Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
[1,0] => [1] => [1] => [.,.]
[1,0,1,0] => [1,2] => [1,2] => [.,[.,.]]
[1,1,0,0] => [2,1] => [2,1] => [[.,.],.]
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [.,[[.,.],.]]
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [[.,.],[.,.]]
[1,1,0,1,0,0] => [2,3,1] => [3,2,1] => [[[.,.],.],.]
[1,1,1,0,0,0] => [3,2,1] => [3,1,2] => [[.,.],[.,.]]
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,3,2] => [.,[[[.,.],.],.]]
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,4,2,3] => [.,[[.,.],[.,.]]]
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,2,3,1] => [[[.,.],[.,.]],.]
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,2,1,3] => [[[.,.],.],[.,.]]
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,1,2,4] => [[.,.],[.,[.,.]]]
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [4,3,2,1] => [[[[.,.],.],.],.]
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [4,1,3,2] => [[.,.],[[.,.],.]]
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,1,2,3] => [[.,.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,5,3,2,4] => [.,[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,5,3,4] => [[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,2,3,1,4] => [[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,2,1,3,5] => [[[.,.],.],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.]
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [5,2,1,4,3] => [[[.,.],.],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,2,1,3,4] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,1,2,5,4] => [[.,.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [5,3,2,1,4] => [[[[.,.],.],.],[.,.]]
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [4,1,3,2,5] => [[.,.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [5,1,3,4,2] => [[.,.],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [5,1,3,2,4] => [[.,.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [5,4,2,3,1] => [[[[.,.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [5,1,4,3,2] => [[.,.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [5,1,2,4,3] => [[.,.],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,6,3,4,2,5] => [.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [1,6,3,2,5,4] => [.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,6,4,3,2,5] => [.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [1,6,2,4,5,3] => [.,[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]]
>>> Load all 1938 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,6,5,3,4,2] => [.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [1,6,2,5,4,3] => [.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,3,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,6,4,3,5] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,5,3,4,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [2,1,6,3,5,4] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,6,3,4,5] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1,6,4,5] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,2,3,4,1,5] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,2,3,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [6,2,3,1,5,4] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,2,3,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [4,2,1,3,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [5,2,4,3,1,6] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [6,2,4,3,1,5] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [5,2,1,4,3,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [6,2,1,4,5,3] => [[[.,.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [6,2,1,4,3,5] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [6,2,5,3,4,1] => [[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [6,2,1,5,4,3] => [[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [6,2,1,3,5,4] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,2,1,3,4,5] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,1,2,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,1,2,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,1,2,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,1,2,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [6,3,2,4,1,5] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [5,3,2,1,4,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [6,3,2,1,5,4] => [[[[.,.],.],.],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,3,2,1,4,5] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [4,1,3,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [4,1,3,2,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [6,4,3,2,1,5] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [5,1,3,4,2,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [6,1,3,4,5,2] => [[.,.],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [6,1,3,4,2,5] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [5,1,3,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [6,5,3,2,4,1] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [6,1,3,5,4,2] => [[.,.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [6,1,3,2,5,4] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [6,1,3,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,1,2,3,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [5,4,2,3,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [6,4,2,3,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [6,4,2,3,1,5] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [5,1,4,3,2,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [6,1,4,3,5,2] => [[.,.],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [6,1,4,3,2,5] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [5,1,2,4,3,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [6,5,2,4,3,1] => [[[[.,.],.],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [6,1,5,4,3,2] => [[.,.],[[[[.,.],.],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [6,1,2,4,5,3] => [[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [6,1,2,4,3,5] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [6,1,5,3,4,2] => [[.,.],[[[.,.],[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [6,1,2,5,4,3] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [6,1,2,3,5,4] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,7,5,4,6] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,7,4,5,3,6] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,6,4,3,5,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,7,4,6,5,3] => [.,[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [1,2,7,4,3,6,5] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,7,4,3,5,6] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,5,3,4,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,7,5,4,6,3] => [.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,7,5,4,3,6] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [1,2,6,3,5,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [1,2,7,3,5,6,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [1,2,7,3,5,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,7,6,4,5,3] => [.