,4,1,3,2] => [[[[[[.,[[.,.],.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [8,7,5,4,3,2,1,6] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [8,7,6,4,3,2,1,5] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [8,7,6,5,4,2,1,3] => [[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [8,7,6,5,4,3,1,2] => [[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [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] => [9,1,2,3,4,5,6,7,8] => [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] => [2,3,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [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] => [9,2,1,3,4,5,6,7,8] => [8,7,6,5,4,3,1,2,9] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,2,3] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [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] => [10,2,1,3,4,5,6,7,8,9] => [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] => [9,3,1,2,4,5,6,7,8] => [8,7,6,5,4,2,1,3,9] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => [1,9,8,7,6,5,3,2,4] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => [1,9,8,7,6,5,2,4,3] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,4,2,3] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [1,11,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [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] => [10,3,1,2,4,5,6,7,8,9] => [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] => [9,4,1,2,3,5,6,7,8] => [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] => [9,3,2,1,4,5,6,7,8] => [8,7,6,5,4,1,2,3,9] => [[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [5,2,3,4,6,7,8,9,1] => [1,9,8,7,6,4,3,2,5] => [.,[[[[[[[.,.],.],[.,.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => [1,9,8,7,6,5,2,3,4] => [.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,3,2,4] => [.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,1] => [1,9,8,7,6,2,5,4,3] => [.,[[[[[.,[[[.,.],.],.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,2,4,3] => [.,[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [10,4,1,2,3,5,6,7,8,9] => [9,8,7,6,5,3,2,1,4,10] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [6,2,3,4,5,7,8,9,1] => [1,9,8,7,5,4,3,2,6] => [.,[[[[[[[.,.],.],.],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [5,2,3,4,6,7,8,9,10,1] => [1,10,9,8,7,6,4,3,2,5] => [.,[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,1] => [1,9,8,7,6,3,2,5,4] => [.,[[[[[[.,.],[[.,.],.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,10,1] => [1,10,9,8,7,6,2,5,4,3] => [.,[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,10,11,1] => [1,11,10,9,8,7,6,5,2,4,3] => [.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [9,6,1,2,3,4,5,7,8] => [8,7,5,4,3,2,1,6,9] => [[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,2,3,4,5,6,8,9,1] => [1,9,8,6,5,4,3,2,7] => [.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [6,2,3,4,5,7,8,9,10,1] => [1,10,9,8,7,5,4,3,2,6] => [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,1] => [1,9,8,2,7,6,5,4,3] => [.,[[[.,[[[[[.,.],.],.],.],.]],.],.]]
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,10,11,1] => [1,11,10,9,8,7,6,2,5,4,3] => [.,[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [10,6,1,2,3,4,5,7,8,9] => [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] => [9,7,1,2,3,4,5,6,8] => [8,6,5,4,3,2,1,7,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,9,8] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [1,9,7,6,5,4,3,2,8] => [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [7,2,3,4,5,6,8,9,10,1] => [1,10,9,8,6,5,4,3,2,7] => [.,[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [2,1,9,8,7,6,5,4,3] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,1] => [1,9,2,8,7,6,5,4,3] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,10,1] => [1,10,9,8,2,7,6,5,4,3] => [.,[[[[.,[[[[[.,.],.],.],.],.]],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [10,7,1,2,3,4,5,6,8,9] => [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] => [9,8,1,2,3,4,5,6,7] => [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] => [9,2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2,9] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,1,3,4,5,6,7] => [7,6,5,4,3,1,2,9,8] => [[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,2,3,4,5,6,7,9,10,1] => [1,10,9,7,6,5,4,3,2,8] => [.,[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,1,2] => [2,1,9,8,7,6,5,3,4] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [1,2,9,8,7,6,5,4,3] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,10,1] => [1,10,9,2,8,7,6,5,4,3] => [.,[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]]
