Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00064: Permutations —reverse⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
[1,0] => [1] => [1] => [1] => [.,.]
[1,0,1,0] => [2,1] => [1,2] => [2,1] => [[.,.],.]
[1,1,0,0] => [1,2] => [2,1] => [1,2] => [.,[.,.]]
[1,0,1,0,1,0] => [3,2,1] => [1,2,3] => [3,2,1] => [[[.,.],.],.]
[1,0,1,1,0,0] => [2,3,1] => [1,3,2] => [3,1,2] => [[.,.],[.,.]]
[1,1,0,0,1,0] => [3,1,2] => [2,1,3] => [2,3,1] => [[.,[.,.]],.]
[1,1,0,1,0,0] => [2,1,3] => [3,1,2] => [1,3,2] => [.,[[.,.],.]]
[1,1,1,0,0,0] => [1,2,3] => [3,2,1] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,2,3,4] => [4,3,2,1] => [[[[.,.],.],.],.]
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [1,2,4,3] => [4,3,1,2] => [[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [1,3,2,4] => [4,2,3,1] => [[[.,.],[.,.]],.]
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [1,4,2,3] => [4,1,3,2] => [[.,.],[[.,.],.]]
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,4,3,2] => [4,1,2,3] => [[.,.],[.,[.,.]]]
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [2,1,3,4] => [3,4,2,1] => [[[.,[.,.]],.],.]
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,1,4,3] => [3,4,1,2] => [[.,[.,.]],[.,.]]
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [3,1,2,4] => [2,4,3,1] => [[.,[[.,.],.]],.]
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [4,1,2,3] => [1,4,3,2] => [.,[[[.,.],.],.]]
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [4,1,3,2] => [1,4,2,3] => [.,[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [3,2,1,4] => [2,3,4,1] => [[.,[.,[.,.]]],.]
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [4,2,1,3] => [1,3,4,2] => [.,[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [4,3,1,2] => [1,2,4,3] => [.,[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [4,3,2,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,2,3,4,5] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [1,2,3,5,4] => [5,4,3,1,2] => [[[[.,.],.],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [1,2,4,3,5] => [5,4,2,3,1] => [[[[.,.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [1,2,5,3,4] => [5,4,1,3,2] => [[[.,.],.],[[.,.],.]]
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [1,2,5,4,3] => [5,4,1,2,3] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [1,3,2,4,5] => [5,3,4,2,1] => [[[[.,.],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [1,3,2,5,4] => [5,3,4,1,2] => [[[.,.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [1,4,2,3,5] => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [1,5,2,3,4] => [5,1,4,3,2] => [[.,.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [1,5,2,4,3] => [5,1,4,2,3] => [[.,.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [1,4,3,2,5] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [1,5,3,2,4] => [5,1,3,4,2] => [[.,.],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [1,5,4,2,3] => [5,1,2,4,3] => [[.,.],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,5,4,3,2] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [2,1,3,4,5] => [4,5,3,2,1] => [[[[.,[.,.]],.],.],.]
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [2,1,3,5,4] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [2,1,4,3,5] => [4,5,2,3,1] => [[[.,[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [2,1,5,3,4] => [4,5,1,3,2] => [[.,[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [2,1,5,4,3] => [4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [3,1,2,4,5] => [3,5,4,2,1] => [[[.,[[.,.],.]],.],.]
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [3,1,2,5,4] => [3,5,4,1,2] => [[.,[[.,.],.]],[.,.]]
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [4,1,2,3,5] => [2,5,4,3,1] => [[.,[[[.,.],.],.]],.]
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [5,1,2,3,4] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [5,1,2,4,3] => [1,5,4,2,3] => [.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [4,1,3,2,5] => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [5,1,3,2,4] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [5,1,4,2,3] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [5,1,4,3,2] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [3,2,1,4,5] => [3,4,5,2,1] => [[[.,[.,[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [3,2,1,5,4] => [3,4,5,1,2] => [[.,[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [4,2,1,3,5] => [2,4,5,3,1] => [[.,[[.,[.,.]],.]],.]
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [5,2,1,3,4] => [1,4,5,3,2] => [.,[[[.,[.,.]],.],.]]
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [5,2,1,4,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [4,3,1,2,5] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [5,3,1,2,4] => [1,3,5,4,2] => [.,[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [5,4,1,2,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [5,4,1,3,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [4,3,2,1,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [5,3,2,1,4] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [5,4,2,1,3] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [5,4,3,1,2] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [5,4,3,2,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [1,2,3,4,6,5] => [6,5,4,3,1,2] => [[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => [6,5,4,2,3,1] => [[[[[.,.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [1,2,3,6,4,5] => [6,5,4,1,3,2] => [[[[.,.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => [6,5,4,1,2,3] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [1,2,4,3,6,5] => [6,5,3,4,1,2] => [[[[.,.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [1,2,5,3,4,6] => [6,5,2,4,3,1] => [[[[.,.],.],[[.,.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [1,2,6,3,4,5] => [6,5,1,4,3,2] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [1,2,6,3,5,4] => [6,5,1,4,2,3] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [1,2,5,4,3,6] => [6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [1,2,6,4,3,5] => [6,5,1,3,4,2] => [[[.,.],.],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,2,6,5,3,4] => [6,5,1,2,4,3] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [1,2,6,5,4,3] => [6,5,1,2,3,4] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [1,3,2,4,5,6] => [6,4,5,3,2,1] => [[[[[.,.],[.,.]],.],.],.]
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [1,3,2,4,6,5] => [6,4,5,3,1,2] => [[[[.,.],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [1,3,2,6,4,5] => [6,4,5,1,3,2] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [1,3,2,6,5,4] => [6,4,5,1,2,3] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [1,4,2,3,5,6] => [6,3,5,4,2,1] => [[[[.,.],[[.,.],.]],.],.]
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [1,4,2,3,6,5] => [6,3,5,4,1,2] => [[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [1,5,2,3,4,6] => [6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [1,6,2,3,4,5] => [6,1,5,4,3,2] => [[.,.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [1,6,2,3,5,4] => [6,1,5,4,2,3] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [1,5,2,4,3,6] => [6,2,5,3,4,1] => [[[.,.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [1,6,2,4,3,5] => [6,1,5,3,4,2] => [[.,.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [1,6,2,5,3,4] => [6,1,5,2,4,3] => [[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [1,6,2,5,4,3] => [6,1,5,2,3,4] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [1,4,3,2,5,6] => [6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [1,4,3,2,6,5] => [6,3,4,5,1,2] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [1,5,3,2,4,6] => [6,2,4,5,3,1] => [[[.,.],[[.,[.,.]],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [1,6,3,2,4,5] => [6,1,4,5,3,2] => [[.,.],[[[.,[.,.]],.],.]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [1,6,3,2,5,4] => [6,1,4,5,2,3] => [[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [1,5,4,2,3,6] => [6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,6,4,2,3,5] => [6,1,3,5,4,2] => [[.,.],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [1,6,5,2,3,4] => [6,1,2,5,4,3] => [[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [1,6,5,2,4,3] => [6,1,2,5,3,4] => [[.,.],[.,[[.,.],[.,.]]]]
>>> Load all 1956 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] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [1,6,4,3,2,5] => [6,1,3,4,5,2] => [[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [1,6,5,3,2,4] => [6,1,2,4,5,3] => [[.,.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [1,6,5,4,2,3] => [6,1,2,3,5,4] => [[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [2,1,3,4,5,6] => [5,6,4,3,2,1] => [[[[[.,[.,.]],.],.],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [2,1,3,5,4,6] => [5,6,4,2,3,1] => [[[[.,[.,.]],.],[.,.]],.]
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [2,1,3,6,4,5] => [5,6,4,1,3,2] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [2,1,3,6,5,4] => [5,6,4,1,2,3] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [2,1,4,3,5,6] => [5,6,3,4,2,1] => [[[[.,[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [2,1,5,3,4,6] => [5,6,2,4,3,1] => [[[.,[.,.]],[[.,.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [2,1,6,3,4,5] => [5,6,1,4,3,2] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [2,1,6,3,5,4] => [5,6,1,4,2,3] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [2,1,5,4,3,6] => [5,6,2,3,4,1] => [[[.,[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [2,1,6,4,3,5] => [5,6,1,3,4,2] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [2,1,6,5,3,4] => [5,6,1,2,4,3] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [2,1,6,5,4,3] => [5,6,1,2,3,4] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [3,1,2,4,5,6] => [4,6,5,3,2,1] => [[[[.,[[.,.],.]],.],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [3,1,2,4,6,5] => [4,6,5,3,1,2] => [[[.,[[.,.],.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [3,1,2,5,4,6] => [4,6,5,2,3,1] => [[[.,[[.,.],.]],[.,.]],.]
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [3,1,2,6,4,5] => [4,6,5,1,3,2] => [[.,[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [3,1,2,6,5,4] => [4,6,5,1,2,3] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [4,1,2,3,5,6] => [3,6,5,4,2,1] => [[[.,[[[.,.],.],.]],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [4,1,2,3,6,5] => [3,6,5,4,1,2] => [[.,[[[.,.],.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [5,1,2,3,4,6] => [2,6,5,4,3,1] => [[.,[[[[.,.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [6,1,2,3,5,4] => [1,6,5,4,2,3] => [.,[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [5,1,2,4,3,6] => [2,6,5,3,4,1] => [[.,[[[.,.],.],[.,.]]],.]
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [6,1,2,4,3,5] => [1,6,5,3,4,2] => [.,[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [6,1,2,5,3,4] => [1,6,5,2,4,3] => [.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [6,1,2,5,4,3] => [1,6,5,2,3,4] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [4,1,3,2,5,6] => [3,6,4,5,2,1] => [[[.,[[.,.],[.,.]]],.],.]
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [4,1,3,2,6,5] => [3,6,4,5,1,2] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [5,1,3,2,4,6] => [2,6,4,5,3,1] => [[.,[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [6,1,3,2,4,5] => [1,6,4,5,3,2] => [.,[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [6,1,3,2,5,4] => [1,6,4,5,2,3] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [5,1,4,2,3,6] => [2,6,3,5,4,1] => [[.,[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [6,1,4,2,3,5] => [1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [6,1,5,2,3,4] => [1,6,2,5,4,3] => [.,[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [6,1,5,2,4,3] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [5,1,4,3,2,6] => [2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [6,1,4,3,2,5] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [6,1,5,3,2,4] => [1,6,2,4,5,3] => [.,[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [6,1,5,4,2,3] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [3,2,1,4,5,6] => [4,5,6,3,2,1] => [[[[.,[.,[.,.]]],.],.],.]
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [3,2,1,4,6,5] => [4,5,6,3,1,2] => [[[.,[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => [4,5,6,2,3,1] => [[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => [4,5,6,1,3,2] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [4,2,1,3,5,6] => [3,5,6,4,2,1] => [[[.,[[.,[.,.]],.]],.],.]
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [4,2,1,3,6,5] => [3,5,6,4,1,2] => [[.,[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [5,2,1,3,4,6] => [2,5,6,4,3,1] => [[.,[[[.,[.,.]],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [6,2,1,3,4,5] => [1,5,6,4,3,2] => [.,[[[[.,[.,.]],.],.],.]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [6,2,1,3,5,4] => [1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => [2,5,6,3,4,1] => [[.,[[.,[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [6,2,1,4,3,5] => [1,5,6,3,4,2] => [.,[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [6,2,1,5,3,4] => [1,5,6,2,4,3] => [.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [6,2,1,5,4,3] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [4,3,1,2,5,6] => [3,4,6,5,2,1] => [[[.,[.,[[.,.],.]]],.],.]
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [4,3,1,2,6,5] => [3,4,6,5,1,2] => [[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [5,3,1,2,4,6] => [2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [6,3,1,2,4,5] => [1,4,6,5,3,2] => [.,[[[.,[[.,.],.]],.],.]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [6,3,1,2,5,4] => [1,4,6,5,2,3] => [.,[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [5,4,1,2,3,6] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [6,4,1,2,3,5] => [1,3,6,5,4,2] => [.,[[.,[[[.,.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [6,5,1,2,4,3] => [1,2,6,5,3,4] => [.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [5,4,1,3,2,6] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [6,4,1,3,2,5] => [1,3,6,4,5,2] => [.,[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [6,5,1,3,2,4] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [6,5,1,4,2,3] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => [3,4,5,6,2,1] => [[[.,[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [3,4,5,6,1,2] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.]
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [6,3,2,1,4,5] => [1,4,5,6,3,2] => [.,[[[.,[.,[.,.]]],.],.]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [6,3,2,1,5,4] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [6,4,2,1,3,5] => [1,3,5,6,4,2] => [.,[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [6,5,2,1,3,4] => [1,2,5,6,4,3] => [.,[.,[[[.,[.,.]],.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [6,5,2,1,4,3] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [6,4,3,1,2,5] => [1,3,4,6,5,2] => [.,[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [6,5,3,1,2,4] => [1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [6,4,3,2,1,5] => [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [6,5,3,2,1,4] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [6,5,4,2,1,3] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[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] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
[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] => [7,6,5,4,3,1,2] => [[[[[[.,.],.],.],.],.],[.,.]]
[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] => [7,6,5,4,2,3,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[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] => [7,6,5,4,1,3,2] => [[[[[.,.],.],.],.],[[.,.],.]]
[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] => [7,6,5,4,1,2,3] => [[[[[.,.],.],.],.],[.,[.,.]]]
[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] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[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] => [7,6,5,3,4,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]]
[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] => [7,6,5,2,4,3,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[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] => [7,6,5,1,4,3,2] => [[[[.,.],.],.],[[[.,.],.],.]]
[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] => [7,6,5,1,4,2,3] => [[[[.,.],.],.],[[.,.],[.,.]]]
[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] => [7,6,5,2,3,4,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[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] => [7,6,5,1,3,4,2] => [[[[.,.],.],.],[[.,[.,.]],.]]
[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] => [7,6,5,1,2,4,3] => [[[[.,.],.],.],[.,[[.,.],.]]]
[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] => [7,6,5,1,2,3,4] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[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] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[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] => [7,6,4,5,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]]
[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] => [7,6,4,5,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[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] => [7,6,4,5,1,3,2] => [[[[.,.],.],[.,.]],[[.,.],.]]
[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] => [7,6,4,5,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[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] => [7,6,3,5,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.]
[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] => [7,6,3,5,4,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]]
[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] => [7,6,2,5,4,3,1] => [[[[.,.],.],[[[.,.],.],.]],.]
[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] => [7,6,1,5,4,3,2] => [[[.,.],.],[[[[.,.],.],.],.]]
[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] => [7,6,1,5,4,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]]
[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] => [7,6,2,5,3,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[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] => [7,6,1,5,3,4,2] => [[[.,.],.],[[[.,.],[.,.]],.]]
[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] => [7,6,1,5,2,4,3] => [[[.,.],.],[[.,.],[[.,.],.]]]
[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] => [7,6,1,5,2,3,4] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[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] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[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] => [7,6,3,4,5,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[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] => [7,6,2,4,5,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.]
[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] => [7,6,1,4,5,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]]
[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] => [7,6,1,4,5,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[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] => [7,6,2,3,5,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[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] => [7,6,1,3,5,4,2] => [[[.,.],.],[[.,[[.,.],.]],.]]
[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] => [7,6,1,2,5,4,3] => [[[.,.],.],[.,[[[.,.],.],.]]]
[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] => [7,6,1,2,5,3,4] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[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] => [7,6,2,3,4,5,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[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] => [7,6,1,3,4,5,2] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[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] => [7,6,1,2,4,5,3] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[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] => [7,6,1,2,3,5,4] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[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] => [7,6,1,2,3,4,5] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[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] => [7,5,6,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.]
[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] => [7,5,6,4,3,1,2] => [[[[[.,.],[.,.]],.],.],[.,.]]
[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] => [7,5,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[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] => [7,5,6,4,1,3,2] => [[[[.,.],[.,.]],.],[[.,.],.]]
[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] => [7,5,6,4,1,2,3] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[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] => [7,5,6,3,4,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[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] => [7,5,6,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[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] => [7,5,6,2,4,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.]
[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] => [7,5,6,1,4,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]]
[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] => [7,5,6,1,4,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[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] => [7,5,6,2,3,4,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[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] => [7,5,6,1,3,4,2] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[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] => [7,5,6,1,2,4,3] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[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] => [7,5,6,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[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] => [7,4,6,5,3,2,1] => [[[[[.,.],[[.,.],.]],.],.],.]
[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] => [7,4,6,5,3,1,2] => [[[[.,.],[[.,.],.]],.],[.,.]]
[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] => [7,4,6,5,2,3,1] => [[[[.,.],[[.,.],.]],[.,.]],.]
[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] => [7,4,6,5,1,3,2] => [[[.,.],[[.,.],.]],[[.,.],.]]
[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] => [7,4,6,5,1,2,3] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[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] => [7,3,6,5,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.]
[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] => [7,3,6,5,4,1,2] => [[[.,.],[[[.,.],.],.]],[.,.]]
[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] => [7,2,6,5,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.]
[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] => [7,1,6,5,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]]
[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] => [7,1,6,5,4,2,3] => [[.,.],[[[[.,.],.],.],[.,.]]]