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [1,2,7,3,6,5,4] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,3,2,7,5,4,6] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,3,2,6,4,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [1,3,2,7,4,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,3,2,7,4,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,4,3,2,7,5,6] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,7,3,4,5,2,6] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,6,3,4,2,5,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,7,3,4,6,5,2] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [1,7,3,4,2,6,5] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,7,3,4,2,5,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,5,3,2,4,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,5,3,2,4,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,6,3,5,4,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,7,3,5,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,7,3,5,4,2,6] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [1,6,3,2,5,4,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [1,7,3,6,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [1,7,3,2,5,6,4] => [.,[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [1,7,3,2,5,4,6] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,6,3,2,4,5,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,7,3,6,4,5,2] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [1,7,3,2,6,5,4] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [1,7,3,2,4,6,5] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,7,3,2,4,5,6] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,4,2,3,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,4,2,3,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,4,2,3,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,4,2,3,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,6,4,3,5,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,7,4,3,5,2,6] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,6,4,3,2,5,7] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,7,4,3,6,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [1,7,4,3,2,6,5] => [.,[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,7,4,3,2,5,6] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [1,5,2,4,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [1,5,2,4,3,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [1,7,5,4,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [1,7,5,4,3,2,6] => [.,[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [1,6,2,4,5,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [1,7,6,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [1,7,2,4,5,6,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [1,7,2,4,5,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [1,6,2,4,3,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [1,7,6,4,3,5,2] => [.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [1,7,2,4,6,5,3] => [.,[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [1,7,2,4,3,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [1,7,2,4,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,5,2,3,4,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,6,5,3,4,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,7,5,3,4,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,7,5,3,4,2,6] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [1,6,2,5,4,3,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [1,7,2,5,4,6,3] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [1,7,2,5,4,3,6] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [1,6,2,3,5,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [1,7,6,3,5,4,2] => [.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [1,7,2,6,5,4,3] => [.,[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [1,7,2,3,5,6,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [1,7,2,3,5,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,7,6,3,4,5,2] => [.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [1,7,2,6,4,5,3] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [1,7,2,3,6,5,4] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [2,1,3,7,5,4,6] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,1,3,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [2,1,3,7,4,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,1,3,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [2,1,7,4,5,3,6] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [2,1,6,4,3,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [2,1,7,4,6,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [2,1,7,4,3,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [2,1,7,4,3,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,1,5,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,1,5,3,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [2,1,7,5,4,6,3] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [2,1,7,5,4,3,6] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [2,1,6,3,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [2,1,7,3,5,6,4] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [2,1,7,3,5,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,1,6,3,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [2,1,7,6,4,5,3] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [2,1,7,3,6,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [2,1,7,3,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,1,7,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [3,2,1,4,7,5,6] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,2,1,7,5,4,6] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [3,2,1,6,4,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [3,2,1,7,4,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,2,1,7,4,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,2,3,1,7,5,6] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [7,2,3,4,1,6,5] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,2,3,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [5,2,3,1,4,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [6,2,3,5,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [7,2,3,5,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [7,2,3,5,4,1,6] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [6,2,3,1,5,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [7,2,3,6,5,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [7,2,3,1,5,6,4] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [7,2,3,1,5,4,6] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,2,3,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [7,2,3,6,4,5,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [7,2,3,1,6,5,4] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [7,2,3,1,4,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,2,3,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,2,1,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [4,2,1,3,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [4,2,1,3,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [4,2,1,3,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [4,2,1,3,7,5,6] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [5,2,4,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [5,2,4,3,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [6,2,4,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [7,2,4,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [7,2,4,3,5,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [6,2,4,3,1,5,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [7,2,4,3,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [7,2,4,3,1,6,5] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [7,2,4,3,1,5,6] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [5,2,1,4,3,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [5,2,1,4,3,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [6,2,5,4,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [7,2,5,4,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [7,2,5,4,3,1,6] => [[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [6,2,1,4,5,3,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [7,2,6,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [7,2,1,4,5,6,3] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [7,2,1,4,5,3,6] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [6,2,1,4,3,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [7,2,6,4,3,5,1] => [[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [7,2,1,4,6,5,3] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [7,2,1,4,3,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [7,2,1,4,3,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,2,1,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [5,2,1,3,4,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [6,2,5,3,4,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [7,2,5,3,4,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [7,2,5,3,4,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [6,2,1,5,4,3,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [7,2,6,5,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [7,2,1,5,4,6,3] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [7,2,1,5,4,3,6] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [6,2,1,3,5,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [7,2,6,3,5,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [7,2,1,6,5,4,3] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [7,2,1,3,5,6,4] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [7,2,1,3,5,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,2,1,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [7,2,6,3,4,5,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [7,2,1,6,4,5,3] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [7,2,1,3,6,5,4] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [7,2,1,3,4,6,5] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,2,1,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [3,1,2,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [3,1,2,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [3,1,2,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [3,1,2,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [3,1,2,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [3,1,2,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [3,1,2,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [3,1,2,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,1,2,7,5,4,6] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [3,1,2,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,1,2,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [3,1,2,7,4,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [3,1,2,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [4,3,2,1,7,5,6] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [5,3,2,4,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [6,3,2,4,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [7,3,2,4,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [7,3,2,4,1,6,5] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [7,3,2,4,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [5,3,2,1,4,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [5,3,2,1,4,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [6,3,2,5,4,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [7,3,2,5,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [7,3,2,5,4,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [6,3,2,1,5,4,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [7,3,2,6,5,4,1] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [7,3,2,1,5,6,4] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [7,3,2,1,5,4,6] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,3,2,1,4,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [7,3,2,6,4,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [7,3,2,1,6,5,4] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [7,3,2,1,4,6,5] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,3,2,1,4,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [4,1,3,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [4,1,3,2,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [4,1,3,2,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [4,1,3,2,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [4,1,3,2,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [7,4,3,2,6,5,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [7,4,3,2,1,6,5] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [5,1,3,4,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [5,1,3,4,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [6,1,3,4,5,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [7,1,3,4,5,6,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [7,1,3,4,5,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [6,1,3,4,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [7,6,3,4,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [7,1,3,4,6,5,2] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [7,1,3,4,2,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [7,1,3,4,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [5,1,3,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [5,1,3,2,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [6,5,3,2,4,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [7,5,3,2,4,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [7,5,3,2,4,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [6,1,3,5,4,2,7] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [7,6,3,5,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [7,1,3,5,4,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [7,1,3,5,4,2,6] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [6,1,3,2,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [7,6,3,2,5,4,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [7,1,3,6,5,4,2] => [[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [7,1,3,2,5,6,4] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [7,1,3,2,5,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [6,1,3,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [7,6,3,2,4,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [7,1,3,6,4,5,2] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [7,1,3,2,6,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [7,1,3,2,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [7,1,3,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [4,1,2,3,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [4,1,2,3,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [4,1,2,3,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [4,1,2,3,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [5,4,2,3,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [5,4,2,3,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [6,4,2,3,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [7,4,2,3,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [7,4,2,3,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [6,4,2,3,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [7,4,2,3,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [7,4,2,3,1,6,5] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [7,4,2,3,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [5,1,4,3,2,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [5,1,4,3,2,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [6,1,4,3,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [7,1,4,3,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [7,1,4,3,5,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [6,1,4,3,2,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [7,6,4,3,2,5,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [7,1,4,3,6,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [7,1,4,3,2,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [7,1,4,3,2,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [5,1,2,4,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [5,1,2,4,3,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [6,5,2,4,3,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [7,5,2,4,3,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [7,5,2,4,3,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [6,1,5,4,3,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [7,1,5,4,3,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [7,1,5,4,3,2,6] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [6,1,2,4,5,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [7,6,2,4,5,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [7,1,6,4,5,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [7,1,2,4,5,6,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [7,1,2,4,5,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [6,1,2,4,3,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [7,6,2,4,3,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [7,1,6,4,3,5,2] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [7,1,2,4,6,5,3] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [7,1,2,4,3,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [7,1,2,4,3,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [5,1,2,3,4,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [6,5,2,3,4,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [7,5,2,3,4,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [7,5,2,3,4,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [6,1,5,3,4,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [7,1,5,3,4,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [7,1,5,3,4,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [6,1,2,5,4,3,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [7,6,2,5,4,3,1] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [7,1,6,5,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [7,1,2,5,4,6,3] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [7,1,2,5,4,3,6] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [6,1,2,3,5,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [7,6,2,3,5,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [7,1,6,3,5,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [7,1,2,6,5,4,3] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [7,1,2,3,5,6,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [7,1,2,3,5,4,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [7,6,2,3,4,5,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [7,1,6,3,4,5,2] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [7,1,2,6,4,5,3] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [7,1,2,3,6,5,4] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [7,1,2,3,4,6,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [1,2,3,4,8,6,5,7] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [1,2,3,4,7,5,6,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,7,6,5] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [1,2,3,4,8,5,7,6] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [1,2,3,5,4,8,6,7] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [1,2,3,8,5,6,4,7] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [1,2,3,7,5,4,6,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [1,2,3,8,5,7,6,4] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [1,2,3,8,5,4,7,6] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [1,2,3,8,5,4,6,7] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [1,2,3,6,4,5,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [1,2,3,7,6,5,4,8] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [1,2,3,8,6,5,7,4] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [1,2,3,8,6,5,4,7] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [1,2,3,7,4,6,5,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [1,2,3,8,7,6,5,4] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [1,2,3,8,4,6,7,5] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [1,2,3,8,4,6,5,7] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [1,2,3,7,4,5,6,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [1,2,3,8,7,5,6,4] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [1,2,3,8,4,7,6,5] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [1,2,3,8,4,5,7,6] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [1,2,4,3,5,8,6,7] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,6,7,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,6,5,8] => [1,2,4,3,7,5,6,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [1,2,4,3,8,7,6,5] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [1,2,4,3,8,5,7,6] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [1,2,4,3,8,5,6,7] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6,8,7] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [1,2,5,4,3,8,6,7] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [1,2,8,4,5,6,3,7] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => [1,2,8,4,5,3,7,6] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [1,2,6,4,3,5,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,6,7,5,8,3] => [1,2,8,4,7,6,5,3] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [1,2,8,4,3,6,7,5] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [1,2,8,4,3,6,5,7] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,6,5,3,8] => [1,2,7,