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,10,11,1] => [1,11,10,9,8,2,7,6,5,4,3] => [.,[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [10,8,1,2,3,4,5,6,7,9] => [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] => [9,10,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,10,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [1,10,8,7,6,5,4,3,2,9] => [.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [8,9,3,1,2,4,5,6,7] => [7,6,5,4,2,1,3,9,8] => [[[[[[.,.],[.,.]],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,1,4,5,6,7] => [7,6,5,4,1,3,2,9,8] => [[[[[.,[[.,.],.]],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [5,3,4,6,7,8,9,1,2] => [2,1,9,8,7,6,4,3,5] => [[.,.],[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [4,5,3,6,7,8,9,1,2] => [2,1,9,8,7,6,3,5,4] => [[.,.],[[[[[.,[[.,.],.]],.],.],.],.]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [2,1,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,10,11,1] => [1,11,10,9,2,8,7,6,5,4,3] => [.,[[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [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] => [10,2,3,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,3,2,10] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [9,10,2,1,3,4,5,6,7,8] => [8,7,6,5,4,3,1,2,10,9] => [[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,3,5,6,7,8,9,10,1,2] => [2,1,10,9,8,7,6,5,3,4] => [[.,.],[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [1,2,10,9,8,7,6,5,4,3] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[] => [] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [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] => [7,8,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,8,7] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8,6,7,5,4,3,2,1,9] => [9,1,2,3,4,5,7,6,8] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => [9,1,2,3,4,5,8,6,7] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,7,8,5,4,3,2,1,9] => [9,1,2,3,4,5,8,7,6] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8,6,5,7,4,3,2,1,9] => [9,1,2,3,4,7,5,6,8] => [[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7,6,5,8,4,3,2,1,9] => [9,1,2,3,4,8,5,6,7] => [[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [7,5,6,8,4,3,2,1,9] => [9,1,2,3,4,8,6,5,7] => [[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => [9,1,2,3,5,4,6,7,8] => [[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => [9,1,2,3,6,4,5,7,8] => [[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,5,2,1,9] => [9,1,2,5,3,4,6,7,8] => [[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,8,2,1,9] => [9,1,2,8,3,4,5,6,7] => [[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,6,5,3,4,8,2,1,9] => [9,1,2,8,4,3,5,6,7] => [[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,1,9] => [9,1,3,2,4,5,6,7,8] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,1,9] => [9,1,8,2,3,4,5,6,7] => [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9] => [9,1,8,2,7,3,6,4,5] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [9,1,8,7,6,5,4,3,2] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [9,2,1,3,4,5,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => [9,2,1,4,3,6,5,8,7] => [[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => [9,2,1,8,7,6,5,4,3] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,1,3,9] => [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] => [8,7,6,5,3,2,1,4,9] => [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] => [8,7,5,4,3,2,1,6,9] => [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] => [8,6,5,4,3,2,1,7,9] => [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] => [7,6,5,4,3,2,1,8,9] => [9,8,1,2,3,4,5,6,7] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,3,2,1,8,9] => [9,8,1,2,3,7,4,5,6] => [[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.],.]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [9,8,1,7,6,5,4,3,2] => [[[.,[[[[[[.,.],.],.],.],.],.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [8,7,6,3,2,1,4,5,9] => [9,5,4,1,2,3,6,7,8] => [[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0] => [8,6,5,3,2,1,4,7,9] => [9,7,4,1,2,3,5,6,8] => [[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,6,5,3,2,1,4,8,9] => [9,8,4,1,2,3,5,6,7] => [[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [7,5,4,3,2,1,6,8,9] => [9,8,6,1,2,3,4,5,7] => [[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [9,8,7,1,2,3,4,5,6] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [9,4,3,2,1,8,7,6,5] => [[[[[.,.],.],.],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => [9,8,7,2,1,4,3,6,5] => [[[[[.,.],[[.,.],[[.,.],.]]],.],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2,1,3,5,7,9] => [9,7,5,3,1,2,4,6,8] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1,5,7,8,9] => [9,8,7,5,1,2,3,4,6] => [[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [9,8,7,6,1,2,3,4,5] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [8,7,6,1,2,3,4,5,9] => [9,5,4,3,2,1,6,7,8] => [[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [9,8,7,3,2,1,6,5,4] => [[[[[[.,.],.],[[[.,.],.],.]],.],.],.]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1,4,6,7,8,9] => [9,8,7,6,4,1,2,3,5] => [[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [9,8,7,6,5,1,2,3,4] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6,9] => [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] => [7,8,1,2,3,4,5,6,9] => [9,6,5,4,3,2,1,8,7] => [[[[[[[.,.],.],.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [7,6,1,2,3,4,5,8,9] => [9,8,5,4,3,2,1,6,7] => [[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1,2,3,6,7,8,9] => [9,8,7,6,3,2,1,4,5] => [[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => [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] => [3,4,1,2,5,6,7,8,9] => [9,8,7,6,5,2,1,4,3] => [[[[[[[.,.],[[.,.],.