[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] => [7,2,6,5,3,4,1] => [[[.,.],[[[.,.],.],[.,.]]],.]
[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] => [7,1,6,5,3,4,2] => [[.,.],[[[[.,.],.],[.,.]],.]]
[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] => [7,1,6,5,2,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]]
[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] => [7,1,6,5,2,3,4] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[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] => [7,3,6,4,5,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.]
[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] => [7,3,6,4,5,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[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] => [7,2,6,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.]
[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] => [7,1,6,4,5,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]]
[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] => [7,1,6,4,5,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[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] => [7,2,6,3,5,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.]
[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] => [7,1,6,3,5,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]]
[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] => [7,1,6,2,5,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]]
[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] => [7,1,6,2,5,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[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] => [7,2,6,3,4,5,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[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] => [7,1,6,3,4,5,2] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[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] => [7,1,6,2,4,5,3] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[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] => [7,1,6,2,3,5,4] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[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] => [7,1,6,2,3,4,5] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[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] => [7,4,5,6,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.]
[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] => [7,4,5,6,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[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] => [7,4,5,6,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[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] => [7,4,5,6,1,3,2] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[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] => [7,4,5,6,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[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] => [7,3,5,6,4,2,1] => [[[[.,.],[[.,[.,.]],.]],.],.]
[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] => [7,3,5,6,4,1,2] => [[[.,.],[[.,[.,.]],.]],[.,.]]
[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] => [7,2,5,6,4,3,1] => [[[.,.],[[[.,[.,.]],.],.]],.]
[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] => [7,1,5,6,4,3,2] => [[.,.],[[[[.,[.,.]],.],.],.]]
[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] => [7,1,5,6,4,2,3] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[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] => [7,2,5,6,3,4,1] => [[[.,.],[[.,[.,.]],[.,.]]],.]
[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] => [7,1,5,6,3,4,2] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[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] => [7,1,5,6,2,4,3] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[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] => [7,1,5,6,2,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[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] => [7,3,4,6,5,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.]
[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] => [7,3,4,6,5,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[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] => [7,2,4,6,5,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.]
[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] => [7,1,4,6,5,3,2] => [[.,.],[[[.,[[.,.],.]],.],.]]
[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] => [7,1,4,6,5,2,3] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[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] => [7,2,3,6,5,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.]
[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] => [7,1,3,6,5,4,2] => [[.,.],[[.,[[[.,.],.],.]],.]]
[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] => [7,1,2,6,5,4,3] => [[.,.],[.,[[[[.,.],.],.],.]]]
[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] => [7,1,2,6,5,3,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[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] => [7,2,3,6,4,5,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[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] => [7,1,3,6,4,5,2] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[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] => [7,1,2,6,4,5,3] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[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] => [7,1,2,6,3,5,4] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[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] => [7,1,2,6,3,4,5] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[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] => [7,3,4,5,6,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[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] => [7,3,4,5,6,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[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] => [7,2,4,5,6,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.]
[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] => [7,1,4,5,6,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]]
[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] => [7,1,4,5,6,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[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] => [7,2,3,5,6,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.]
[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] => [7,1,3,5,6,4,2] => [[.,.],[[.,[[.,[.,.]],.]],.]]
[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] => [7,1,2,5,6,4,3] => [[.,.],[.,[[[.,[.,.]],.],.]]]
[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] => [7,1,2,5,6,3,4] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[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] => [7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[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] => [7,1,3,4,6,5,2] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[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] => [7,1,2,4,6,5,3] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[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] => [7,1,2,3,6,5,4] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[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] => [7,1,2,3,6,4,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[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] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[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] => [7,1,3,4,5,6,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[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] => [7,1,2,4,5,6,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[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] => [7,1,2,3,5,6,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[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] => [7,1,2,3,4,6,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[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] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[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] => [6,7,5,4,3,2,1] => [[[[[[.,[.,.]],.],.],.],.],.]
[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] => [6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]]
[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] => [6,7,5,4,2,3,1] => [[[[[.,[.,.]],.],.],[.,.]],.]
[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] => [6,7,5,4,1,3,2] => [[[[.,[.,.]],.],.],[[.,.],.]]
[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] => [6,7,5,4,1,2,3] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[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] => [6,7,5,3,4,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.]
[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] => [6,7,5,3,4,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[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] => [6,7,5,2,4,3,1] => [[[[.,[.,.]],.],[[.,.],.]],.]
[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] => [6,7,5,1,4,3,2] => [[[.,[.,.]],.],[[[.,.],.],.]]
[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] => [6,7,5,1,4,2,3] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[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] => [6,7,5,2,3,4,1] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[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] => [6,7,5,1,3,4,2] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[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] => [6,7,5,1,2,4,3] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[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] => [6,7,5,1,2,3,4] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[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] => [6,7,4,5,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.]
[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] => [6,7,4,5,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[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] => [6,7,4,5,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[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] => [6,7,4,5,1,3,2] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[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] => [6,7,4,5,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[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] => [6,7,3,5,4,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.]
[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] => [6,7,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
[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] => [6,7,2,5,4,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.]
[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] => [6,7,1,5,4,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]]
[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] => [6,7,1,5,4,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[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] => [6,7,2,5,3,4,1] => [[[.,[.,.]],[[.,.],[.,.]]],.]
[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] => [6,7,1,5,3,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[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] => [6,7,1,5,2,4,3] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[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] => [6,7,1,5,2,3,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[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] => [6,7,3,4,5,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[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] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[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] => [6,7,2,4,5,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.]
[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] => [6,7,1,4,5,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]]
[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] => [6,7,1,4,5,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[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] => [6,7,2,3,5,4,1] => [[[.,[.,.]],[.,[[.,.],.]]],.]
[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] => [6,7,1,3,5,4,2] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[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] => [6,7,1,2,5,4,3] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[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] => [6,7,1,2,5,3,4] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[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] => [6,7,2,3,4,5,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[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] => [6,7,1,3,4,5,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[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] => [6,7,1,2,4,5,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[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] => [6,7,1,2,3,5,4] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[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] => [6,7,1,2,3,4,5] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[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] => [5,7,6,4,3,2,1] => [[[[[.,[[.,.],.]],.],.],.],.]
[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] => [5,7,6,4,3,1,2] => [[[[.,[[.,.],.]],.],.],[.,.]]
[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] => [5,7,6,4,2,3,1] => [[[[.,[[.,.],.]],.],[.,.]],.]
[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] => [5,7,6,4,1,3,2] => [[[.,[[.,.],.]],.],[[.,.],.]]
[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] => [5,7,6,4,1,2,3] => [[[.,[[.,.],.]],.],[.,[.,.]]]
[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] => [5,7,6,3,4,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.]
[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] => [5,7,6,3,4,1,2] => [[[.,[[.,.],.]],[.,.]],[.,.]]
[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] => [5,7,6,2,4,3,1] => [[[.,[[.,.],.]],[[.,.],.]],.]
[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] => [5,7,6,1,4,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]]
[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] => [5,7,6,1,4,2,3] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[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] => [5,7,6,2,3,4,1] => [[[.,[[.,.],.]],[.,[.,.]]],.]
[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] => [5,7,6,1,3,4,2] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[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] => [5,7,6,1,2,4,3] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[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] => [5,7,6,1,2,3,4] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[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] => [4,7,6,5,3,2,1] => [[[[.,[[[.,.],.],.]],.],.],.]
[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] => [4,7,6,5,3,1,2] => [[[.,[[[.,.],.],.]],.],[.,.]]
[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] => [4,7,6,5,2,3,1] => [[[.,[[[.,.],.],.]],[.,.]],.]
[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] => [4,7,6,5,1,3,2] => [[.,[[[.,.],.],.]],[[.,.],.]]
[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] => [4,7,6,5,1,2,3] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[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] => [3,7,6,5,4,2,1] => [[[.,[[[[.,.],.],.],.]],.],.]
[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] => [3,7,6,5,4,1,2] => [[.,[[[[.,.],.],.],.]],[.,.]]
[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] => [2,7,6,5,4,3,1] => [[.,[[[[[.,.],.],.],.],.]],.]
[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] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]]
[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] => [1,7,6,5,4,2,3] => [.,[[[[[.,.],.],.],.],[.,.]]]
[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] => [2,7,6,5,3,4,1] => [[.,[[[[.,.],.],.],[.,.]]],.]
[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] => [1,7,6,5,3,4,2] => [.,[[[[[.,.],.],.],[.,.]],.]]
[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] => [1,7,6,5,2,4,3] => [.,[[[[.,.],.],.],[[.,.],.]]]
[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] => [1,7,6,5,2,3,4] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[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] => [3,7,6,4,5,2,1] => [[[.,[[[.,.],.],[.,.]]],.],.]
[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] => [3,7,6,4,5,1,2] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[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] => [2,7,6,4,5,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.]
[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] => [1,7,6,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]]
[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] => [1,7,6,4,5,2,3] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[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] => [2,7,6,3,5,4,1] => [[.,[[[.,.],.],[[.,.],.]]],.]
[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] => [1,7,6,3,5,4,2] => [.,[[[[.,.],.],[[.,.],.]],.]]
[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] => [1,7,6,2,5,4,3] => [.,[[[.,.],.],[[[.,.],.],.]]]
[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] => [1,7,6,2,5,3,4] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[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] => [2,7,6,3,4,5,1] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[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] => [1,7,6,3,4,5,2] => [.,[[[[.,.],.],[.,[.,.]]],.]]
[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] => [1,7,6,2,4,5,3] => [.,[[[.,.],.],[[.,[.,.]],.]]]
[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] => [1,7,6,2,3,5,4] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[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] => [1,7,6,2,3,4,5] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[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] => [4,7,5,6,3,2,1] => [[[[.,[[.,.],[.,.]]],.],.],.]
[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] => [4,7,5,6,3,1,2] => [[[.,[[.,.],[.,.]]],.],[.,.]]
[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] => [4,7,5,6,2,3,1] => [[[.,[[.,.],[.,.]]],[.,.]],.]
[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] => [4,7,5,6,1,3,2] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[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] => [4,7,5,6,1,2,3] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[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] => [3,7,5,6,4,2,1] => [[[.,[[[.,.],[.,.]],.]],.],.]
[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] => [3,7,5,6,4,1,2] => [[.,[[[.,.],[.,.]],.]],[.,.]]
[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] => [2,7,5,6,4,3,1] => [[.,[[[[.,.],[.,.]],.],.]],.]
[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] => [1,7,5,6,4,3,2] => [.,[[[[[.,.],[.,.]],.],.],.]]
[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] => [1,7,5,6,4,2,3] => [.,[[[[.,.],[.,.]],.],[.,.]]]
[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] => [2,7,5,6,3,4,1] => [[.,[[[.,.],[.,.]],[.,.]]],.]
[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] => [1,7,5,6,3,4,2] => [.,[[[[.,.],[.,.]],[.,.]],.]]
[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] => [1,7,5,6,2,4,3] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[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] => [1,7,5,6,2,3,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[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] => [3,7,4,6,5,2,1] => [[[.,[[.,.],[[.,.],.]]],.],.]
[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] => [3,7,4,6,5,1,2] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[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] => [2,7,4,6,5,3,1] => [[.,[[[.,.],[[.,.],.]],.]],.]
[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] => [1,7,4,6,5,3,2] => [.,[[[[.,.],[[.,.],.]],.],.]]
[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] => [1,7,4,6,5,2,3] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[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] => [2,7,3,6,5,4,1] => [[.,[[.,.],[[[.,.],.],.]]],.]
[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] => [1,7,3,6,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]]
[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] => [1,7,2,6,5,4,3] => [.,[[.,.],[[[[.,.],.],.],.]]]
[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] => [1,7,2,6,5,3,4] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[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] => [2,7,3,6,4,5,1] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[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] => [1,7,3,6,4,5,2] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[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] => [1,7,2,6,4,5,3] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[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] => [1,7,2,6,3,5,4] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[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] => [1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[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] => [3,7,4,5,6,2,1] => [[[.,[[.,.],[.,[.,.]]]],.],.]
[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] => [3,7,4,5,6,1,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[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] => [2,7,4,5,6,3,1] => [[.,[[[.,.],[.,[.,.]]],.]],.]
[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] => [1,7,4,5,6,3,2] => [.,[[[[.,.],[.,[.,.]]],.],.]]
[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] => [1,7,4,5,6,2,3] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[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] => [2,7,3,5,6,4,1] => [[.,[[.,.],[[.,[.,.]],.]]],.]
[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] => [1,7,3,5,6,4,2] => [.,[[[.,.],[[.,[.,.]],.]],.]]
[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] => [1,7,2,5,6,4,3] => [.,[[.,.],[[[.,[.,.]],.],.]]]
[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] => [1,7,2,5,6,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[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] => [2,7,3,4,6,5,1] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[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] => [1,7,3,4,6,5,2] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[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] => [1,7,2,4,6,5,3] => [.,[[.,.],[[.,[[.,.],.]],.]]]
[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] => [1,7,2,3,6,5,4] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[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] => [1,7,2,3,6,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[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] => [2,7,3,4,5,6,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[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] => [1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[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] => [1,7,2,4,5,6,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[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] => [1,7,2,3,5,6,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]]
[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] => [1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[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] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[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] => [5,6,7,4,3,2,1] => [[[[[.,[.,[.,.]]],.],.],.],.]
[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] => [5,6,7,4,3,1,2] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[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] => [5,6,7,4,2,3,1] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[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] => [5,6,7,4,1,3,2] => [[[.,[.,[.,.]]],.],[[.,.],.]]
[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] => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[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] => [5,6,7,3,4,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.]
[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] => [5,6,7,3,4,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[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] => [5,6,7,2,4,3,1] => [[[.,[.,[.,.]]],[[.,.],.]],.]
[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] => [5,6,7,1,4,3,2] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[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] => [5,6,7,1,4,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[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] => [5,6,7,2,3,4,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[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] => [5,6,7,1,3,4,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[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] => [5,6,7,1,2,4,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[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] => [5,6,7,1,2,3,4] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[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] => [4,6,7,5,3,2,1] => [[[[.,[[.,[.,.]],.]],.],.],.]
[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] => [4,6,7,5,3,1,2] => [[[.,[[.,[.,.]],.]],.],[.,.]]
[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] => [4,6,7,5,2,3,1] => [[[.,[[.,[.,.]],.]],[.,.]],.]
[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] => [4,6,7,5,1,3,2] => [[.,[[.,[.,.]],.]],[[.,.],.]]
[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] => [4,6,7,5,1,2,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]]
[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] => [3,6,7,5,4,2,1] => [[[.,[[[.,[.,.]],.],.]],.],.]
[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] => [3,6,7,5,4,1,2] => [[.,[[[.,[.,.]],.],.]],[.,.]]
[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] => [2,6,7,5,4,3,1] => [[.,[[[[.,[.,.]],.],.],.]],.]
[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] => [1,6,7,5,4,3,2] => [.,[[[[[.,[.,.]],.],.],.],.]]
[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] => [1,6,7,5,4,2,3] => [.,[[[[.,[.,.]],.],.],[.,.]]]
[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] => [2,6,7,5,3,4,1] => [[.,[[[.,[.,.]],.],[.,.]]],.]
[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] => [1,6,7,5,3,4,2] => [.,[[[[.,[.,.]],.],[.,.]],.]]
[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] => [1,6,7,5,2,4,3] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[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] => [1,6,7,5,2,3,4] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[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] => [3,6,7,4,5,2,1] => [[[.,[[.,[.,.]],[.,.]]],.],.]
[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] => [3,6,7,4,5,1,2] => [[.,[[.,[.,.]],[.,.]]],[.,.]]
[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] => [2,6,7,4,5,3,1] => [[.,[[[.,[.,.]],[.,.]],.]],.]
[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] => [1,6,7,4,5,3,2] => [.,[[[[.,[.,.]],[.,.]],.],.]]
[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] => [1,6,7,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[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] => [2,6,7,3,5,4,1] => [[.,[[.,[.,.]],[[.,.],.]]],.]
[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] => [1,6,7,3,5,4,2] => [.,[[[.,[.,.]],[[.,.],.]],.]]
[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] => [1,6,7,2,5,4,3] => [.,[[.,[.,.]],[[[.,.],.],.]]]
[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] => [1,6,7,2,5,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[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] => [2,6,7,3,4,5,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.]
[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] => [1,6,7,3,4,5,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]]
[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] => [1,6,7,2,4,5,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[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] => [1,6,7,2,3,5,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[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] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[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] => [4,5,7,6,3,2,1] => [[[[.,[.,[[.,.],.]]],.],.],.]
[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] => [4,5,7,6,3,1,2] => [[[.,[.,[[.,.],.]]],.],[.,.]]
[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] => [4,5,7,6,2,3,1] => [[[.,[.,[[.,.],.]]],[.,.]],.]
[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] => [4,5,7,6,1,3,2] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[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] => [4,5,7,6,1,2,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[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] => [3,5,7,6,4,2,1] => [[[.,[[.,[[.,.],.]],.]],.],.]
[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] => [3,5,7,6,4,1,2] => [[.,[[.,[[.,.],.]],.]],[.,.]]