4,3,5,6,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,6,8,5,3] => [1,2,8,4,3,7,6,5] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [1,2,8,4,3,5,7,6] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [1,2,8,4,3,5,6,7] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [1,2,5,3,4,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [1,2,5,3,4,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,4,3,7,6,8] => [1,2,5,3,4,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [1,2,5,3,4,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [1,2,5,3,4,8,6,7] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,4,6,3,7,8] => [1,2,6,5,4,3,7,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [1,2,7,5,4,6,3,8] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [1,2,8,5,4,6,7,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [1,2,8,5,4,3,6,7] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [1,2,6,3,5,4,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,4,7,3,8] => [1,2,7,6,5,4,3,8] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [1,2,8,6,5,4,7,3] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,5,6,4,8,7,3] => [1,2,8,6,5,4,3,7] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [1,2,8,7,5,6,4,3] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [1,2,8,3,5,6,7,4] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [1,2,8,3,5,6,4,7] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => [1,2,7,3,5,4,6,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [1,2,8,7,5,4,6,3] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [1,2,8,3,5,7,6,4] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,6,4,3] => [1,2,8,3,5,4,7,6] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,7,6,4,3] => [1,2,8,3,5,4,6,7] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [1,2,6,3,4,5,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,5,4,3,8,7] => [1,2,6,3,4,5,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [1,2,8,6,4,5,7,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,5,7,4,8,3] => [1,2,8,7,6,5,4,3] => [.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [1,2,8,3,6,5,7,4] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [1,2,8,3,6,5,4,7] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,5,4,3,8] => [1,2,7,3,4,6,5,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,6,7,5,4,8,3] => [1,2,8,7,4,6,5,3] => [.,[.,[[[[.,.],.],[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,6,7,5,8,4,3] => [1,2,8,3,7,6,5,4] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [1,2,8,3,4,6,7,5] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,6,8,7,5,4,3] => [1,2,8,3,4,6,5,7] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [1,2,7,3,4,5,6,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [1,2,8,7,4,5,6,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [1,2,8,3,4,7,6,5] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [1,2,8,3,4,5,7,6] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [1,3,2,4,5,8,6,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [1,3,2,4,8,6,5,7] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [1,3,2,4,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,7,8,6,5] => [1,3,2,4,8,5,7,6] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [1,3,2,4,8,5,6,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,8,6,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [1,3,2,8,5,6,4,7] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [1,3,2,7,5,4,6,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [1,3,2,8,5,7,6,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [1,3,2,8,5,4,7,6] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [1,3,2,8,5,4,6,7] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [1,3,2,6,4,5,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [1,3,2,7,6,5,4,8] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [1,3,2,8,6,5,7,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [1,3,2,8,6,5,4,7] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,5,4,8] => [1,3,2,7,4,6,5,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [1,3,2,8,7,6,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [1,3,2,8,4,6,7,5] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => [1,3,2,8,4,6,5,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [1,3,2,7,4,5,6,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,7,8,6,5,4] => [1,3,2,8,4,5,7,6] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [1,3,2,8,4,5,6,7] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [1,4,3,2,5,8,6,7] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [1,4,3,2,8,6,7,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [1,4,3,2,8,7,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [1,4,3,2,8,5,6,7] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [1,5,3,4,2,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [1,8,3,4,5,6,2,7] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [1,8,3,4,5,2,7,6] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [1,8,3,4,5,2,6,7] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,5,2,7,8] => [1,6,3,4,2,5,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,5,2,8,7] => [1,6,3,4,2,5,8,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [1,7,3,4,2,6,5,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,5,8,2] => [1,8,3,4,7,6,5,2] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [1,8,3,4,2,6,7,5] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,6,8,5,2] => [1,8,3,4,2,7,6,5] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [1,8,3,4,2,5,6,7] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [1,5,3,2,4,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [1,5,3,2,4,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [1,5,3,2,4,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [1,5,3,2,4,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,4,2,8,7,6] => [1,5,3,2,4,8,6,7] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,4,6,2,7,8] => [1,6,3,5,4,2,7,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,4,6,7,2,8] => [1,7,3,5,4,6,2,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [1,8,3,5,4,6,7,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [1,7,3,5,4,2,6,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [1,8,3,5,4,7,6,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,4,7,8,6,2] => [1,8,3,5,4,2,7,6] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [1,6,3,2,5,4,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [1,7,3,6,5,4,2,8] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,4,7,8,2] => [1,8,3,6,5,4,7,2] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => [1,7,3,2,5,6,4,8] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => [1,8,3,7,5,6,4,2] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [1,8,3,2,5,6,7,4] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,7,4,2] => [1,8,3,2,5,6,4,7] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [1,7,3,2,5,4,6,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [1,8,3,2,5,4,7,6] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [1,8,3,2,5,4,6,7] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,5,4,2,7,8] => [1,6,3,2,4,5,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [1,8,3,6,4,5,2,7] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [1,8,3,7,6,5,4,2] => [.