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => [9,7,6,5,4,3,1,2,8] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [4,2,1,3,5,6,7,8,9] => [9,8,7,6,5,3,1,2,4] => [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [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] => [2,3,1,4,5,6,7,8,9] => [9,8,7,6,5,4,1,3,2] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [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] => [7,1,2,3,4,5,6,8,9] => [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] => [6,1,2,3,4,5,7,8,9] => [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] => [5,1,2,3,4,6,7,8,9] => [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] => [4,1,2,3,5,6,7,8,9] => [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] => [3,1,2,4,5,6,7,8,9] => [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] => [2,1,3,4,5,6,7,8,9] => [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] => [1,2,3,4,5,6,7,8,9] => [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] => [9,8,7,6,5,4,3,2,1] => [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] => [8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [1,2,3,4,5,6,9,7,8] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => [1,2,3,4,5,9,6,7,8] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => [1,2,3,4,9,5,6,7,8] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => [1,2,3,9,4,5,6,7,8] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => [1,2,9,3,4,5,6,7,8] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,7,8] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [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] => [9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,10,8,9] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => [1,2,3,4,5,9,7,6,8] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [1,2,3,4,5,6,10,7,8,9] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [8,7,5,6,9,4,3,2,1] => [1,2,3,4,9,6,5,7,8] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [1,2,3,4,5,10,6,7,8,9] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,9,3,2,1] => [1,2,3,9,5,4,6,7,8] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [1,2,3,4,10,5,6,7,8,9] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => [1,2,9,4,3,5,6,7,8] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [1,2,3,10,4,5,6,7,8,9] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => [1,9,3,2,4,5,6,7,8] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [1,2,10,3,4,5,6,7,8,9] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [1,10,2,3,4,5,6,7,8,9] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [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] => [11,10,9,8,7,6,5,4,3,2,1] => [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] => [10,11,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,11,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [1,2,3,4,5,9,8,7,6] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,1,2,10] => [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] => [10,9,8,7,6,5,4,3,2,11,1] => [1,11,2,3,4,5,6,7,8,9,10] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [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] => [9,10,11,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,11,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [11,10,12,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,12,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [1,2,3,4,5,6,10,9,8,7] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,2,1,3,10] => [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] => [10,9,8,7,6,5,4,3,1,2,11] => [11,2,1,3,4,5,6,7,8,9,10] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [1,2,3,4,9,8,7,6,5] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,3,2,1,4,10] => [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] => [10,9,8,7,6,5,4,2,1,3,11] => [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] => [6,7,8,9,10,5,4,3,2,1] => [1,2,3,4,5,10,9,8,7,6] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,3,2,1,4,11] => [11,4,1,2,3,5,6,7,8,9,10] => [[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,3,2,1,4,5,10] => [10,5,4,1,2,3,6,7,8,9] => [[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,4,3,2,1,6,10] => [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] => [4,5,6,7,8,9,3,2,1] => [1,2,3,9,8,7,6,5,4] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9,8,6,5,4,3,2,1,7,10] => [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] => [5,6,7,8,9,10,4,3,2,1] => [1,2,3,4,10,9,8,7,6,5] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,5,4,3,2,1,6,11] => [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] => [10,9,8,6,5,4,3,2,1,7,11] => [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] => [9,7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,7,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [9,8,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,9,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,4,3,2,1] => [1,2,3,4,6,5,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,4,3,2,1] => [1,2,3,4,6,5,8,7,9] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,4,3,2,1] => [1,2,3,4,6,5,9,8,7] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,3,2,1] => [1,2,3,5,4,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,3,2,1] => [1,2,3,5,4,7,6,9,8] => [.