[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] => [2,5,7,6,4,3,1] => [[.,[[[.,[[.,.],.]],.],.]],.]
[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] => [1,5,7,6,4,3,2] => [.,[[[[.,[[.,.],.]],.],.],.]]
[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] => [1,5,7,6,4,2,3] => [.,[[[.,[[.,.],.]],.],[.,.]]]
[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] => [2,5,7,6,3,4,1] => [[.,[[.,[[.,.],.]],[.,.]]],.]
[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] => [1,5,7,6,3,4,2] => [.,[[[.,[[.,.],.]],[.,.]],.]]
[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] => [1,5,7,6,2,4,3] => [.,[[.,[[.,.],.]],[[.,.],.]]]
[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] => [1,5,7,6,2,3,4] => [.,[[.,[[.,.],.]],[.,[.,.]]]]
[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] => [3,4,7,6,5,2,1] => [[[.,[.,[[[.,.],.],.]]],.],.]
[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] => [3,4,7,6,5,1,2] => [[.,[.,[[[.,.],.],.]]],[.,.]]
[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] => [2,4,7,6,5,3,1] => [[.,[[.,[[[.,.],.],.]],.]],.]
[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] => [1,4,7,6,5,3,2] => [.,[[[.,[[[.,.],.],.]],.],.]]
[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] => [1,4,7,6,5,2,3] => [.,[[.,[[[.,.],.],.]],[.,.]]]
[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] => [2,3,7,6,5,4,1] => [[.,[.,[[[[.,.],.],.],.]]],.]
[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] => [1,3,7,6,5,4,2] => [.,[[.,[[[[.,.],.],.],.]],.]]
[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] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]]
[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] => [1,2,7,6,5,3,4] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[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] => [2,3,7,6,4,5,1] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[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] => [1,3,7,6,4,5,2] => [.,[[.,[[[.,.],.],[.,.]]],.]]
[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] => [1,2,7,6,4,5,3] => [.,[.,[[[[.,.],.],[.,.]],.]]]
[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] => [1,2,7,6,3,5,4] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[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] => [1,2,7,6,3,4,5] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[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] => [3,4,7,5,6,2,1] => [[[.,[.,[[.,.],[.,.]]]],.],.]
[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] => [3,4,7,5,6,1,2] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[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] => [2,4,7,5,6,3,1] => [[.,[[.,[[.,.],[.,.]]],.]],.]
[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] => [1,4,7,5,6,3,2] => [.,[[[.,[[.,.],[.,.]]],.],.]]
[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] => [1,4,7,5,6,2,3] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[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] => [2,3,7,5,6,4,1] => [[.,[.,[[[.,.],[.,.]],.]]],.]
[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] => [1,3,7,5,6,4,2] => [.,[[.,[[[.,.],[.,.]],.]],.]]
[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] => [1,2,7,5,6,4,3] => [.,[.,[[[[.,.],[.,.]],.],.]]]
[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] => [1,2,7,5,6,3,4] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[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] => [2,3,7,4,6,5,1] => [[.,[.,[[.,.],[[.,.],.]]]],.]
[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] => [1,3,7,4,6,5,2] => [.,[[.,[[.,.],[[.,.],.]]],.]]
[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] => [1,2,7,4,6,5,3] => [.,[.,[[[.,.],[[.,.],.]],.]]]
[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] => [1,2,7,3,6,5,4] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[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] => [1,2,7,3,6,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[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] => [2,3,7,4,5,6,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[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] => [1,3,7,4,5,6,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[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] => [1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[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] => [1,2,7,3,5,6,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]]
[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] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[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] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[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] => [4,5,6,7,3,2,1] => [[[[.,[.,[.,[.,.]]]],.],.],.]
[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] => [4,5,6,7,3,1,2] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[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] => [4,5,6,7,2,3,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[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] => [4,5,6,7,1,3,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[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] => [4,5,6,7,1,2,3] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[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] => [3,5,6,7,4,2,1] => [[[.,[[.,[.,[.,.]]],.]],.],.]
[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] => [3,5,6,7,4,1,2] => [[.,[[.,[.,[.,.]]],.]],[.,.]]
[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] => [2,5,6,7,4,3,1] => [[.,[[[.,[.,[.,.]]],.],.]],.]
[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] => [1,5,6,7,4,3,2] => [.,[[[[.,[.,[.,.]]],.],.],.]]
[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] => [1,5,6,7,4,2,3] => [.,[[[.,[.,[.,.]]],.],[.,.]]]
[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] => [2,5,6,7,3,4,1] => [[.,[[.,[.,[.,.]]],[.,.]]],.]
[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] => [1,5,6,7,3,4,2] => [.,[[[.,[.,[.,.]]],[.,.]],.]]
[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] => [1,5,6,7,2,4,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[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] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[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] => [3,4,6,7,5,2,1] => [[[.,[.,[[.,[.,.]],.]]],.],.]
[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] => [3,4,6,7,5,1,2] => [[.,[.,[[.,[.,.]],.]]],[.,.]]
[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] => [2,4,6,7,5,3,1] => [[.,[[.,[[.,[.,.]],.]],.]],.]
[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] => [1,4,6,7,5,3,2] => [.,[[[.,[[.,[.,.]],.]],.],.]]
[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] => [1,4,6,7,5,2,3] => [.,[[.,[[.,[.,.]],.]],[.,.]]]
[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] => [2,3,6,7,5,4,1] => [[.,[.,[[[.,[.,.]],.],.]]],.]
[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] => [1,3,6,7,5,4,2] => [.,[[.,[[[.,[.,.]],.],.]],.]]
[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] => [1,2,6,7,5,4,3] => [.,[.,[[[[.,[.,.]],.],.],.]]]
[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] => [1,2,6,7,5,3,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]]
[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] => [2,3,6,7,4,5,1] => [[.,[.,[[.,[.,.]],[.,.]]]],.]
[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] => [1,3,6,7,4,5,2] => [.,[[.,[[.,[.,.]],[.,.]]],.]]
[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] => [1,2,6,7,4,5,3] => [.,[.,[[[.,[.,.]],[.,.]],.]]]
[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] => [1,2,6,7,3,5,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[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] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[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] => [3,4,5,7,6,2,1] => [[[.,[.,[.,[[.,.],.]]]],.],.]
[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] => [3,4,5,7,6,1,2] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[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] => [2,4,5,7,6,3,1] => [[.,[[.,[.,[[.,.],.]]],.]],.]
[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] => [1,4,5,7,6,3,2] => [.,[[[.,[.,[[.,.],.]]],.],.]]
[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] => [1,4,5,7,6,2,3] => [.,[[.,[.,[[.,.],.]]],[.,.]]]
[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] => [2,3,5,7,6,4,1] => [[.,[.,[[.,[[.,.],.]],.]]],.]
[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] => [1,3,5,7,6,4,2] => [.,[[.,[[.,[[.,.],.]],.]],.]]
[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] => [1,2,5,7,6,4,3] => [.,[.,[[[.,[[.,.],.]],.],.]]]
[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] => [1,2,5,7,6,3,4] => [.,[.,[[.,[[.,.],.]],[.,.]]]]
[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] => [2,3,4,7,6,5,1] => [[.,[.,[.,[[[.,.],.],.]]]],.]
[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] => [1,3,4,7,6,5,2] => [.,[[.,[.,[[[.,.],.],.]]],.]]
[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] => [1,2,4,7,6,5,3] => [.,[.,[[.,[[[.,.],.],.]],.]]]
[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] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]]
[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] => [1,2,3,7,6,4,5] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[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] => [2,3,4,7,5,6,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[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] => [1,3,4,7,5,6,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
[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] => [1,2,4,7,5,6,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]]
[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] => [1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[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] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[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] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[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] => [3,4,5,6,7,2,1] => [[[.,[.,[.,[.,[.,.]]]]],.],.]
[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] => [3,4,5,6,7,1,2] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[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] => [2,4,5,6,7,3,1] => [[.,[[.,[.,[.,[.,.]]]],.]],.]
[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] => [1,4,5,6,7,3,2] => [.,[[[.,[.,[.,[.,.]]]],.],.]]
[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] => [1,4,5,6,7,2,3] => [.,[[.,[.,[.,[.,.]]]],[.,.]]]
[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] => [2,3,5,6,7,4,1] => [[.,[.,[[.,[.,[.,.]]],.]]],.]
[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] => [1,3,5,6,7,4,2] => [.,[[.,[[.,[.,[.,.]]],.]],.]]
[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] => [1,2,5,6,7,4,3] => [.,[.,[[[.,[.,[.,.]]],.],.]]]
[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] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]]
[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] => [2,3,4,6,7,5,1] => [[.,[.,[.,[[.,[.,.]],.]]]],.]
[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] => [1,3,4,6,7,5,2] => [.,[[.,[.,[[.,[.,.]],.]]],.]]
[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] => [1,2,4,6,7,5,3] => [.,[.,[[.,[[.,[.,.]],.]],.]]]
[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] => [1,2,3,6,7,5,4] => [.,[.,[.,[[[.,[.,.]],.],.]]]]
[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] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
[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] => [2,3,4,5,7,6,1] => [[.,[.,[.,[.,[[.,.],.]]]]],.]
[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] => [1,3,4,5,7,6,2] => [.,[[.,[.,[.,[[.,.],.]]]],.]]
[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] => [1,2,4,5,7,6,3] => [.,[.,[[.,[.,[[.,.],.]]],.]]]
[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] => [1,2,3,5,7,6,4] => [.,[.,[.,[[.,[[.,.],.]],.]]]]
[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] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[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] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[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] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[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] => [1,3,4,5,6,7,2] => [.,[[.,[.,[.,[.,[.,.]]]]],.]]
[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] => [1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]]
[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] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]]
[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] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]]
[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] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
[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] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[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] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[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] => [8,7,6,5,4,3,1,2] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[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] => [8,7,6,5,4,2,3,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[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] => [8,7,6,5,4,1,3,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[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] => [8,7,6,5,4,1,2,3] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[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] => [8,7,6,5,3,4,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[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] => [8,7,6,5,3,4,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[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] => [8,7,6,5,2,4,3,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[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] => [8,7,6,5,1,4,3,2] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[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] => [8,7,6,5,1,4,2,3] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[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] => [8,7,6,5,2,3,4,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[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] => [8,7,6,5,1,3,4,2] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[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] => [8,7,6,5,1,2,4,3] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[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] => [8,7,6,5,1,2,3,4] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[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] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[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] => [8,7,6,4,5,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[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] => [8,7,6,4,5,2,3,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[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] => [8,7,6,4,5,1,3,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[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] => [8,7,6,4,5,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[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] => [8,7,6,3,5,4,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[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] => [8,7,6,3,5,4,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[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] => [8,7,6,2,5,4,3,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[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] => [8,7,6,1,5,4,3,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[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] => [8,7,6,1,5,4,2,3] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[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] => [8,7,6,2,5,3,4,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[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] => [8,7,6,1,5,3,4,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[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] => [8,7,6,1,5,2,4,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[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] => [8,7,6,1,5,2,3,4] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[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] => [8,7,6,3,4,5,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[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] => [8,7,6,3,4,5,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[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] => [8,7,6,1,4,5,3,2] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[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] => [8,7,6,1,4,5,2,3] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[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] => [8,7,6,1,3,5,4,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]]
[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] => [8,7,6,1,2,5,4,3] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[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] => [8,7,6,1,2,5,3,4] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[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] => [8,7,6,2,3,4,5,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[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] => [8,7,6,1,3,4,5,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[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] => [8,7,6,1,2,4,5,3] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[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] => [8,7,6,1,2,3,5,4] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[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] => [8,7,6,1,2,3,4,5] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[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] => [8,7,5,6,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[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] => [8,7,5,6,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[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] => [8,7,5,6,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[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] => [8,7,5,6,4,1,3,2] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[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] => [8,7,5,6,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[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] => [8,7,5,6,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[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] => [8,7,5,6,1,4,3,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[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] => [8,7,5,6,1,4,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [1,2,4,3,7,6,5,8] => [8,7,5,6,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,2,1] => [1,2,4,3,8,6,5,7] => [8,7,5,6,1,3,4,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[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] => [8,7,5,6,1,2,4,3] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[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] => [8,7,5,6,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[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] => [8,7,4,6,5,3,2,1] => [[[[[[.,.],.],[[.,.],.]],.],.],.]
[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] => [8,7,4,6,5,3,1,2] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[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] => [8,7,4,6,5,2,3,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[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] => [8,7,4,6,5,1,3,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[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] => [8,7,3,6,5,4,2,1] => [[[[[.,.],.],[[[.,.],.],.]],.],.]
[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] => [8,7,1,6,5,4,3,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [1,2,8,3,4,7,5,6] => [8,7,1,6,5,2,4,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[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] => [8,7,1,6,5,2,3,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[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] => [8,7,3,6,4,5,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.]
[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] => [8,7,2,6,4,5,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[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] => [8,7,1,6,4,5,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]]
[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] => [8,7,1,6,4,5,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[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] => [8,7,2,6,3,5,4,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[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] => [8,7,1,6,3,5,4,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]]
[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] => [8,7,1,6,2,5,4,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[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] => [8,7,1,6,2,5,3,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[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] => [8,7,1,6,2,4,5,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[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] => [8,7,1,6,2,3,5,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[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] => [8,7,1,6,2,3,4,5] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[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] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [1,2,5,4,3,7,6,8] => [8,7,4,5,6,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[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] => [8,7,4,5,6,1,3,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[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] => [8,7,4,5,6,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[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] => [8,7,3,5,6,4,2,1] => [[[[[.,.],.],[[.,[.,.]],.]],.],.]
[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] => [8,7,2,5,6,4,3,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.]
[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] => [8,7,1,5,6,4,3,2] => [[[.,.],.],[[[[.,[.,.]],.],.],.]]
[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] => [8,7,1,5,6,2,4,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[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] => [8,7,1,5,6,2,3,4] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[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] => [8,7,3,4,6,5,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,2,1] => [1,2,6,5,3,4,8,7] => [8,7,3,4,6,5,1,2] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[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] => [8,7,2,4,6,5,3,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.]
[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] => [8,7,1,4,6,5,3,2] => [[[.,.],.],[[[.,[[.,.],.]],.],.]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,8,2,1] => [1,2,8,5,3,4,7,6] => [8,7,1,4,6,5,2,3] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[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] => [8,7,2,3,6,5,4,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [1,2,8,6,3,4,5,7] => [8,7,1,3,6,5,4,2] => [[[.,.],.],[[.,[[[.,.],.],.]],.]]
[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] => [8,7,1,2,6,5,4,3] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[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] => [8,7,1,2,6,5,3,4] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[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] => [8,7,1,2,6,3,4,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[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] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [1,2,6,5,4,3,8,7] => [8,7,3,4,5,6,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,7,2,1] => [1,2,7,5,4,3,6,8] => [8,7,2,4,5,6,3,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[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] => [8,7,1,4,5,6,3,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,2,1] => [1,2,8,7,5,3,4,6] => [8,7,1,2,4,6,5,3] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[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] => [8,7,1,2,3,6,5,4] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[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] => [8,7,1,2,3,6,4,5] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[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] => [8,7,2,3,4,5,6,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[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] => [8,7,1,3,4,5,6,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[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] => [8,7,1,2,4,5,6,3] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[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] => [8,7,1,2,3,4,6,5] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[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] => [8,7,1,2,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[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] => [8,6,7,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.]
[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] => [8,6,7,5,4,3,1,2] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[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] => [8,6,7,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[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] => [8,6,7,5,4,1,3,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]]
[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] => [8,6,7,5,3,4,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [1,3,2,4,7,5,6,8] => [8,6,7,5,2,4,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.]
[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] => [8,6,7,5,1,4,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[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] => [8,6,7,5,1,4,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[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] => [8,6,7,5,2,3,4,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[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] => [8,6,7,5,1,2,3,4] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[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] => [8,6,7,4,5,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,2,3,1] => [1,3,2,5,4,6,8,7] => [8,6,7,4,5,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[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] => [8,6,7,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[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] => [8,6,7,4,5,1,3,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[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] => [8,6,7,4,5,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[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] => [8,6,7,3,5,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.]
[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] => [8,6,7,2,5,4,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.]
[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] => [8,6,7,1,5,4,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]]
[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] => [8,6,7,2,5,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[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] => [8,6,7,1,5,3,4,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[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] => [8,6,7,1,5,2,4,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,3,1] => [1,3,2,8,4,7,6,5] => [8,6,7,1,5,2,3,4] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[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] => [8,6,7,3,4,5,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[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] => [8,6,7,3,4,5,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[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] => [8,6,7,1,4,5,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[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] => [8,6,7,2,3,5,4,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[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] => [8,6,7,1,2,5,3,4] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[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] => [8,6,7,2,3,4,5,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[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] => [8,6,7,1,3,4,5,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[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] => [8,6,7,1,2,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[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] => [8,5,7,6,4,3,2,1] => [[[[[[.,.],[[.,.],.]],.],.],.],.]
[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] => [8,5,7,6,4,3,1,2] => [[[[[.,.],[[.,.],.]],.],.],[.,.]]