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,5,3,2,1] => [1,2,3,5,4,9,8,7,6] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,3,2,1] => [1,2,3,6,5,4,9,8,7] => [.,[.,[.,[[[.,.],.],[[[.,.],.],.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,2,1] => [1,2,4,3,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,3,4,2,1] => [1,2,4,3,6,5,9,8,7] => [.,[.,[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,2,1] => [1,2,4,3,9,8,7,6,5] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,2,3,1] => [1,3,2,4,5,6,9,8,7] => [.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,2,3,1] => [1,3,2,5,4,6,7,8,9] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,9,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,5,2,3,1] => [1,3,2,5,4,9,8,7,6] => [.,[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,2,3,1] => [1,3,2,6,5,4,9,8,7] => [.,[[.,.],[[[.,.],.],[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [1,3,2,9,8,7,6,5,4] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,4,1] => [1,4,3,2,5,6,7,8,9] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,4,1] => [1,4,3,2,9,8,7,6,5] => [.,[[[.,.],.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,5,1] => [1,5,4,3,2,9,8,7,6] => [.,[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,6,7,1] => [1,7,6,5,4,3,2,9,8] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => [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] => [8,9,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,1,2] => [2,1,3,4,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => [2,1,4,3,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => [2,1,4,3,6,5,7,8,9] => [[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,3,4,1,2] => [2,1,4,3,6,5,9,8,7] => [[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,1,2] => [2,1,4,3,9,8,7,6,5] => [[.,.],[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,3,4,5,1,2] => [2,1,5,4,3,9,8,7,6] => [[.,.],[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => [2,1,8,7,6,5,4,3,9] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => [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] => [9,8,7,6,4,5,1,2,3] => [3,2,1,5,4,6,7,8,9] => [[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => [3,2,1,5,4,7,6,9,8] => [[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => [3,2,1,6,5,4,7,8,9] => [[[.,.],.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => [3,2,1,6,5,4,9,8,7] => [[[.,.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [3,2,1,9,8,7,6,5,4] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [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] => [9,8,7,5,6,1,2,3,4] => [4,3,2,1,6,5,7,8,9] => [[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => [4,3,2,1,6,5,8,7,9] => [[[[.,.],.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => [4,3,2,1,7,6,5,8,9] => [[[[.,.],.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => [4,3,2,1,7,6,5,9,8] => [[[[.,.],.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5,9] => [[[[.,.],.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [4,3,2,1,9,8,7,6,5] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [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] => [9,8,6,7,1,2,3,4,5] => [5,4,3,2,1,7,6,8,9] => [[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => [5,4,3,2,1,8,7,6,9] => [[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [5,4,3,2,1,9,8,7,6] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [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] => [9,7,8,1,2,3,4,5,6] => [6,5,4,3,2,1,8,7,9] => [[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [6,5,4,3,2,1,9,8,7] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [10,8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8,10] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [10,9,7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,7,9,10] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [9,10,7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,7,10,9] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [10,9,8,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,8,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,4,3,2,1] => [1,2,3,4,6,5,7,8,9,10] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,4,3,2,1] => [1,2,3,4,6,5,8,7,10,9] => [.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,3,2,1] => [1,2,3,5,4,6,7,8,9,10] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [1,2,3,10,9,8,7,6,5,4] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,2,1] => [1,2,4,3,5,6,7,8,9,10] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,2,1] => [1,2,4,3,6,5,8,7,10,9] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,3,4,5,6,2,1] => [1,2,6,5,4,3,10,9,8,7] => [.,[.,[[[[.,.],.],.],[[[[.,.],.],.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [8,9,10,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,10,9,8] => [.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,4,5,6,2,3,1] => [1,3,2,6,5,4,10,9,8,7] => [.,[[.,.],[[[.,.],.],[[[[.,.],.],.],.]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,2,3,1] => [1,3,2,10,9,8,7,6,5,4] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,2,3,4,1] => [1,4,3,2,7,6,5,10,9,8] => [.,[[[.,.],.],[[[.,.],.],[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,2,3,4,1] => [1,4,3,2,10,9,8,7,6,5] => [.,[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,2,3,4,5,1] => [1,5,4,3,2,10,9,8,7,6] => [.,[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => [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] => [9,10,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => [2,1,4,3,5,6,7,8,9,10] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => [2,1,4,3,6,5,7,8,9,10] => [[.,.],[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,9,10] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,5,6,3,4,1,2] => [2,1,4,3,6,5,10,9,8,7] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,3,4,1,2] => [2,1,4,3,7,6,5,10,9,8] => [[.,.],[[.,.],[[[.,.],.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,3,4,5,6,1,2] => [2,1,6,5,4,3,10,9,8,7] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => [3,2,1,5,4,6,7,8,9,10] => [[[.,.],.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => [3,2,1,5,4,7,6,9,8,10] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [3,2,1,6,5,4,8,7,10,9] => [[[.,.],.],[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,4,5,6,1,2,3] => [3,2,1,6,5,4,10,9,8,7] => [[[.,.],.],[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [3,2,1,10,9,8,7,6,5,4] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => [4,3,2,1,5,6,7,8,9,10] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => [4,3,2,1,6,5,8,7,10,9] => [[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => [4,3,2,1,7,6,5,10,9,8] => [[[[.,.],.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5,9,10] => [[[[.,.],.],.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5,10,9] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [4,3,2,1,10,9,8,7,6,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => [5,4,3,2,1,6,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => [5,4,3,2,1,7,6,9,8,10] => [[[[[.,.],.],.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => [5,4,3,2,1,9,8,7,6,10] => [[[[[.,.],.],.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => [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] => [10,7,8,9,1,2,3,4,5,6] => [6,5,4,3,2,1,9,8,7,10] => [[[[[[.,.],.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [6,5,4,3,2,1,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [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] => [10,8,9,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,9,8,10] => [[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,10,9,8] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [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] => [9,8,7,6,5,4,2,1,3] => [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] => [9,8,7,6,5,3,2,1,4] => [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] => [9,8,7,6,4,3,2,1,5] => [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] => [9,8,7,5,4,3,2,1,6] => [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] => [9,8,6,5,4,3,2,1,7] => [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] => [9,7,6,5,4,3,2,1,8] => [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] => [10,9,8,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,1,4] => [4,1,2,3,5,6,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,1,5] => [5,1,2,3,4,6,7,8,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,4,3,2,1,6] => [6,1,2,3,4,5,7,8,9,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,4,3,2,1,7] => [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] => [9,6,7,5,4,3,2,1,8] => [8,1,2,3,4,5,7,6,9] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,2,1,8] => [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] => [10,8,7,6,5,4,3,2,1,9] => [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] => [11,10,9,8,7,6,5,4,3,1,2] => [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] => [8,7,9,6,5,4,3,1,2] => [2,1,3,4,5,6,9,7,8] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,9,8] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,2,1,3] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,10,8,9] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,1,3] => [3,1,2,4,5,6,9,7,8] => [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,3,1] => [1,3,2,4,5,6,9,7,8] => [.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,9,8] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,1,3,4] => [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] => [2,3,4,5,6,7,8,9,1,10] => [10,1,9,8,7,6,5,4,3,2] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [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] => [10,1,2,3,4,5,6,7,8,9,11] => [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] => [9,2,1,3,4,5,6,7,8,10] => [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] => [2,1,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [11,10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,5,1,10] => [10,1,5,2,3,4,6,7,8,9] => [[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,5,2,1,10] => [10,1,2,5,3,4,6,7,8,9] => [[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,5,3,2,1,10] => [10,1,2,3,5,4,6,7,8,9] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,7,8,9,10,1] => [1,10,9,8,7,2,3,4,5,6] => [.