[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] => [8,5,7,6,4,2,3,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.]
[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] => [8,5,7,6,4,1,3,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]
[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] => [8,5,7,6,4,1,2,3] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[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] => [8,5,7,6,3,4,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[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] => [8,5,7,6,2,4,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.]
[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] => [8,5,7,6,1,4,3,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[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] => [8,5,7,6,1,4,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [1,4,2,3,7,6,5,8] => [8,5,7,6,2,3,4,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[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] => [8,5,7,6,1,2,4,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[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] => [8,5,7,6,1,2,3,4] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[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] => [8,4,7,6,5,3,2,1] => [[[[[.,.],[[[.,.],.],.]],.],.],.]
[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] => [8,4,7,6,5,3,1,2] => [[[[.,.],[[[.,.],.],.]],.],[.,.]]
[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] => [8,4,7,6,5,2,3,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.]
[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] => [8,4,7,6,5,1,3,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]]
[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] => [8,4,7,6,5,1,2,3] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[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] => [8,3,7,6,5,4,2,1] => [[[[.,.],[[[[.,.],.],.],.]],.],.]
[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] => [8,2,7,6,5,4,3,1] => [[[.,.],[[[[[.,.],.],.],.],.]],.]
[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] => [8,1,7,6,5,4,3,2] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[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] => [8,1,7,6,5,4,2,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[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] => [8,2,7,6,5,3,4,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.]
[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] => [8,1,7,6,5,3,4,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[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] => [8,1,7,6,5,2,4,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[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] => [8,1,7,6,5,2,3,4] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,6,1] => [1,6,2,3,5,4,8,7] => [8,3,7,6,4,5,1,2] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[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] => [8,2,7,6,4,5,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.]
[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] => [8,1,7,6,4,5,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => [1,8,2,3,5,4,7,6] => [8,1,7,6,4,5,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[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] => [8,2,7,6,3,5,4,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.]
[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] => [8,1,7,6,3,5,4,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => [1,8,2,3,7,4,5,6] => [8,1,7,6,2,5,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,7,1] => [1,7,2,3,6,5,4,8] => [8,2,7,6,3,4,5,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[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] => [8,1,7,6,3,4,5,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[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] => [8,1,7,6,2,4,5,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[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] => [8,1,7,6,2,3,4,5] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[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] => [8,4,7,5,6,3,2,1] => [[[[[.,.],[[.,.],[.,.]]],.],.],.]
[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] => [8,4,7,5,6,2,3,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[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] => [8,4,7,5,6,1,3,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[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] => [8,3,7,5,6,4,2,1] => [[[[.,.],[[[.,.],[.,.]],.]],.],.]
[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] => [8,2,7,5,6,4,3,1] => [[[.,.],[[[[.,.],[.,.]],.],.]],.]
[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] => [8,1,7,5,6,4,3,2] => [[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,8,1] => [1,8,2,4,3,5,7,6] => [8,1,7,5,6,4,2,3] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[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] => [8,2,7,5,6,3,4,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[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] => [8,1,7,5,6,3,4,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[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] => [8,1,7,5,6,2,4,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[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] => [8,1,7,5,6,2,3,4] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[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] => [8,3,7,4,6,5,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.]
[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] => [8,3,7,4,6,5,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[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] => [8,2,7,4,6,5,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.]
[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] => [8,1,7,4,6,5,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]]
[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] => [8,2,7,3,6,5,4,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.]
[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] => [8,1,7,3,6,5,4,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[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] => [8,1,7,2,6,5,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[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] => [8,2,7,3,6,4,5,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[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] => [8,1,7,3,6,4,5,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[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] => [8,1,7,2,6,4,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[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] => [8,1,7,2,6,3,5,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[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] => [8,1,7,2,6,3,4,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,6,1] => [1,6,2,5,4,3,7,8] => [8,3,7,4,5,6,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,6,1] => [1,6,2,5,4,3,8,7] => [8,3,7,4,5,6,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[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] => [8,2,7,4,5,6,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,2,8,1] => [1,8,2,5,4,3,7,6] => [8,1,7,4,5,6,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[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] => [8,1,7,3,5,6,4,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[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] => [8,1,7,2,5,6,4,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[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] => [8,1,7,2,5,6,3,4] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => [1,7,2,6,5,3,4,8] => [8,2,7,3,4,6,5,1] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[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] => [8,1,7,2,4,6,5,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[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] => [8,1,7,2,3,6,5,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[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] => [8,1,7,2,3,6,4,5] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[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] => [8,2,7,3,4,5,6,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [1,8,2,6,5,4,3,7] => [8,1,7,3,4,5,6,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[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] => [8,1,7,2,4,5,6,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[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] => [8,1,7,2,3,5,6,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[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] => [8,1,7,2,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[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] => [8,5,6,7,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[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] => [8,5,6,7,4,2,3,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[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] => [8,5,6,7,4,1,3,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[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] => [8,5,6,7,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [1,4,3,2,6,5,7,8] => [8,5,6,7,3,4,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => [1,4,3,2,6,5,8,7] => [8,5,6,7,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => [1,4,3,2,7,5,6,8] => [8,5,6,7,2,4,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[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] => [8,5,6,7,1,4,3,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => [1,4,3,2,8,5,7,6] => [8,5,6,7,1,4,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[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] => [8,5,6,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[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] => [8,5,6,7,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[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] => [8,4,6,7,5,3,2,1] => [[[[[.,.],[[.,[.,.]],.]],.],.],.]
[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] => [8,4,6,7,5,3,1,2] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]]
[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] => [8,4,6,7,5,1,3,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[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] => [8,4,6,7,5,1,2,3] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[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] => [8,2,6,7,5,4,3,1] => [[[.,.],[[[[.,[.,.]],.],.],.]],.]
[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] => [8,1,6,7,5,4,3,2] => [[.,.],[[[[[.,[.,.]],.],.],.],.]]
[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] => [8,1,6,7,5,4,2,3] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[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] => [8,2,6,7,5,3,4,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [1,8,3,2,4,6,5,7] => [8,1,6,7,5,3,4,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[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] => [8,1,6,7,5,2,4,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => [1,8,3,2,4,7,6,5] => [8,1,6,7,5,2,3,4] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[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] => [8,1,6,7,4,5,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[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] => [8,1,6,7,4,5,2,3] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[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] => [8,1,6,7,3,5,4,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [1,8,3,2,7,4,5,6] => [8,1,6,7,2,5,4,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [1,8,3,2,7,4,6,5] => [8,1,6,7,2,5,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[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] => [8,1,6,7,2,4,5,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[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] => [8,1,6,7,2,3,5,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[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] => [8,1,6,7,2,3,4,5] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[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] => [8,4,5,7,6,3,2,1] => [[[[[.,.],[.,[[.,.],.]]],.],.],.]
[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] => [8,4,5,7,6,2,3,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[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] => [8,4,5,7,6,1,3,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[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] => [8,3,5,7,6,4,2,1] => [[[[.,.],[[.,[[.,.],.]],.]],.],.]
[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] => [8,2,5,7,6,4,3,1] => [[[.,.],[[[.,[[.,.],.]],.],.]],.]
[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] => [8,1,5,7,6,2,4,3] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[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] => [8,1,5,7,6,2,3,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [1,6,5,2,3,4,7,8] => [8,3,4,7,6,5,2,1] => [[[[.,.],[.,[[[.,.],.],.]]],.],.]
[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] => [8,2,4,7,6,5,3,1] => [[[.,.],[[.,[[[.,.],.],.]],.]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,8,1] => [1,8,5,2,3,4,6,7] => [8,1,4,7,6,5,3,2] => [[.,.],[[[.,[[[.,.],.],.]],.],.]]
[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] => [8,1,4,7,6,5,2,3] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[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] => [8,2,3,7,6,5,4,1] => [[[.,.],[.,[[[[.,.],.],.],.]]],.]
[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] => [8,1,3,7,6,5,4,2] => [[.,.],[[.,[[[[.,.],.],.],.]],.]]
[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] => [8,1,2,7,6,5,4,3] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => [1,7,6,2,3,5,4,8] => [8,2,3,7,6,4,5,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,8,1] => [1,8,6,2,3,5,4,7] => [8,1,3,7,6,4,5,2] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[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] => [8,1,2,7,6,4,5,3] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[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] => [8,1,2,7,6,3,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[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] => [8,1,2,7,6,3,4,5] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,5,7,1] => [1,7,5,2,4,3,6,8] => [8,2,4,7,5,6,3,1] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[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] => [8,2,3,7,5,6,4,1] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[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] => [8,1,3,7,5,6,4,2] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,8,1] => [1,8,7,2,4,3,6,5] => [8,1,2,7,5,6,3,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[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] => [8,1,3,7,4,6,5,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[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] => [8,1,2,7,4,6,5,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[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] => [8,1,2,7,3,6,5,4] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[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] => [8,1,2,7,3,6,4,5] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [1,7,6,2,5,4,3,8] => [8,2,3,7,4,5,6,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,6,8,1] => [1,8,6,2,5,4,3,7] => [8,1,3,7,4,5,6,2] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[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] => [8,1,2,7,4,5,6,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,8,1] => [1,8,7,2,6,4,3,5] => [8,1,2,7,3,5,6,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[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] => [8,1,2,7,3,4,6,5] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[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] => [8,1,2,7,3,4,5,6] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[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] => [8,4,5,6,7,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[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] => [8,4,5,6,7,2,3,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[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] => [8,4,5,6,7,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,6,1] => [1,6,4,3,2,5,8,7] => [8,3,5,6,7,4,1,2] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]]
[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] => [8,2,5,6,7,4,3,1] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.]
[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] => [8,1,5,6,7,4,3,2] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[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] => [8,1,5,6,7,4,2,3] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => [1,8,4,3,2,6,5,7] => [8,1,5,6,7,3,4,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[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] => [8,1,5,6,7,2,4,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[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] => [8,1,5,6,7,2,3,4] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[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] => [8,3,4,6,7,5,1,2] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[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] => [8,2,4,6,7,5,3,1] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.]
[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] => [8,1,4,6,7,5,2,3] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[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] => [8,1,3,6,7,5,4,2] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]]
[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] => [8,1,2,6,7,5,4,3] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[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] => [8,1,2,6,7,5,3,4] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[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] => [8,2,3,6,7,4,5,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
[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] => [8,1,3,6,7,4,5,2] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[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] => [8,1,2,6,7,4,5,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[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] => [8,1,2,6,7,3,5,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,5,6,1] => [1,6,5,4,2,3,7,8] => [8,3,4,5,7,6,2,1] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[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] => [8,3,4,5,7,6,1,2] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,7,1] => [1,7,5,4,2,3,6,8] => [8,2,4,5,7,6,3,1] => [[[.,.],[[.,[.,[[.,.],.]]],.]],.]
[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] => [8,1,4,5,7,6,3,2] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[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] => [8,1,4,5,7,6,2,3] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[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] => [8,2,3,5,7,6,4,1] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.]
[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] => [8,1,3,5,7,6,4,2] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => [1,7,6,5,2,3,4,8] => [8,2,3,4,7,6,5,1] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[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] => [8,1,2,4,7,6,5,3] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]]
[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] => [8,1,2,3,7,6,5,4] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,5,7,8,1] => [1,8,7,5,2,4,3,6] => [8,1,2,4,7,5,6,3] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[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] => [8,1,2,3,7,5,6,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[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] => [8,1,2,3,7,4,5,6] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[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] => [8,3,4,5,6,7,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[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] => [8,3,4,5,6,7,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[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] => [8,2,4,5,6,7,3,1] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[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] => [8,1,4,5,6,7,3,2] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[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] => [8,1,4,5,6,7,2,3] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,7,1] => [1,7,6,4,3,2,5,8] => [8,2,3,5,6,7,4,1] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => [1,8,6,4,3,2,5,7] => [8,1,3,5,6,7,4,2] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]]
[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] => [8,1,2,5,6,7,4,3] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[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] => [8,1,2,5,6,7,3,4] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[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] => [8,1,2,4,6,7,5,3] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]]
[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] => [8,1,2,3,6,7,5,4] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[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] => [8,1,2,3,6,7,4,5] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[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] => [8,2,3,4,5,7,6,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[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] => [8,1,3,4,5,7,6,2] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[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] => [8,1,2,3,5,7,6,4] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[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] => [8,1,2,3,4,7,6,5] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[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] => [8,1,2,3,4,7,5,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[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] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[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] => [8,1,3,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[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] => [8,1,2,4,5,6,7,3] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[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] => [8,1,2,3,5,6,7,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[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] => [8,1,2,3,4,6,7,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[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] => [8,1,2,3,4,5,7,6] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[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] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[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] => [7,8,6,5,4,3,2,1] => [[[[[[[.,[.,.]],.],.],.],.],.],.]
[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] => [7,8,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[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] => [7,8,6,5,4,2,3,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.]
[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] => [7,8,6,5,4,1,3,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]]
[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] => [7,8,6,5,4,1,2,3] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[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] => [7,8,6,5,3,4,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.]
[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] => [7,8,6,5,3,4,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[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] => [7,8,6,5,2,4,3,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.]
[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] => [7,8,6,5,1,4,3,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[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] => [7,8,6,5,1,4,2,3] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[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] => [7,8,6,5,1,2,4,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[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] => [7,8,6,5,1,2,3,4] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[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] => [7,8,6,4,5,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.]
[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] => [7,8,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[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] => [7,8,6,3,5,4,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.]
[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] => [7,8,6,1,5,4,3,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]]
[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] => [7,8,6,1,5,3,4,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[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] => [7,8,6,1,5,2,3,4] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,1,2] => [2,1,3,6,5,4,7,8] => [7,8,6,3,4,5,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[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] => [7,8,6,3,4,5,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [2,1,3,7,6,4,5,8] => [7,8,6,2,3,5,4,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.]
[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] => [7,8,6,1,3,5,4,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,1,2] => [2,1,3,7,6,5,4,8] => [7,8,6,2,3,4,5,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[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] => [7,8,6,1,3,4,5,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[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] => [7,8,6,1,2,4,5,3] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[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] => [7,8,6,1,2,3,4,5] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[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] => [7,8,5,6,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.]
[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] => [7,8,5,6,4,3,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[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] => [7,8,5,6,4,1,3,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[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] => [7,8,5,6,4,1,2,3] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[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] => [7,8,5,6,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[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] => [7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [2,1,4,3,7,5,6,8] => [7,8,5,6,2,4,3,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[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] => [7,8,5,6,1,4,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[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] => [7,8,5,6,1,4,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [2,1,4,3,7,6,5,8] => [7,8,5,6,2,3,4,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[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] => [7,8,5,6,1,3,4,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[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] => [7,8,5,6,1,2,4,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[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] => [7,8,5,6,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[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] => [7,8,4,6,5,3,1,2] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[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] => [7,8,3,6,5,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[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] => [7,8,2,6,5,4,3,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.]
[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] => [7,8,1,6,5,4,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => [2,1,8,3,4,7,5,6] => [7,8,1,6,5,2,4,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[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] => [7,8,1,6,5,2,3,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[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] => [7,8,3,6,4,5,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,7,1,2] => [2,1,7,3,5,4,6,8] => [7,8,2,6,4,5,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.]
[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] => [7,8,1,6,4,5,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[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] => [7,8,2,6,3,5,4,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[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] => [7,8,1,6,3,5,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[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] => [7,8,1,6,2,5,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[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] => [7,8,1,6,2,5,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,1,2] => [2,1,8,3,6,5,4,7] => [7,8,1,6,3,4,5,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[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] => [7,8,1,6,2,4,5,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[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] => [7,8,1,6,2,3,5,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[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] => [7,8,1,6,2,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[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] => [7,8,4,5,6,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[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] => [7,8,4,5,6,2,3,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,1,2] => [2,1,5,4,3,8,6,7] => [7,8,4,5,6,1,3,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[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] => [7,8,4,5,6,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => [2,1,8,4,3,5,6,7] => [7,8,1,5,6,4,3,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]]
[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] => [7,8,1,5,6,4,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[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] => [7,8,1,5,6,3,4,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[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] => [7,8,1,5,6,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => [2,1,6,5,3,4,7,8] => [7,8,3,4,6,5,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.]
[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] => [7,8,3,4,6,5,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[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] => [7,8,1,4,6,5,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[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] => [7,8,1,2,6,5,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[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] => [7,8,1,2,6,5,3,4] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,7,1,2] => [2,1,7,6,3,5,4,8] => [7,8,2,3,6,4,5,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[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] => [7,8,1,3,6,4,5,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [2,1,6,5,4,3,7,8] => [7,8,3,4,5,6,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[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] => [7,8,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[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] => [7,8,1,4,5,6,3,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[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] => [7,8,1,4,5,6,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[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] => [7,8,1,2,5,6,3,4] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[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] => [7,8,2,3,4,6,5,1] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[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] => [7,8,1,2,4,6,5,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[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] => [7,8,1,2,3,6,5,4] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[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] => [7,8,1,2,3,6,4,5] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[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] => [7,8,2,3,4,5,6,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[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] => [7,8,1,3,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[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] => [7,8,1,2,4,5,6,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[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] => [7,8,1,2,3,5,6,4] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[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] => [7,8,1,2,3,4,6,5] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[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] => [7,8,1,2,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[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] => [6,8,7,5,4,3,2,1] => [[[[[[.,[[.,.],.]],.],.],.],.],.]