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,1,2,8] => [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] => [7,8,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,8,7] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,9,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,9,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,1,2] => [2,1,9,3,4,5,6,7,8] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [7,8,9,5,4,3,2,1,6] => [6,1,2,3,4,5,9,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7,8,9,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,9,8,7] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [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] => [8,1,2,3,4,5,6,7,9,10] => [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] => [7,1,2,3,4,5,6,8,9,10] => [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] => [6,1,2,3,4,5,7,8,9,10] => [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] => [5,1,2,3,4,6,7,8,9,10] => [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] => [4,1,2,3,5,6,7,8,9,10] => [10,9,8,7,6,5,3,2,1,4] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [8,9,6,5,7,4,3,2,1] => [1,2,3,4,7,5,6,9,8] => [.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => [10,1,2,3,4,6,5,7,8,9] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,4,3,2,1,5] => [5,1,2,3,4,7,6,8,9] => [[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,2,1,3] => [3,1,2,5,4,7,6,9,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,2,3,1,4] => [4,1,3,2,6,5,8,7,10,9] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,2,3,1,6] => [6,1,3,2,5,4,8,7,10,9] => [[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [9,10,6,7,4,5,2,3,1,8] => [8,1,3,2,5,4,7,6,10,9] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,2,3,1,10] => [10,1,3,2,5,4,7,6,9,8] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [8,9,6,4,5,7,2,1,3] => [3,1,2,7,5,4,6,9,8] => [[.,[.,.]],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,2,3,5,1] => [1,5,3,2,4,7,6,9,8] => [.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,1,3] => [3,1,2,5,4,7,6,9,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,3,2,1,4] => [4,1,2,3,5,9,6,7,8] => [[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,7,9,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,9,7,8] => [[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,6,9,5,4,3,2,1,10] => [10,1,2,3,4,5,9,6,7,8] => [[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,9,3,2,1,10] => [10,1,2,3,9,4,5,6,7,8] => [[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1,10] => [10,1,2,9,3,4,5,6,7,8] => [[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [10,9,1,2,3,4,5,6,7,8] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,8,10,7,6,5,4,3,2,1,11] => [11,1,2,3,4,5,6,7,10,8,9] => [[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,6,7,9,5,4,3,2,1,10] => [10,1,2,3,4,5,9,7,6,8] => [[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,8,7,10,6,5,4,3,2,1,11] => [11,1,2,3,4,5,6,10,7,8,9] => [[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,10,4,3,2,1,11] => [11,1,2,3,4,10,5,6,7,8,9] => [[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,10,3,2,1,11] => [11,1,2,3,10,4,5,6,7,8,9] => [[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,10,1,11] => [11,1,10,2,3,4,5,6,7,8,9] => [[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,1,10,11] => [11,10,1,2,3,4,5,6,7,8,9] => [[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [10,9,8,7,6,5,2,1,4,3] => [[[[[[[[.,.],[[.,.],.]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [10,9,8,7,3,2,1,6,5,4] => [[[[[[[.,.],.],[[[.,.],.],.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [10,9,4,3,2,1,8,7,6,5] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [10,8,6,4,2,1,3,5,7,9] => [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] => [1,2,3,4,5,6,7,8,9,10,11] => [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] => [3,4,5,6,7,8,9,10,11,1,2] => [2,1,11,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [10,5,4,3,2,1,6,7,8,9] => [9,8,7,6,1,2,3,4,5,10] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => [11,1,10,9,8,7,6,5,4,3,2] => [[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [11,1,2,3,4,5,6,7,8,9,10,12] => [12,10,9,8,7,6,5,4,3,2,1,11] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [9,3,1,2,4,5,6,7,8,10] => [10,8,7,6,5,4,2,1,3,9] => [[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,8,9,10,11] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,8,6,9,5,4,3,2,1] => [1,2,3,4,5,9,6,8,7] => [.