[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] => [6,8,7,5,4,3,1,2] => [[[[[.,[[.,.],.]],.],.],.],[.,.]]
[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] => [6,8,7,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],[[.,.],.]]
[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] => [6,8,7,5,3,4,1,2] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[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] => [6,8,7,5,1,4,3,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]]
[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] => [6,8,7,5,1,3,4,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[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] => [6,8,7,5,1,2,4,3] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[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] => [6,8,7,5,1,2,3,4] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [3,1,2,5,4,6,7,8] => [6,8,7,4,5,3,2,1] => [[[[[.,[[.,.],.]],[.,.]],.],.],.]
[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] => [6,8,7,4,5,3,1,2] => [[[[.,[[.,.],.]],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,1,3] => [3,1,2,5,4,8,6,7] => [6,8,7,4,5,1,3,2] => [[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,1,3] => [3,1,2,6,4,5,7,8] => [6,8,7,3,5,4,2,1] => [[[[.,[[.,.],.]],[[.,.],.]],.],.]
[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] => [6,8,7,2,5,4,3,1] => [[[.,[[.,.],.]],[[[.,.],.],.]],.]
[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] => [6,8,7,1,5,4,3,2] => [[.,[[.,.],.]],[[[[.,.],.],.],.]]
[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] => [6,8,7,1,5,4,2,3] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [3,1,2,8,4,7,6,5] => [6,8,7,1,5,2,3,4] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,1,3] => [3,1,2,6,5,4,7,8] => [6,8,7,3,4,5,2,1] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,1,3] => [3,1,2,6,5,4,8,7] => [6,8,7,3,4,5,1,2] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[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] => [6,8,7,2,4,5,3,1] => [[[.,[[.,.],.]],[[.,[.,.]],.]],.]
[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] => [6,8,7,2,3,5,4,1] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.]
[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] => [6,8,7,1,3,5,4,2] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [3,1,2,7,6,5,4,8] => [6,8,7,2,3,4,5,1] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.]
[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] => [6,8,7,1,3,4,5,2] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[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] => [6,8,7,1,2,3,4,5] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[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] => [5,8,7,6,4,3,2,1] => [[[[[.,[[[.,.],.],.]],.],.],.],.]
[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] => [5,8,7,6,4,3,1,2] => [[[[.,[[[.,.],.],.]],.],.],[.,.]]
[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] => [5,8,7,6,4,2,3,1] => [[[[.,[[[.,.],.],.]],.],[.,.]],.]
[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] => [5,8,7,6,4,1,3,2] => [[[.,[[[.,.],.],.]],.],[[.,.],.]]
[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] => [5,8,7,6,4,1,2,3] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[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] => [5,8,7,6,3,4,2,1] => [[[[.,[[[.,.],.],.]],[.,.]],.],.]
[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] => [5,8,7,6,3,4,1,2] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[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] => [5,8,7,6,2,4,3,1] => [[[.,[[[.,.],.],.]],[[.,.],.]],.]
[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] => [5,8,7,6,1,4,3,2] => [[.,[[[.,.],.],.]],[[[.,.],.],.]]
[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] => [5,8,7,6,1,4,2,3] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[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] => [5,8,7,6,2,3,4,1] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.]
[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] => [5,8,7,6,1,3,4,2] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[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] => [5,8,7,6,1,2,4,3] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[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] => [5,8,7,6,1,2,3,4] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[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] => [4,8,7,6,5,3,2,1] => [[[[.,[[[[.,.],.],.],.]],.],.],.]
[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] => [4,8,7,6,5,3,1,2] => [[[.,[[[[.,.],.],.],.]],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [5,1,2,3,4,7,6,8] => [4,8,7,6,5,2,3,1] => [[[.,[[[[.,.],.],.],.]],[.,.]],.]
[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] => [4,8,7,6,5,1,3,2] => [[.,[[[[.,.],.],.],.]],[[.,.],.]]
[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] => [4,8,7,6,5,1,2,3] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[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] => [3,8,7,6,5,4,2,1] => [[[.,[[[[[.,.],.],.],.],.]],.],.]
[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] => [3,8,7,6,5,4,1,2] => [[.,[[[[[.,.],.],.],.],.]],[.,.]]
[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] => [2,8,7,6,5,4,3,1] => [[.,[[[[[[.,.],.],.],.],.],.]],.]
[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] => [1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]]
[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] => [1,8,7,6,5,4,2,3] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[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] => [2,8,7,6,5,3,4,1] => [[.,[[[[[.,.],.],.],.],[.,.]]],.]
[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] => [1,8,7,6,5,3,4,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]]
[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] => [1,8,7,6,5,2,4,3] => [.,[[[[[.,.],.],.],.],[[.,.],.]]]
[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] => [1,8,7,6,5,2,3,4] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[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] => [3,8,7,6,4,5,2,1] => [[[.,[[[[.,.],.],.],[.,.]]],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => [6,1,2,3,5,4,8,7] => [3,8,7,6,4,5,1,2] => [[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[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] => [2,8,7,6,4,5,3,1] => [[.,[[[[[.,.],.],.],[.,.]],.]],.]
[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] => [1,8,7,6,4,5,3,2] => [.,[[[[[[.,.],.],.],[.,.]],.],.]]
[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] => [1,8,7,6,4,5,2,3] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[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] => [1,8,7,6,3,5,4,2] => [.,[[[[[.,.],.],.],[[.,.],.]],.]]
[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] => [1,8,7,6,2,5,4,3] => [.,[[[[.,.],.],.],[[[.,.],.],.]]]
[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] => [2,8,7,6,3,4,5,1] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[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] => [1,8,7,6,3,4,5,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[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] => [1,8,7,6,2,4,5,3] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]]
[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] => [1,8,7,6,2,3,4,5] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[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] => [4,8,7,5,6,3,2,1] => [[[[.,[[[.,.],.],[.,.]]],.],.],.]
[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] => [4,8,7,5,6,3,1,2] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,1,5] => [5,1,2,4,3,8,6,7] => [4,8,7,5,6,1,3,2] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[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] => [3,8,7,5,6,4,2,1] => [[[.,[[[[.,.],.],[.,.]],.]],.],.]
[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] => [3,8,7,5,6,4,1,2] => [[.,[[[[.,.],.],[.,.]],.]],[.,.]]
[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] => [2,8,7,5,6,4,3,1] => [[.,[[[[[.,.],.],[.,.]],.],.]],.]
[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] => [1,8,7,5,6,4,3,2] => [.,[[[[[[.,.],.],[.,.]],.],.],.]]
[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] => [1,8,7,5,6,4,2,3] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [7,1,2,4,3,6,5,8] => [2,8,7,5,6,3,4,1] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[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] => [1,8,7,5,6,3,4,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[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] => [1,8,7,5,6,2,3,4] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,1,6] => [6,1,2,5,3,4,8,7] => [3,8,7,4,6,5,1,2] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[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] => [2,8,7,4,6,5,3,1] => [[.,[[[[.,.],.],[[.,.],.]],.]],.]
[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] => [1,8,7,4,6,5,3,2] => [.,[[[[[.,.],.],[[.,.],.]],.],.]]
[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] => [1,8,7,3,6,5,4,2] => [.,[[[[.,.],.],[[[.,.],.],.]],.]]
[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] => [1,8,7,2,6,5,4,3] => [.,[[[.,.],.],[[[[.,.],.],.],.]]]
[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] => [1,8,7,2,6,5,3,4] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[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] => [1,8,7,2,6,4,5,3] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[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] => [1,8,7,2,6,3,5,4] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[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] => [1,8,7,2,6,3,4,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[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] => [3,8,7,4,5,6,1,2] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,1,7] => [7,1,2,5,4,3,6,8] => [2,8,7,4,5,6,3,1] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[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] => [1,8,7,4,5,6,3,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,2,1,8] => [8,1,2,5,4,3,7,6] => [1,8,7,4,5,6,2,3] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,1,8] => [8,1,2,7,4,3,5,6] => [1,8,7,2,5,6,4,3] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]]
[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] => [1,8,7,2,5,6,3,4] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[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] => [2,8,7,3,4,6,5,1] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[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] => [1,8,7,3,4,6,5,2] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[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] => [1,8,7,2,3,6,5,4] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[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] => [1,8,7,2,3,6,4,5] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[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] => [2,8,7,3,4,5,6,1] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[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] => [1,8,7,3,4,5,6,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[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] => [1,8,7,2,4,5,6,3] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,2,1,8] => [8,1,2,7,6,4,3,5] => [1,8,7,2,3,5,6,4] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,1,8] => [8,1,2,7,6,5,3,4] => [1,8,7,2,3,4,6,5] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[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] => [1,8,7,2,3,4,5,6] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[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] => [5,8,6,7,4,3,2,1] => [[[[[.,[[.,.],[.,.]]],.],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [4,1,3,2,5,6,8,7] => [5,8,6,7,4,3,1,2] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [4,1,3,2,5,8,6,7] => [5,8,6,7,4,1,3,2] => [[[.,[[.,.],[.,.]]],.],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => [4,1,3,2,5,8,7,6] => [5,8,6,7,4,1,2,3] => [[[.,[[.,.],[.,.]]],.],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [4,1,3,2,6,5,7,8] => [5,8,6,7,3,4,2,1] => [[[[.,[[.,.],[.,.]]],[.,.]],.],.]
[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] => [5,8,6,7,3,4,1,2] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[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] => [5,8,6,7,1,4,3,2] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[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] => [5,8,6,7,1,4,2,3] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[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] => [5,8,6,7,1,3,4,2] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[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] => [5,8,6,7,1,2,3,4] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [5,1,3,2,4,6,7,8] => [4,8,6,7,5,3,2,1] => [[[[.,[[[.,.],[.,.]],.]],.],.],.]
[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] => [4,8,6,7,5,3,1,2] => [[[.,[[[.,.],[.,.]],.]],.],[.,.]]
[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] => [4,8,6,7,5,1,3,2] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [5,1,3,2,4,8,7,6] => [4,8,6,7,5,1,2,3] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,1,6] => [6,1,3,2,4,5,7,8] => [3,8,6,7,5,4,2,1] => [[[.,[[[[.,.],[.,.]],.],.]],.],.]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,3,1,6] => [6,1,3,2,4,5,8,7] => [3,8,6,7,5,4,1,2] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[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] => [2,8,6,7,5,4,3,1] => [[.,[[[[[.,.],[.,.]],.],.],.]],.]
[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] => [1,8,6,7,5,4,3,2] => [.,[[[[[[.,.],[.,.]],.],.],.],.]]
[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] => [1,8,6,7,5,4,2,3] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [7,1,3,2,4,6,5,8] => [2,8,6,7,5,3,4,1] => [[.,[[[[.,.],[.,.]],.],[.,.]]],.]
[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] => [1,8,6,7,5,3,4,2] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[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] => [1,8,6,7,5,2,3,4] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]]
[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] => [3,8,6,7,4,5,1,2] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[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] => [1,8,6,7,4,5,3,2] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]]
[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] => [1,8,6,7,4,5,2,3] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [8,1,3,2,7,4,5,6] => [1,8,6,7,2,5,4,3] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[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] => [1,8,6,7,2,5,3,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[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] => [1,8,6,7,3,4,5,2] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[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] => [1,8,6,7,2,3,4,5] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[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] => [4,8,5,7,6,3,2,1] => [[[[.,[[.,.],[[.,.],.]]],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,1,5] => [5,1,4,2,3,6,8,7] => [4,8,5,7,6,3,1,2] => [[[.,[[.,.],[[.,.],.]]],.],[.,.]]
[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] => [3,8,5,7,6,4,2,1] => [[[.,[[[.,.],[[.,.],.]],.]],.],.]
[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] => [2,8,5,7,6,4,3,1] => [[.,[[[[.,.],[[.,.],.]],.],.]],.]
[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] => [1,8,5,7,6,4,3,2] => [.,[[[[[.,.],[[.,.],.]],.],.],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,4,1,7] => [7,1,4,2,3,6,5,8] => [2,8,5,7,6,3,4,1] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[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] => [1,8,5,7,6,2,4,3] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[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] => [1,8,5,7,6,2,3,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[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] => [3,8,4,7,6,5,2,1] => [[[.,[[.,.],[[[.,.],.],.]]],.],.]
[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] => [3,8,4,7,6,5,1,2] => [[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,1,7] => [7,1,5,2,3,4,6,8] => [2,8,4,7,6,5,3,1] => [[.,[[[.,.],[[[.,.],.],.]],.]],.]
[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] => [1,8,4,7,6,5,3,2] => [.,[[[[.,.],[[[.,.],.],.]],.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [8,1,5,2,3,4,7,6] => [1,8,4,7,6,5,2,3] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[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] => [2,8,3,7,6,5,4,1] => [[.,[[.,.],[[[[.,.],.],.],.]]],.]
[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] => [1,8,3,7,6,5,4,2] => [.,[[[.,.],[[[[.,.],.],.],.]],.]]
[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] => [1,8,2,7,6,5,4,3] => [.,[[.,.],[[[[[.,.],.],.],.],.]]]
[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] => [1,8,3,7,6,4,5,2] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,2,7,1,8] => [8,1,7,2,3,5,4,6] => [1,8,2,7,6,4,5,3] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[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] => [1,8,2,7,6,3,5,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[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] => [1,8,2,7,6,3,4,5] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => [6,1,5,2,4,3,7,8] => [3,8,4,7,5,6,2,1] => [[[.,[[.,.],[[.,.],[.,.]]]],.],.]
[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] => [3,8,4,7,5,6,1,2] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[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] => [1,8,4,7,5,6,2,3] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,1,7] => [7,1,6,2,4,3,5,8] => [2,8,3,7,5,6,4,1] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.]
[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] => [1,8,3,7,5,6,4,2] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[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] => [1,8,2,7,5,6,3,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[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] => [2,8,3,7,4,6,5,1] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[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] => [1,8,3,7,4,6,5,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[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] => [1,8,2,7,4,6,5,3] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[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] => [1,8,2,7,3,6,5,4] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[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] => [1,8,2,7,3,6,4,5] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[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] => [2,8,3,7,4,5,6,1] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,6,1,8] => [8,1,6,2,5,4,3,7] => [1,8,3,7,4,5,6,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[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] => [1,8,2,7,4,5,6,3] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[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] => [1,8,2,7,3,5,6,4] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [8,1,7,2,6,5,3,4] => [1,8,2,7,3,4,6,5] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[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] => [1,8,2,7,3,4,5,6] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [5,1,4,3,2,7,6,8] => [4,8,5,6,7,2,3,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [6,1,4,3,2,5,8,7] => [3,8,5,6,7,4,1,2] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[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] => [2,8,5,6,7,4,3,1] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.]
[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] => [1,8,5,6,7,4,3,2] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]]
[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] => [1,8,5,6,7,2,3,4] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[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] => [1,8,4,6,7,5,3,2] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]]
[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] => [1,8,4,6,7,5,2,3] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => [7,1,6,3,2,4,5,8] => [2,8,3,6,7,5,4,1] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,1,8] => [8,1,6,3,2,4,5,7] => [1,8,3,6,7,5,4,2] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]]
[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] => [1,8,2,6,7,5,4,3] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]]
[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] => [1,8,3,6,7,4,5,2] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]
[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] => [1,8,2,6,7,4,5,3] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]]
[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] => [1,8,2,6,7,3,4,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[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] => [2,8,3,5,7,6,4,1] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[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] => [1,8,3,5,7,6,4,2] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]]
[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] => [1,8,2,5,7,6,4,3] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]]
[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] => [1,8,2,5,7,6,3,4] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[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] => [1,8,3,4,7,6,5,2] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]]
[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] => [1,8,2,4,7,6,5,3] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]]
[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] => [1,8,2,3,7,6,5,4] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,1,8] => [8,1,7,6,2,3,5,4] => [1,8,2,3,7,6,4,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[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] => [2,8,3,4,7,5,6,1] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[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] => [1,8,2,4,7,5,6,3] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[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] => [1,8,2,3,7,5,6,4] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [6,1,5,4,3,2,7,8] => [3,8,4,5,6,7,2,1] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,1,7] => [7,1,5,4,3,2,6,8] => [2,8,4,5,6,7,3,1] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[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] => [1,8,4,5,6,7,3,2] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[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] => [1,8,4,5,6,7,2,3] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => [7,1,6,4,3,2,5,8] => [2,8,3,5,6,7,4,1] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,1,8] => [8,1,6,4,3,2,5,7] => [1,8,3,5,6,7,4,2] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,1,8] => [8,1,7,4,3,2,5,6] => [1,8,2,5,6,7,4,3] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]]
[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] => [1,8,2,5,6,7,3,4] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [8,1,6,5,3,2,4,7] => [1,8,3,4,6,7,5,2] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]]
[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] => [1,8,2,4,6,7,5,3] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]]
[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] => [1,8,2,3,6,7,5,4] => [.,[[.,.],[.,[[[.,[.,.]],.],.]]]]
[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] => [2,8,3,4,5,7,6,1] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[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] => [1,8,2,4,5,7,6,3] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[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] => [1,8,2,3,4,7,6,5] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[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] => [1,8,2,3,4,7,5,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[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] => [2,8,3,4,5,6,7,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[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] => [1,8,3,4,5,6,7,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[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] => [1,8,2,4,5,6,7,3] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[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] => [1,8,2,3,5,6,7,4] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[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] => [1,8,2,3,4,6,7,5] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[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] => [1,8,2,3,4,5,7,6] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[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] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[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] => [6,7,8,5,4,3,2,1] => [[[[[[.,[.,[.,.]]],.],.],.],.],.]
[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] => [6,7,8,5,4,3,1,2] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[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] => [6,7,8,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [3,2,1,4,6,5,8,7] => [6,7,8,5,3,4,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[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] => [6,7,8,5,1,4,3,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[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] => [6,7,8,5,1,4,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[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] => [6,7,8,5,2,3,4,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [3,2,1,4,8,7,5,6] => [6,7,8,5,1,2,4,3] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[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] => [6,7,8,5,1,2,3,4] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,1,2,3] => [3,2,1,5,4,6,8,7] => [6,7,8,4,5,3,1,2] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[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] => [6,7,8,4,5,2,3,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [3,2,1,5,4,8,7,6] => [6,7,8,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[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] => [6,7,8,3,5,4,2,1] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.]
[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] => [6,7,8,2,5,4,3,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.]
[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] => [6,7,8,1,5,4,3,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[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] => [6,7,8,1,5,4,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[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] => [6,7,8,1,5,3,4,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[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] => [6,7,8,1,5,2,4,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[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] => [6,7,8,1,5,2,3,4] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[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] => [6,7,8,3,4,5,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[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] => [6,7,8,2,4,5,3,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.]
[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] => [6,7,8,1,4,5,3,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[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] => [6,7,8,1,4,5,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[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] => [6,7,8,2,3,5,4,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.]
[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] => [6,7,8,1,3,5,4,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[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] => [6,7,8,1,2,5,4,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[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] => [6,7,8,1,2,5,3,4] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[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] => [6,7,8,2,3,4,5,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[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] => [6,7,8,1,3,4,5,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[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] => [6,7,8,1,2,4,5,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[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] => [6,7,8,1,2,3,5,4] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[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] => [6,7,8,1,2,3,4,5] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[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] => [5,7,8,6,4,3,2,1] => [[[[[.,[[.,[.,.]],.]],.],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [4,2,1,3,5,7,6,8] => [5,7,8,6,4,2,3,1] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.]
[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] => [5,7,8,6,4,1,2,3] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[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] => [5,7,8,6,3,4,2,1] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.]
[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] => [5,7,8,6,3,4,1,2] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[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] => [5,7,8,6,1,4,3,2] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[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] => [5,7,8,6,1,4,2,3] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,1,2,4] => [4,2,1,3,7,6,5,8] => [5,7,8,6,2,3,4,1] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[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] => [5,7,8,6,1,3,4,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[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] => [5,7,8,6,1,2,4,3] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[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] => [5,7,8,6,1,2,3,4] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]
[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] => [4,7,8,6,5,3,2,1] => [[[[.,[[[.,[.,.]],.],.]],.],.],.]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,1,2,5] => [5,2,1,3,4,8,6,7] => [4,7,8,6,5,1,3,2] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[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] => [4,7,8,6,5,1,2,3] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [6,2,1,3,4,5,7,8] => [3,7,8,6,5,4,2,1] => [[[.,[[[[.,[.,.]],.],.],.]],.],.]
[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] => [2,7,8,6,5,4,3,1] => [[.,[[[[[.,[.,.]],.],.],.],.]],.]
[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] => [1,7,8,6,5,4,3,2] => [.,[[[[[[.,[.,.]],.],.],.],.],.]]
[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] => [1,7,8,6,5,4,2,3] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[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] => [1,7,8,6,5,3,4,2] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]]
[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] => [1,7,8,6,5,2,4,3] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => [8,2,1,3,5,4,6,7] => [1,7,8,6,4,5,3,2] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,1,2,7] => [7,2,1,3,6,4,5,8] => [2,7,8,6,3,5,4,1] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.]
[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] => [1,7,8,6,3,5,4,2] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,1,2,8] => [8,2,1,3,7,4,5,6] => [1,7,8,6,2,5,4,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]]
[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] => [1,7,8,6,3,4,5,2] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]]
[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] => [1,7,8,6,2,3,5,4] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[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] => [1,7,8,6,2,3,4,5] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [5,2,1,4,3,7,6,8] => [4,7,8,5,6,2,3,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[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] => [4,7,8,5,6,1,3,2] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[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] => [4,7,8,5,6,1,2,3] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[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] => [3,7,8,5,6,4,2,1] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [8,2,1,4,3,5,6,7] => [1,7,8,5,6,4,3,2] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]]
[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] => [1,7,8,5,6,4,2,3] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[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] => [2,7,8,5,6,3,4,1] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]
[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] => [1,7,8,5,6,3,4,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,1,2,8] => [8,2,1,5,3,4,7,6] => [1,7,8,4,6,5,2,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[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] => [1,7,8,3,6,5,4,2] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]]
[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] => [2,7,8,3,6,4,5,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,1,2,8] => [8,2,1,6,3,5,4,7] => [1,7,8,3,6,4,5,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]]
[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] => [1,7,8,2,6,4,5,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[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] => [3,7,8,4,5,6,2,1] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.]
[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] => [3,7,8,4,5,6,1,2] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[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] => [2,7,8,4,5,6,3,1] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.]
[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] => [1,7,8,4,5,6,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[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] => [1,7,8,3,5,6,4,2] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]
[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] => [1,7,8,2,5,6,3,4] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[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] => [1,7,8,2,3,6,5,4] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]]
[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] => [1,7,8,2,3,6,4,5] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[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] => [2,7,8,3,4,5,6,1] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,1,2,8] => [8,2,1,6,5,4,3,7] => [1,7,8,3,4,5,6,2] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[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] => [1,7,8,2,4,5,6,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[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] => [1,7,8,2,3,5,6,4] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[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] => [1,7,8,2,3,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[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] => [5,6,8,7,4,3,2,1] => [[[[[.,[.,[[.,.],.]]],.],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [4,3,1,2,5,6,8,7] => [5,6,8,7,4,3,1,2] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [4,3,1,2,5,8,7,6] => [5,6,8,7,4,1,2,3] => [[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[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] => [5,6,8,7,3,4,1,2] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [4,3,1,2,7,5,6,8] => [5,6,8,7,2,4,3,1] => [[[.,[.,[[.,.],.]]],[[.,.],.]],.]
[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] => [5,6,8,7,1,4,3,2] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[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] => [5,6,8,7,1,4,2,3] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[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] => [5,6,8,7,1,3,4,2] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[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] => [5,6,8,7,1,2,4,3] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[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] => [5,6,8,7,1,2,3,4] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[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] => [4,6,8,7,5,3,2,1] => [[[[.,[[.,[[.,.],.]],.]],.],.],.]
[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] => [4,6,8,7,5,3,1,2] => [[[.,[[.,[[.,.],.]],.]],.],[.,.]]
[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] => [4,6,8,7,5,1,2,3] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[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] => [3,6,8,7,5,4,2,1] => [[[.,[[[.,[[.,.],.]],.],.]],.],.]
[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] => [3,6,8,7,5,4,1,2] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[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] => [2,6,8,7,5,4,3,1] => [[.,[[[[.,[[.,.],.]],.],.],.]],.]
[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] => [1,6,8,7,5,4,3,2] => [.,[[[[[.,[[.,.],.]],.],.],.],.]]
[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] => [2,6,8,7,5,3,4,1] => [[.,[[[.,[[.,.],.]],.],[.,.]]],.]
[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] => [1,6,8,7,5,3,4,2] => [.,[[[[.,[[.,.],.]],.],[.,.]],.]]
[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] => [1,6,8,7,5,2,4,3] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[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] => [1,6,8,7,5,2,3,4] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]]
[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] => [1,6,8,7,4,5,3,2] => [.,[[[[.,[[.,.],.]],[.,.]],.],.]]
[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] => [1,6,8,7,3,5,4,2] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]]
[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] => [1,6,8,7,2,5,4,3] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,1,3,8] => [8,3,1,2,7,4,6,5] => [1,6,8,7,2,5,3,4] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [7,3,1,2,6,5,4,8] => [2,6,8,7,3,4,5,1] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.]
[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] => [1,6,8,7,3,4,5,2] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]]
[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] => [1,6,8,7,2,3,5,4] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]]
[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] => [1,6,8,7,2,3,4,5] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]
[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] => [4,5,8,7,6,3,2,1] => [[[[.,[.,[[[.,.],.],.]]],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [5,4,1,2,3,6,8,7] => [4,5,8,7,6,3,1,2] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]]
[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] => [4,5,8,7,6,1,3,2] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[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] => [4,5,8,7,6,1,2,3] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[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] => [3,5,8,7,6,4,2,1] => [[[.,[[.,[[[.,.],.],.]],.]],.],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [6,4,1,2,3,5,8,7] => [3,5,8,7,6,4,1,2] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[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] => [2,5,8,7,6,4,3,1] => [[.,[[[.,[[[.,.],.],.]],.],.]],.]
[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] => [1,5,8,7,6,4,3,2] => [.,[[[[.,[[[.,.],.],.]],.],.],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,1,4,8] => [8,4,1,2,3,6,5,7] => [1,5,8,7,6,3,4,2] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]]
[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] => [1,5,8,7,6,2,4,3] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,1,4,8] => [8,4,1,2,3,7,6,5] => [1,5,8,7,6,2,3,4] => [.,[[.,[[[.,.],.],.]],[.,[.,.]]]]
[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] => [3,4,8,7,6,5,1,2] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[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] => [2,4,8,7,6,5,3,1] => [[.,[[.,[[[[.,.],.],.],.]],.]],.]
[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] => [1,4,8,7,6,5,3,2] => [.,[[[.,[[[[.,.],.],.],.]],.],.]]
[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] => [2,3,8,7,6,5,4,1] => [[.,[.,[[[[[.,.],.],.],.],.]]],.]
[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] => [1,3,8,7,6,5,4,2] => [.,[[.,[[[[[.,.],.],.],.],.]],.]]
[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] => [1,2,8,7,6,5,4,3] => [.,[.,[[[[[[.,.],.],.],.],.],.]]]
[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] => [1,2,8,7,6,3,5,4] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[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] => [1,2,8,7,6,3,4,5] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [6,5,1,2,4,3,7,8] => [3,4,8,7,5,6,2,1] => [[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[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] => [3,4,8,7,5,6,1,2] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [7,5,1,2,4,3,6,8] => [2,4,8,7,5,6,3,1] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.]
[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] => [1,3,8,7,5,6,4,2] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]]
[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] => [1,2,8,7,5,6,4,3] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[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] => [1,2,8,7,5,6,3,4] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[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] => [1,3,8,7,4,6,5,2] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]]
[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] => [1,2,8,7,4,6,5,3] => [.,[.,[[[[.,.],.],[[.,.],.]],.]]]
[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] => [1,2,8,7,3,6,5,4] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[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] => [2,3,8,7,4,5,6,1] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[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] => [1,3,8,7,4,5,6,2] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]]
[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] => [1,2,8,7,4,5,6,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[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] => [1,2,8,7,3,4,6,5] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[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] => [1,2,8,7,3,4,5,6] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [5,4,1,3,2,7,6,8] => [4,5,8,6,7,2,3,1] => [[[.,[.,[[.,.],[.,.]]]],[.,.]],.]
[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] => [4,5,8,6,7,1,2,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[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] => [2,5,8,6,7,4,3,1] => [[.,[[[.,[[.,.],[.,.]]],.],.]],.]
[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] => [1,5,8,6,7,4,2,3] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[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] => [2,5,8,6,7,3,4,1] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.]
[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] => [1,5,8,6,7,3,4,2] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]]
[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] => [1,4,8,6,7,5,3,2] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]]
[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] => [1,4,8,6,7,5,2,3] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,1,6,7] => [7,6,1,3,2,4,5,8] => [2,3,8,6,7,5,4,1] => [[.,[.,[[[[.,.],[.,.]],.],.]]],.]
[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] => [1,2,8,6,7,5,4,3] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]]
[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] => [1,2,8,6,7,5,3,4] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,1,6,8] => [8,6,1,3,2,5,4,7] => [1,3,8,6,7,4,5,2] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]]
[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] => [1,2,8,6,7,3,5,4] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[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] => [3,4,8,5,7,6,1,2] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[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] => [2,4,8,5,7,6,3,1] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.]
[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] => [1,4,8,5,7,6,3,2] => [.,[[[.,[[.,.],[[.,.],.]]],.],.]]
[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] => [1,4,8,5,7,6,2,3] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[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] => [2,3,8,5,7,6,4,1] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[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] => [1,3,8,5,7,6,4,2] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]]
[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] => [1,2,8,4,7,6,5,3] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[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] => [1,2,8,3,7,6,5,4] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[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] => [1,2,8,3,7,6,4,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[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] => [2,3,8,4,7,5,6,1] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[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] => [1,2,8,3,7,4,6,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[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] => [1,2,8,3,7,4,5,6] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[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] => [3,4,8,5,6,7,2,1] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[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] => [3,4,8,5,6,7,1,2] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => [8,5,1,4,3,2,7,6] => [1,4,8,5,6,7,2,3] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[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] => [2,3,8,5,6,7,4,1] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[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] => [1,3,8,5,6,7,4,2] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [8,7,1,4,3,2,5,6] => [1,2,8,5,6,7,4,3] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]]
[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] => [1,2,8,5,6,7,3,4] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [7,6,1,5,3,2,4,8] => [2,3,8,4,6,7,5,1] => [[.,[.,[[.,.],[[.,[.,.]],.]]]],.]
[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] => [1,3,8,4,6,7,5,2] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,1,7,8] => [8,7,1,5,3,2,4,6] => [1,2,8,4,6,7,5,3] => [.,[.,[[[.,.],[[.,[.,.]],.]],.]]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,1,7,8] => [8,7,1,6,3,2,5,4] => [1,2,8,3,6,7,4,5] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[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] => [1,2,8,3,5,7,6,4] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[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] => [1,2,8,3,4,7,6,5] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [7,6,1,5,4,3,2,8] => [2,3,8,4,5,6,7,1] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[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] => [1,3,8,4,5,6,7,2] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [8,7,1,5,4,3,2,6] => [1,2,8,4,5,6,7,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[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] => [1,2,8,3,5,6,7,4] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[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] => [1,2,8,3,4,6,7,5] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [8,7,1,6,5,4,2,3] => [1,2,8,3,4,5,7,6] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[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] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[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] => [5,6,7,8,4,3,2,1] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[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] => [5,6,7,8,4,3,1,2] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[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] => [5,6,7,8,4,2,3,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[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] => [5,6,7,8,4,1,3,2] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[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] => [5,6,7,8,4,1,2,3] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[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] => [5,6,7,8,3,4,2,1] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[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] => [5,6,7,8,3,4,1,2] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[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] => [5,6,7,8,2,4,3,1] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]
[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] => [5,6,7,8,1,4,3,2] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[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] => [5,6,7,8,1,4,2,3] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[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] => [5,6,7,8,2,3,4,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[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] => [5,6,7,8,1,3,4,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[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] => [5,6,7,8,1,2,4,3] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[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] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[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] => [4,6,7,8,5,2,3,1] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.]
[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] => [4,6,7,8,5,1,3,2] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[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] => [3,6,7,8,5,4,1,2] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]]
[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] => [2,6,7,8,5,4,3,1] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.]
[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] => [1,6,7,8,5,4,3,2] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[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] => [2,6,7,8,5,3,4,1] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.]
[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] => [1,6,7,8,5,3,4,2] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]]
[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] => [1,6,7,8,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[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] => [3,6,7,8,4,5,2,1] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]
[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] => [1,6,7,8,4,5,3,2] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]]
[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] => [1,6,7,8,3,5,4,2] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[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] => [1,6,7,8,2,5,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[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] => [1,6,7,8,3,4,5,2] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,1,2,3,8] => [8,3,2,1,7,5,4,6] => [1,6,7,8,2,4,5,3] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[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] => [1,6,7,8,2,3,5,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[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] => [1,6,7,8,2,3,4,5] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[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] => [3,5,7,8,6,4,2,1] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.]
[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] => [1,5,7,8,6,4,2,3] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [7,4,2,1,3,6,5,8] => [2,5,7,8,6,3,4,1] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.]
[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] => [1,5,7,8,6,3,4,2] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
[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] => [1,5,7,8,6,2,4,3] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[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] => [1,5,7,8,6,2,3,4] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [7,5,2,1,3,4,6,8] => [2,4,7,8,6,5,3,1] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.]