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1,11,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [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] => [9,8,7,2,1,3,4,5,6] => [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] => [9,8,7,6,2,1,3,4,5] => [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] => [9,8,7,6,5,3,2,4,1] => [1,4,2,3,5,6,7,8,9] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,1,2] => [2,1,10,3,4,5,6,7,8,9] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,2,1,3] => [3,1,2,9,4,5,6,7,8] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [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] => [11,9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,10,9,11] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [9,8,7,10,5,4,3,2,1,6] => [6,1,2,3,4,5,10,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,9,6,5,4,3,2,7,1] => [1,7,2,3,4,5,6,9,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [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] => [4,3,2,1,5,6,7,8,9,10] => [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] => [11,9,8,7,6,5,4,3,2,1,10] => [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] => [9,7,6,5,4,3,2,8,1] => [1,8,2,3,4,5,6,7,9] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [10,7,6,5,4,3,2,1,9,8] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => [10,2,1,9,8,7,6,5,4,3] => [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [5,3,1,2,4,6,7,8,9,10] => [10,9,8,7,6,4,2,1,3,5] => [[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,2,1,3,4] => [4,3,1,2,5,6,7,8,9,10] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,10,7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7,10,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,7,9,5,4,3,2,1,6] => [6,1,2,3,4,5,9,7,8] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,2,1,3,4,5,6] => [6,5,4,3,1,2,7,8,9,10] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,2,1,3,4,5,6,7] => [7,6,5,4,3,1,2,8,9,10] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [8,7,9,5,6,3,4,1,2] => [2,1,4,3,6,5,9,7,8] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [11,10,1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1,10,11] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [9,8,4,1,2,3,5,6,7] => [7,6,5,3,2,1,4,8,9] => [[[[[[.,.],.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,8,7,6,5,4,3,2,1,9,11] => [11,9,1,2,3,4,5,6,7,8,10] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,7,8,10] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,3,2,1,4] => [4,1,2,3,9,5,6,7,8] => [[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [7,8,2,3,4,5,6,9,1] => [1,9,6,5,4,3,2,8,7] => [.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [9,7,5,6,3,4,1,2,8] => [8,2,1,4,3,6,5,7,9] => [[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => [8,2,1,7,6,5,4,3,9] => [[[.,.],[[[[[.,.],.],.],.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,10,1] => [1,10,2,3,4,5,6,7,9,8] => [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,8,1,2] => [2,1,8,3,4,5,6,7,9] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [9,8,1,2,3,4,5,6,7,10] => [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] => [9,8,10,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,10,8,9] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [8,9,7,10,4,5,2,3,1,6] => [6,1,3,2,5,4,10,7,9,8] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [10,7,8,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,8,7,10] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [8,6,4,2,1,3,5,7,9,10] => [10,9,7,5,3,1,2,4,6,8] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,3,1,2,4,6,8,10] => [10,8,6,4,2,1,3,5,7,9] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => [10,9,2,1,4,3,6,5,8,7] => [[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.],.]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [1,2,11,10,9,8,7,6,5,4,3] => [.,[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => [12,11,10,9,8,7,6,5,4,2,1,3] => [[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,2,4,1] => [1,4,2,3,6,5,8,7,10,9] => [.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [8,7,6,9,4,3,2,1,5] => [5,1,2,3,4,9,6,7,8] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,7,8,5,4,3,2,9,1] => [1,9,2,3,4,5,8,7,6] => [.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9,10,8,7,6,5,4,3,2,11,1] => [1,11,2,3,4,5,6,7,8,10,9] => [.,[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,3,6,1,2] => [2,1,6,3,5,4,8,7,10,9] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [9,10,6,7,5,8,3,4,1,2] => [2,1,4,3,8,5,7,6,10,9] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [8,9,7,10,5,6,3,4,1,2] => [2,1,4,3,6,5,10,7,9,8] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,5,10,3,4,1,2] => [2,1,4,3,10,5,7,6,9,8] => [[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,3,10,1,2] => [2,1,10,3,5,4,7,6,9,8] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,11,1] => [1,11,2,10,9,8,7,6,5,4,3] => [.,[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1,10] => [10,1,9,2,8,3,7,4,6,5] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => [10,3,2,1,6,5,4,9,8,7] => [[[[.,.],.],[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [9,8,10,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,10,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [12,11,10,9,8,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,8,9,10,11,12] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [12,6,5,4,3,2,1,7,8,9,10,11] => [11,10,9,8,7,1,2,3,4,5,6,12] => [[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,6,5,4,3,2,8,9,10,11,12,1] => [1,12,11,10,9,8,2,3,4,5,6,7] => [.,[[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => [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] => [9,8,6,4,2,1,3,5,7] => [7,5,3,1,2,4,6,8,9] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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.