[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] => [1,4,7,8,6,5,3,2] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => [8,6,2,1,3,4,5,7] => [1,3,7,8,6,5,4,2] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]]
[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] => [1,2,7,8,6,5,4,3] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[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] => [1,2,7,8,6,5,3,4] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]]
[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] => [1,2,7,8,6,4,5,3] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]]
[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] => [1,2,7,8,6,3,5,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[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] => [1,2,7,8,6,3,4,5] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[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] => [3,4,7,8,5,6,1,2] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => [7,5,2,1,4,3,6,8] => [2,4,7,8,5,6,3,1] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.]
[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] => [1,4,7,8,5,6,3,2] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]]
[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] => [1,4,7,8,5,6,2,3] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[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] => [1,3,7,8,5,6,4,2] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]
[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] => [1,2,7,8,5,6,4,3] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]]
[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] => [1,2,7,8,5,6,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[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] => [1,3,7,8,4,6,5,2] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]]
[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] => [1,2,7,8,3,6,5,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,1,2,7,8] => [8,7,2,1,6,3,5,4] => [1,2,7,8,3,6,4,5] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[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] => [1,3,7,8,4,5,6,2] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]
[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] => [1,2,7,8,4,5,6,3] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,1,2,7,8] => [8,7,2,1,6,4,3,5] => [1,2,7,8,3,5,6,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [8,7,2,1,6,5,3,4] => [1,2,7,8,3,4,6,5] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[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] => [1,2,7,8,3,4,5,6] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[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] => [4,5,6,8,7,3,2,1] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.]
[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] => [3,5,6,8,7,4,2,1] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[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] => [3,5,6,8,7,4,1,2] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
[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] => [1,5,6,8,7,4,2,3] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]]
[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] => [2,5,6,8,7,3,4,1] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.]
[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] => [1,5,6,8,7,2,3,4] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]
[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] => [3,4,6,8,7,5,1,2] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]
[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] => [2,4,6,8,7,5,3,1] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[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] => [1,4,6,8,7,5,3,2] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,1,3,6,8] => [8,6,3,1,2,4,5,7] => [1,3,6,8,7,5,4,2] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]]
[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] => [1,2,6,8,7,5,3,4] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]]
[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] => [1,3,6,8,7,4,5,2] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]]
[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] => [1,2,6,8,7,3,5,4] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [8,7,3,1,2,6,5,4] => [1,2,6,8,7,3,4,5] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[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] => [3,4,5,8,7,6,1,2] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[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] => [1,4,5,8,7,6,3,2] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [7,6,4,1,2,3,5,8] => [2,3,5,8,7,6,4,1] => [[.,[.,[[.,[[[.,.],.],.]],.]]],.]
[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] => [1,3,5,8,7,6,4,2] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]]
[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] => [1,2,5,8,7,6,4,3] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]]
[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] => [1,2,5,8,7,6,3,4] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]]
[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] => [2,3,4,8,7,6,5,1] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[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] => [1,3,4,8,7,6,5,2] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[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] => [1,2,4,8,7,6,5,3] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]]
[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] => [1,2,3,8,7,6,5,4] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[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] => [1,2,3,8,7,6,4,5] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[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] => [2,3,4,8,7,5,6,1] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[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] => [1,2,3,8,7,5,6,4] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[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] => [1,2,3,8,7,4,6,5] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[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] => [1,2,3,8,7,4,5,6] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [6,5,4,1,3,2,7,8] => [3,4,5,8,6,7,2,1] => [[[.,[.,[.,[[.,.],[.,.]]]]],.],.]
[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] => [3,4,5,8,6,7,1,2] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[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] => [1,4,5,8,6,7,3,2] => [.,[[[.,[.,[[.,.],[.,.]]]],.],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,1,4,6,7] => [7,6,4,1,3,2,5,8] => [2,3,5,8,6,7,4,1] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,1,4,7,8] => [8,7,4,1,3,2,5,6] => [1,2,5,8,6,7,4,3] => [.,[.,[[[.,[[.,.],[.,.]]],.],.]]]
[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] => [1,2,5,8,6,7,3,4] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[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] => [2,3,4,8,6,7,5,1] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[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] => [1,2,3,8,6,7,5,4] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[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] => [1,2,3,8,6,7,4,5] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[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] => [2,3,4,8,5,7,6,1] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[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] => [1,2,3,8,5,7,6,4] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[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] => [1,2,3,8,4,7,6,5] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[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] => [1,2,3,8,4,7,5,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[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] => [2,3,4,8,5,6,7,1] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[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] => [1,3,4,8,5,6,7,2] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[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] => [1,2,4,8,5,6,7,3] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[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] => [1,2,3,8,5,6,7,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[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] => [1,2,3,8,4,6,7,5] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[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] => [1,2,3,8,4,5,7,6] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[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] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[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] => [4,5,6,7,8,3,2,1] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[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] => [4,5,6,7,8,3,1,2] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[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] => [4,5,6,7,8,2,3,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[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] => [4,5,6,7,8,1,3,2] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[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] => [4,5,6,7,8,1,2,3] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[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] => [3,5,6,7,8,4,2,1] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[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] => [3,5,6,7,8,4,1,2] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[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] => [2,5,6,7,8,4,3,1] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.]
[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] => [1,5,6,7,8,4,3,2] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[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] => [1,5,6,7,8,4,2,3] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[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] => [2,5,6,7,8,3,4,1] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]
[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] => [1,5,6,7,8,3,4,2] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[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] => [1,5,6,7,8,2,4,3] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[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] => [1,5,6,7,8,2,3,4] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[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] => [3,4,6,7,8,5,2,1] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]
[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] => [3,4,6,7,8,5,1,2] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[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] => [2,4,6,7,8,5,3,1] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]
[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] => [1,4,6,7,8,5,3,2] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[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] => [2,3,6,7,8,5,4,1] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.]
[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] => [1,3,6,7,8,5,4,2] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]
[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] => [1,2,6,7,8,5,4,3] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]]
[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] => [1,2,6,7,8,5,3,4] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]
[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] => [1,2,6,7,8,4,5,3] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]
[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] => [1,2,6,7,8,3,5,4] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[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] => [1,2,6,7,8,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[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] => [3,4,5,7,8,6,2,1] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[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] => [3,4,5,7,8,6,1,2] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [8,6,3,1,2,4,5,7] => [7,5,4,2,1,3,6,8] => [2,4,5,7,8,6,3,1] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]
[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] => [2,3,5,7,8,6,4,1] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.]
[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] => [1,3,5,7,8,6,4,2] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]
[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] => [1,2,5,7,8,6,3,4] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[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] => [1,2,4,7,8,6,5,3] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]
[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] => [1,2,3,7,8,6,5,4] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,5,3,1,2,6,7,8] => [8,7,6,2,1,3,5,4] => [1,2,3,7,8,6,4,5] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[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] => [2,3,4,7,8,5,6,1] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,4,1,2,5,7,8] => [8,7,5,2,1,4,3,6] => [1,2,4,7,8,5,6,3] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]
[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] => [1,2,3,7,8,5,6,4] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[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] => [1,2,3,7,8,4,6,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [8,7,6,2,1,5,4,3] => [1,2,3,7,8,4,5,6] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[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] => [3,4,5,6,8,7,2,1] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[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] => [3,4,5,6,8,7,1,2] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [6,7,2,1,3,4,5,8] => [8,5,4,3,1,2,7,6] => [1,4,5,6,8,7,2,3] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[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] => [2,3,5,6,8,7,4,1] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.]
[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] => [1,3,5,6,8,7,4,2] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1,3,4,7,8] => [8,7,4,3,1,2,5,6] => [1,2,5,6,8,7,4,3] => [.,[.,[[[.,[.,[[.,.],.]]],.],.]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [8,7,4,3,1,2,6,5] => [1,2,5,6,8,7,3,4] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [7,6,5,3,1,2,4,8] => [2,3,4,6,8,7,5,1] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.]
[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] => [1,2,4,6,8,7,5,3] => [.,[.,[[.,[[.,[[.,.],.]],.]],.]]]
[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] => [1,2,3,6,8,7,5,4] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [8,7,6,3,1,2,5,4] => [1,2,3,6,8,7,4,5] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[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] => [2,3,4,5,8,7,6,1] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[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] => [1,3,4,5,8,7,6,2] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[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] => [1,2,4,5,8,7,6,3] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]]
[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] => [1,2,3,5,8,7,6,4] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[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] => [1,2,3,4,8,7,6,5] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[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] => [1,2,3,4,8,7,5,6] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[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] => [2,3,4,5,8,6,7,1] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[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] => [1,3,4,5,8,6,7,2] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[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] => [1,2,4,5,8,6,7,3] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[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] => [1,2,3,5,8,6,7,4] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[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] => [1,2,3,4,8,6,7,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[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] => [1,2,3,4,8,5,7,6] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[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] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[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] => [3,4,5,6,7,8,2,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[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] => [3,4,5,6,7,8,1,2] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[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] => [2,4,5,6,7,8,3,1] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]
[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] => [1,4,5,6,7,8,3,2] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[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] => [1,4,5,6,7,8,2,3] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[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] => [2,3,5,6,7,8,4,1] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]
[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] => [1,3,5,6,7,8,4,2] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]
[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] => [1,2,5,6,7,8,4,3] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]
[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] => [1,2,5,6,7,8,3,4] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[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] => [2,3,4,6,7,8,5,1] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]
[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] => [1,3,4,6,7,8,5,2] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]
[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] => [1,2,4,6,7,8,5,3] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]
[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] => [1,2,3,6,7,8,5,4] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[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] => [1,2,3,6,7,8,4,5] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[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] => [2,3,4,5,7,8,6,1] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[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] => [1,3,4,5,7,8,6,2] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [8,7,5,4,2,1,3,6] => [1,2,4,5,7,8,6,3] => [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]
[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] => [1,2,3,5,7,8,6,4] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[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] => [1,2,3,4,7,8,6,5] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[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] => [1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[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] => [2,3,4,5,6,8,7,1] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[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] => [1,3,4,5,6,8,7,2] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[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] => [1,2,4,5,6,8,7,3] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[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] => [1,2,3,5,6,8,7,4] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[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] => [1,2,3,4,6,8,7,5] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[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] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[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] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[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] => [2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[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] => [1,3,4,5,6,7,8,2] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[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] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[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] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[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] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[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] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[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] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,9,1] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[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] => [9,1,2,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[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] => [2,3,4,5,6,7,9,8,1] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[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] => [9,1,2,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[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] => [10,1,2,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[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] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,1,2,10] => [2,3,4,5,6,7,8,10,9,1] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[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] => [2,3,4,5,6,8,9,7,1] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => [8,7,6,5,4,1,3,2,9] => [2,3,4,5,6,9,7,8,1] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[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] => [9,1,2,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[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] => [9,1,2,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[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] => [10,1,2,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[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] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[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] => [2,3,4,5,6,7,8,9,10,11,12,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,1,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,1,2,11] => [2,3,4,5,6,7,8,9,11,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,1,4,5,6,7,8,9] => [9,8,7,6,5,4,1,3,2,10] => [2,3,4,5,6,7,10,8,9,1] => [[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[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] => [2,3,4,5,6,9,8,7,1] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,1,5,6,7,8] => [8,7,6,5,1,4,3,2,9] => [2,3,4,5,9,6,7,8,1] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[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] => [9,1,2,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[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] => [9,1,2,3,4,8,5,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[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] => [10,1,2,3,4,5,6,9,7,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,2,1,4,5,6,7,8,9] => [9,8,7,6,5,4,1,2,3,10] => [2,3,4,5,6,7,10,9,8,1] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,1,6,7,8] => [8,7,6,1,5,4,3,2,9] => [2,3,4,9,5,6,7,8,1] => [[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[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] => [9,1,2,3,4,7,8,5,6] => [[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,2,3,4] => [10,1,2,3,4,5,6,9,8,7] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[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] => [10,1,2,3,4,5,9,6,7,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,1,6,7,8,9] => [9,8,7,6,1,5,4,3,2,10] => [2,3,4,5,10,6,7,8,9,1] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,1,7,8] => [8,7,1,6,5,4,3,2,9] => [2,3,9,4,5,6,7,8,1] => [[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[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] => [10,1,2,3,4,6,7,8,9,5] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,3,6,7,8,9,1] => [1,9,8,7,6,3,2,4,5] => [9,1,2,3,4,7,8,6,5] => [[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[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] => [9,1,2,8,3,4,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,1,7,8,9] => [9,8,7,1,6,5,4,3,2,10] => [2,3,4,10,5,6,7,8,9,1] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,1,8] => [8,1,7,6,5,4,3,2,9] => [2,9,3,4,5,6,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[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] => [3,4,5,6,7,8,9,1,2] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[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] => [9,1,3,4,5,6,7,8,2] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[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] => [8,9,1,2,3,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[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] => [9,1,8,2,3,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[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] => [10,1,2,3,9,4,5,6,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[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] => [3,4,5,6,7,8,9,2,1] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[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] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[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] => [9,8,1,2,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[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] => [10,1,2,9,3,4,5,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,1,9] => [9,1,8,7,6,5,4,3,2,10] => [2,10,3,4,5,6,7,8,9,1] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[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] => [3,4,5,6,7,8,9,10,1,2] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[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] => [10,1,3,4,5,6,7,8,9,2] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[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] => [9,10,1,2,3,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,9,10] => [3,4,5,6,7,8,9,10,2,1] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[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] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[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] => [10,9,1,2,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[] => [] => [] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[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] => [1,9,8,7,6,5,4,2,3] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[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] => [1,9,8,7,6,5,2,4,3] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[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] => [1,9,8,7,6,5,2,3,4] => [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[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] => [1,9,8,7,6,2,5,4,3] => [.,[[[[[.,.],.],.],.],[[[.,.],.],.]]]
[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] => [1,9,8,7,5,6,4,3,2] => [.,[[[[[[[.,.],.],.],[.,.]],.],.],.]]
[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] => [1,9,8,5,7,6,4,3,2] => [.,[[[[[[.,.],.],[[.,.],.]],.],.],.]]
[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] => [1,9,8,2,7,6,5,4,3] => [.,[[[.,.],.],[[[[[.,.],.],.],.],.]]]
[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] => [1,9,2,8,7,6,5,4,3] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,1,9] => [9,1,7,6,5,4,3,2,8] => [1,9,3,4,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1,9] => [9,1,8,7,6,5,4,2,3] => [1,9,2,3,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[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] => [1,9,2,3,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[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] => [1,8,9,6,7,4,5,2,3] => [.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]
[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] => [1,8,9,2,3,4,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[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] => [1,3,9,8,7,6,5,4,2] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[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] => [1,2,9,8,7,6,5,4,3] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,1,7,9] => [9,7,1,6,5,4,3,2,8] => [1,3,9,4,5,6,7,8,2] => [.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,2,3,4,5,6,1,8,9] => [9,8,1,6,5,4,3,2,7] => [1,2,9,4,5,6,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[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] => [1,2,9,3,4,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => [9,3,2,1,8,7,6,5,4] => [1,7,8,9,2,3,4,5,6] => [.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [8,6,4,3,2,1,5,7,9] => [9,7,5,1,2,3,4,6,8] => [1,3,5,9,8,7,6,4,2] => [.,[[.,[[.,[[[[.,.],.],.],.]],.]],.]]
[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] => [1,2,4,9,8,7,6,5,3] => [.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]
[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] => [1,2,3,9,8,7,6,5,4] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [6,2,3,4,5,1,7,8,9] => [9,8,7,1,5,4,3,2,6] => [1,2,3,9,5,6,7,8,4] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [9,8,7,1,6,5,4,3,2] => [1,2,3,9,4,5,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[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] => [1,6,7,8,9,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[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] => [1,2,3,8,9,6,7,4,5] => [.,[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]]
[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] => [1,3,5,7,9,8,6,4,2] => [.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[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] => [1,2,3,5,9,8,7,6,4] => [.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]
[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] => [1,2,3,4,9,8,7,6,5] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,2,3,4,1,6,7,8,9] => [9,8,7,6,1,4,3,2,5] => [1,2,3,4,9,6,7,8,5] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8,9] => [9,8,7,6,1,5,4,2,3] => [1,2,3,4,9,5,6,8,7] => [.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [9,8,7,6,1,5,4,3,2] => [1,2,3,4,9,5,6,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => [9,5,4,3,2,1,8,7,6] => [1,5,6,7,8,9,2,3,4] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[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] => [1,2,3,7,8,9,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1,2,4,6,8,9] => [9,8,6,4,2,1,3,5,7] => [1,2,4,6,8,9,7,5,3] => [.,[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8,9] => [9,8,7,6,2,1,5,4,3] => [1,2,3,4,8,9,5,6,7] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[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] => [1,2,3,4,6,9,8,7,5] => [.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]]
[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] => [1,2,3,4,5,9,8,7,6] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,1,5,6,7,8,9] => [9,8,7,6,5,1,3,2,4] => [1,2,3,4,5,9,7,8,6] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9] => [9,8,7,6,5,1,4,2,3] => [1,2,3,4,5,9,6,8,7] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [9,8,7,6,5,1,4,3,2] => [1,2,3,4,5,9,6,7,8] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[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] => [1,4,5,6,7,8,9,3,2] => [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]
[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] => [1,4,5,6,7,8,9,2,3] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[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] => [1,2,3,4,5,8,9,7,6] => [.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]
[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] => [1,2,3,4,5,8,9,6,7] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[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] => [1,3,4,5,6,7,9,8,2] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[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] => [1,2,3,4,5,7,9,8,6] => [.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[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] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[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] => [1,2,3,4,5,6,9,7,8] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[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] => [1,3,4,5,6,7,8,9,2] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[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] => [1,2,4,5,6,7,8,9,3] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[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] => [1,2,3,5,6,7,8,9,4] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[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] => [1,2,3,4,6,7,8,9,5] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[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] => [1,2,3,4,5,7,8,9,6] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[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] => [1,2,3,4,5,6,8,9,7] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[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] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => [9,8,7,6,5,4,3,1,2] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[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] => [9,8,7,6,5,4,1,3,2] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[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] => [9,1,8,7,6,5,4,3,2] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[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] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,10,9] => [10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[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] => [9,8,7,6,5,4,1,2,3] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[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] => [9,8,7,1,5,6,4,3,2] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]
[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] => [9,1,7,8,6,5,4,3,2] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]
[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] => [10,1,9,8,7,6,5,4,3,2] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[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] => [11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,11,10] => [11,10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[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] => [10,9,8,7,6,5,4,1,2,3] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[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] => [9,8,7,6,5,1,2,3,4] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[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] => [11,1,10,9,8,7,6,5,4,3,2] => [[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [11,1,2,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[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] => [10,9,8,7,6,5,1,2,3,4] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[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] => [9,8,7,6,1,2,3,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[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] => [10,9,8,7,6,1,2,3,4,5] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[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] => [9,8,7,1,2,3,4,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[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] => [10,9,8,7,1,2,3,4,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,7,6,5,4,3,2,1,8,10] => [10,8,1,2,3,4,5,6,7,9] => [1,3,10,9,8,7,6,5,4,2] => [.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]
[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] => [9,8,7,6,5,4,2,3,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[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] => [9,8,7,6,5,3,4,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[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] => [9,8,7,6,5,3,4,1,2] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [9,6,7,8,5,4,3,2,1] => [1,2,3,4,5,8,7,6,9] => [9,8,7,6,5,2,3,4,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[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] => [9,8,7,6,4,5,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[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] => [9,8,7,6,4,5,2,3,1] => [[[[[[[.,.],.],.],.],[.,.]],[.,.]],.]
[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] => [9,8,7,6,4,5,1,2,3] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[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] => [9,8,7,5,6,4,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[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] => [9,8,7,5,6,3,4,1,2] => [[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]
[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] => [9,8,7,5,6,1,2,3,4] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,3,2,1] => [1,2,3,6,5,4,7,8,9] => [9,8,7,4,5,6,3,2,1] => [[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[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] => [9,8,6,7,1,2,3,4,5] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [7,8,9,3,4,5,6,2,1] => [1,2,6,5,4,3,9,8,7] => [9,8,4,5,6,7,1,2,3] => [[[[.,.],.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [8,9,3,4,5,6,7,2,1] => [1,2,7,6,5,4,3,9,8] => [9,8,3,4,5,6,7,1,2] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,2,1] => [1,2,8,7,6,5,4,3,9] => [9,8,2,3,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[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] => [9,7,8,6,5,4,3,2,1] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[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] => [9,7,8,6,5,4,3,1,2] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[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] => [9,7,8,5,6,3,4,1,2] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[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] => [9,7,8,1,2,3,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[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] => [9,6,7,8,5,4,3,2,1] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[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] => [9,6,7,8,1,2,3,4,5] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[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] => [9,5,6,7,8,1,2,3,4] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,3,4,5,6,7,1] => [1,7,6,5,4,3,2,8,9] => [9,3,4,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[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] => [9,3,4,5,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[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] => [8,9,7,6,5,4,3,2,1] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[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] => [8,9,7,6,5,4,3,1,2] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[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] => [8,9,7,6,5,4,2,3,1] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]
[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] => [8,9,6,7,5,4,3,2,1] => [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]
[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] => [8,9,6,7,4,5,2,3,1] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[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] => [8,9,6,7,4,5,1,2,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[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] => [8,9,2,3,4,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[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] => [7,8,9,6,5,4,3,2,1] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[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] => [7,8,9,4,5,6,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[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] => [7,8,9,1,2,3,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[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] => [6,7,8,9,5,4,3,2,1] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[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] => [6,7,8,9,2,3,4,5,1] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.]
[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] => [6,7,8,9,1,2,3,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[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] => [5,6,7,8,9,4,3,2,1] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[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] => [5,6,7,8,9,1,2,3,4] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[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] => [4,5,6,7,8,9,3,2,1] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[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] => [4,5,6,7,8,9,2,3,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[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] => [4,5,6,7,8,9,1,2,3] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[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] => [10,9,8,7,6,5,4,2,3,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[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] => [10,9,8,7,6,5,3,4,1,2] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[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] => [10,9,8,7,5,6,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[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] => [10,9,8,7,5,6,3,4,1,2] => [[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]]
[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] => [10,9,8,6,7,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[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] => [10,9,8,1,2,3,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[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] => [10,9,7,8,5,6,3,4,1,2] => [[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [9,10,3,4,5,6,7,8,2,1] => [1,2,8,7,6,5,4,3,10,9] => [10,9,3,4,5,6,7,8,1,2] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,2,1] => [1,2,9,8,7,6,5,4,3,10] => [10,9,2,3,4,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[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] => [10,8,9,7,6,5,4,3,2,1] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[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] => [10,8,9,6,7,4,5,2,3,1] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[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] => [10,7,8,9,4,5,6,1,2,3] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[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] => [10,7,8,9,1,2,3,4,5,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[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] => [10,6,7,8,9,1,2,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [10,9,2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2,9,10] => [10,3,4,5,6,7,8,9,2,1] => [[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [9,10,2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2,10,9] => [10,3,4,5,6,7,8,9,1,2] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[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] => [9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[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] => [9,10,8,7,6,5,4,3,1,2] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[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] => [9,10,7,8,5,6,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[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] => [9,10,7,8,5,6,1,2,3,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[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] => [9,10,5,6,7,8,1,2,3,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [9,10,3,4,5,6,7,8,1,2] => [2,1,8,7,6,5,4,3,10,9] => [9,10,3,4,5,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[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] => [8,9,10,7,6,5,4,3,2,1] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[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] => [8,9,10,1,2,3,4,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[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] => [7,8,9,10,6,5,4,3,2,1] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[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] => [7,8,9,10,1,2,3,4,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[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] => [6,7,8,9,10,5,4,3,2,1] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[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] => [6,7,8,9,10,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[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] => [5,6,7,8,9,10,4,3,2,1] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[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] => [5,6,7,8,9,10,1,2,3,4] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[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] => [4,5,6,7,8,9,10,3,2,1] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[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] => [4,5,6,7,8,9,10,2,3,1] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]
[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] => [4,5,6,7,8,9,10,1,2,3] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[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] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[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] => [3,9,8,7,6,5,4,2,1] => [[[.,[[[[[[.,.],.],.],.],.],.]],.],.]
[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] => [2,9,8,7,6,5,4,3,1] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
[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] => [2,10,9,8,7,6,5,4,3,1] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[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] => [10,11,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[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] => [8,9,7,6,5,4,1,3,2] => [[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]
[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] => [1,10,9,8,7,6,5,4,2,3] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,1,3,2] => [1,2,3,4,5,6,7,10,8,9] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[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] => [1,2,3,4,5,6,7,9,10,8] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10,11] => [11,10,9,8,7,6,5,4,1,3,2] => [1,2,3,4,5,6,7,8,11,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [11,10,9,8,7,6,5,4,2,1,3] => [1,2,3,4,5,6,7,8,10,11,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[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] => [9,10,8,7,6,5,4,1,3,2] => [[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]
[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] => [9,7,8,6,5,4,1,3,2] => [[[[[[.,.],[.,.]],.],.],.],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,1,7,8] => [8,7,1,2,3,4,5,6,9] => [2,3,9,8,7,6,5,4,1] => [[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]
[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] => [1,10,2,3,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[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] => [1,3,4,5,6,7,8,9,10,2] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [11,9,8,7,6,5,4,3,2,1,10] => [1,3,4,5,6,7,8,9,10,11,2] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[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] => [1,3,4,5,6,7,8,10,9,2] => [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [9,8,6,1,2,3,4,5,7] => [7,5,4,3,2,1,6,8,9] => [3,5,6,7,8,9,4,2,1] => [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]
[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] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [10,9,8,7,6,5,1,4,3,2] => [1,2,3,4,5,6,10,7,8,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [10,9,8,7,6,1,5,4,3,2] => [1,2,3,4,5,10,6,7,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [10,9,8,7,1,6,5,4,3,2] => [1,2,3,4,10,5,6,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [10,9,8,1,7,6,5,4,3,2] => [1,2,3,10,4,5,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [10,9,1,8,7,6,5,4,3,2] => [1,2,10,3,4,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[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] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [8,9,7,6,4,3,2,1,5] => [5,1,2,3,4,6,7,9,8] => [5,9,8,7,6,4,3,1,2] => [[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]
[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] => [1,10,9,8,6,7,5,4,3,2] => [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]
[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] => [3,9,8,7,6,5,4,1,2] => [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]
[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] => [8,9,1,7,6,5,4,3,2] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[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] => [1,2,3,10,9,8,7,6,5,4] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,9,1,2,3,4,5,6] => [6,5,4,3,2,1,9,7,8] => [4,5,6,7,8,9,1,3,2] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[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] => [1,2,4,5,6,7,8,9,10,3] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[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] => [1,2,3,5,6,7,8,9,10,4] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[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] => [1,2,3,4,6,7,8,9,10,5] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[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] => [1,2,3,4,5,7,8,9,10,6] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[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] => [1,2,3,4,5,6,8,9,10,7] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[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] => [1,10,9,8,7,6,5,2,4,3] => [.,[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]]
[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] => [1,10,9,8,7,6,2,5,4,3] => [.,[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]]
[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] => [1,10,9,8,2,7,6,5,4,3] => [.,[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]]
[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] => [1,10,9,2,8,7,6,5,4,3] => [.,[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]]
[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] => [1,2,10,9,8,7,6,5,4,3] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,8,10,7,6,5,4,3,2,1,11] => [11,1,2,3,4,5,6,7,10,8,9] => [1,11,10,9,8,7,6,5,2,4,3] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]]
[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] => [1,11,10,9,8,7,6,2,5,4,3] => [.,[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]]
[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] => [1,11,10,9,8,2,7,6,5,4,3] => [.,[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]]
[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] => [1,11,10,9,2,8,7,6,5,4,3] => [.,[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]]
[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] => [1,11,2,10,9,8,7,6,5,4,3] => [.,[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[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] => [1,2,11,10,9,8,7,6,5,4,3] => [.,[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]]
[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] => [1,2,3,4,5,6,9,10,7,8] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[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] => [1,2,3,4,8,9,10,5,6,7] => [.,[.,[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]]
[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] => [1,2,7,8,9,10,3,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5,10] => [10,5,4,3,2,1,9,8,7,6] => [1,6,7,8,9,10,2,3,4,5] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [6,5,7,4,8,3,9,2,10,1] => [1,10,2,9,3,8,4,7,5,6] => [10,1,9,2,8,3,7,4,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[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] => [1,2,3,4,5,6,7,8,9,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[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] => [10,11,1,2,3,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1,10] => [10,1,9,8,7,6,5,4,2,3] => [1,10,2,3,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[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] => [1,11,2,3,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[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] => [1,3,4,5,6,7,8,9,10,11,12,2] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,1,2,3] => [3,2,1,9,4,5,6,7,8] => [7,8,9,1,6,5,4,3,2] => [[.,[.,[.,.]]],[[[[[.,.],.],.],.],.]]
[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] => [3,4,5,6,7,8,9,10,11,1,2] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[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] => [1,2,3,4,10,9,8,7,6,5] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [4,2,1,3,5,6,7,8,9,10] => [10,9,8,7,6,5,3,1,2,4] => [1,2,3,4,5,6,8,10,9,7] => [.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [7,8,9,1,2,3,4,5,6,10] => [10,6,5,4,3,2,1,9,8,7] => [1,5,6,7,8,9,10,2,3,4] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[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] => [9,10,1,8,7,6,5,4,3,2] => [[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[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] => [1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [9,7,6,8,5,4,3,2,1] => [1,2,3,4,5,8,6,7,9] => [9,8,7,6,5,2,4,3,1] => [[[[[[[.,.],.],.],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,2,8,1] => [1,8,2,3,4,5,6,7,9,10] => [10,3,9,8,7,6,5,4,2,1] => [[[[.,.],[[[[[[.,.],.],.],.],.],.]],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,4,3,2,1,5] => [5,1,2,3,4,6,7,8,10,9] => [6,10,9,8,7,5,4,3,1,2] => [[[[[.,[[[[.,.],.],.],.]],.],.],.],[.,.]]
[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] => [1,2,3,4,5,10,9,8,7,6] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[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] => [1,2,3,4,5,6,10,9,8,7] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => [1,11,9,8,7,6,5,4,3,2,10] => [11,1,3,4,5,6,7,8,9,10,2] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,9,8,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,8,9,11] => [2,11,10,9,8,7,6,5,4,3,1] => [[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]
[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] => [9,2,8,7,6,5,4,3,1] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,8,9,10,11] => [11,9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[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] => [1,4,5,6,7,8,9,10,2,3] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => [10,4,3,2,1,9,8,7,6,5] => [1,7,8,9,10,2,3,4,5,6] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3,10] => [10,3,2,1,9,8,7,6,5,4] => [1,8,9,10,2,3,4,5,6,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]]
[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] => [1,9,10,2,3,4,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,4,3,2,1,5,7,8,9,10] => [10,9,8,7,5,1,2,3,4,6] => [1,2,3,4,6,10,9,8,7,5] => [.,[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]]
[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] => [1,2,3,4,5,7,9,10,8,6] => [.,[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [7,5,4,3,2,1,6,8,9,10] => [10,9,8,6,1,2,3,4,5,7] => [1,2,3,5,10,9,8,7,6,4] => [.,[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]]
[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] => [3,4,5,6,7,8,9,10,11,2,1] => [[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,6,3,2,1] => [1,2,3,6,4,5,7,8,9] => [9,8,7,4,6,5,3,2,1] => [[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,4,6,3,2,1] => [1,2,3,6,4,5,7,8,9,10] => [10,9,8,5,7,6,4,3,2,1] => [[[[[[[[.,.],.],.],[[.,.],.]],.],.],.],.]
[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] => [10,2,9,8,7,6,5,4,3,1] => [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,7,2,1] => [1,2,7,3,4,5,6,8,9] => [9,8,3,7,6,5,4,2,1] => [[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,8,2,1] => [1,2,8,3,4,5,6,7,9,10] => [10,9,3,8,7,6,5,4,2,1] => [[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,3,4,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,4,3,2,11] => [11,2,3,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1] => [1,9,2,8,3,7,4,6,5] => [9,1,8,2,7,3,6,4,5] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[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] => [1,2,4,6,8,10,9,7,5,3] => [.,[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,2,3,10,1] => [1,10,3,2,5,4,7,6,9,8] => [10,1,8,9,6,7,4,5,2,3] => [[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,1,10] => [10,1,8,7,6,5,4,3,2,9] => [1,10,3,4,5,6,7,8,9,2] => [.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[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] => [1,3,5,7,9,10,8,6,4,2] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[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] => [11,12,9,10,7,8,5,6,3,4,1,2] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[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] => [1,2,9,10,7,8,5,6,3,4] => [.,[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]]
[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] => [11,10,1,2,3,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [9,7,5,4,3,2,1,6,8,10] => [10,8,6,1,2,3,4,5,7,9] => [1,3,5,10,9,8,7,6,4,2] => [.,[[.,[[.,[[[[[.,.],.],.],.],.]],.]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,6,5,4,3,2,1,7,9,10] => [10,9,7,1,2,3,4,5,6,8] => [1,2,4,10,9,8,7,6,5,3] => [.,[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [9,8,10,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,10,8,9] => [4,5,6,7,8,9,10,1,3,2] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5,11] => [11,5,4,3,2,1,10,9,8,7,6] => [1,7,8,9,10,11,2,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]]
[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] => [1,8,9,10,5,6,7,2,3,4] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,2,3,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,3,2,11,10] => [11,3,4,5,6,7,8,9,10,1,2] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
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 σ of length n is given by τ with τ(i)=σ(n+1−i).
The reverse of a permutation σ of length n is given by τ with τ(i)=σ(n+1−i).
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length 0 to the empty tree, and sending a permutation σ of length n≥1 to a root node with two subtrees L and R by splitting σ at the index σ−1(1), normalizing both sides again to permutations and sending the permutations on the left and on the right of σ−1(1) to the trees L and R, respectively.
This tree is recursively obtained by sending the unique permutation of length 0 to the empty tree, and sending a permutation σ of length n≥1 to a root node with two subtrees L and R by splitting σ at the index σ−1(1), normalizing both sides again to permutations and sending the permutations on the left and on the right of σ−1(1) to the trees L and R, respectively.
searching the database
Sorry, this map was not found in the database.