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => [1,7,3,2,4,6,5,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [1,8,3,2,7,6,5,4] => [.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [1,7,3,2,4,5,6,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,6,5,8,4,2] => [1,8,3,2,7,5,6,4] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [1,8,3,2,4,5,7,6] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [1,8,3,2,4,5,6,7] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [1,4,2,3,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [1,4,2,3,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [1,4,2,3,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [1,4,2,3,5,8,6,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,3,2,6,5,7,8] => [1,4,2,3,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,3,2,6,5,8,7] => [1,4,2,3,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [1,4,2,3,8,6,5,7] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [1,4,2,3,7,5,6,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,7,8,6,5] => [1,4,2,3,8,5,7,6] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [1,4,2,3,8,5,6,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [1,5,4,3,2,6,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [1,5,4,3,2,7,6,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => [1,5,4,3,2,8,7,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [1,6,4,3,5,2,7,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [1,8,4,3,5,6,7,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,3,5,7,6,8,2] => [1,8,4,3,5,7,6,2] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [1,8,4,3,5,2,7,6] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [1,6,4,3,2,5,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [1,8,4,3,6,5,7,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [1,8,4,3,6,5,2,7] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => [1,8,4,3,2,6,7,5] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,3,7,6,5,2,8] => [1,7,4,3,2,5,6,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [1,8,4,3,2,7,6,5] => [.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [1,8,4,3,2,5,7,6] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [1,8,4,3,2,5,6,7] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => [1,5,2,4,3,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,5,3,2,6,8,7] => [1,5,2,4,3,6,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => [1,5,2,4,3,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,3,2,7,8,6] => [1,5,2,4,3,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [1,5,2,4,3,8,6,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [1,6,5,4,3,2,7,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [1,8,5,4,3,6,7,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [1,8,5,4,3,6,2,7] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,4,5,3,7,6,2,8] => [1,7,5,4,3,2,6,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => [1,8,5,4,3,2,7,6] => [.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [1,8,5,4,3,2,6,7] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,3,2,7,8] => [1,6,2,4,5,3,7,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,3,7,2,8] => [1,7,6,4,5,3,2,8] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,5,6,3,7,8,2] => [1,8,6,4,5,3,7,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [1,7,2,4,5,6,3,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [1,8,7,4,5,6,3,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [1,8,2,4,5,6,7,3] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,6,3,2,8] => [1,7,2,4,5,3,6,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,5,7,6,3,8,2] => [1,8,7,4,5,3,6,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,4,5,7,6,8,3,2] => [1,8,2,4,5,7,6,3] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,5,3,2,7,8] => [1,6,2,4,3,5,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,6,5,3,7,8,2] => [1,8,6,4,3,5,7,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,5,7,3,2,8] => [1,7,2,4,6,5,3,8] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,5,8,7,3,2] => [1,8,2,4,6,5,3,7] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [1,8,7,4,3,6,5,2] => [.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [1,8,2,4,7,6,5,3] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [1,8,2,4,3,6,5,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [1,7,2,4,3,5,6,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,7,6,5,3,8,2] => [1,8,7,4,3,5,6,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [1,8,2,4,7,5,6,3] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,4,7,6,8,5,3,2] => [1,8,2,4,3,7,6,5] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [1,8,2,4,3,5,6,7] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,4,3,2,6,8,7] => [1,5,2,3,4,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [1,5,2,3,4,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [1,5,2,3,4,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [1,5,2,3,4,8,6,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [1,8,5,3,4,6,7,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [1,8,5,3,4,6,2,7] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,4,3,7,6,8,2] => [1,8,5,3,4,7,6,2] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [1,7,6,5,4,3,2,8] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [1,8,6,5,4,3,7,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,4,6,3,8,7,2] => [1,8,6,5,4,3,2,7] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,4,6,7,3,2,8] => [1,7,2,5,4,6,3,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [1,8,7,5,4,6,3,2] => [.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [1,8,2,5,4,6,7,3] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,4,7,6,3,2,8] => [1,7,2,5,4,3,6,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,4,7,6,3,8,2] => [1,8,7,5,4,3,6,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,4,7,6,8,3,2] => [1,8,2,5,4,7,6,3] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,5,6,4,3,7,2,8] => [1,7,6,3,5,4,2,8] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => [1,8,6,3,5,4,2,7] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,5,6,4,7,3,2,8] => [1,7,2,6,5,4,3,8] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [1,8,2,3,5,6,7,4] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,5,6,8,7,4,3,2] => [1,8,2,3,5,6,4,7] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,5,7,6,4,3,2,8] => [1,7,2,3,5,4,6,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [1,8,2,3,5,4,6,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [1,6,2,3,4,5,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [1,6,2,3,4,5,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,5,4,3,7,2,8] => [1,7,6,3,4,5,2,8] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [1,8,6,3,4,5,2,7] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [1,8,7,3,6,5,4,2] => [.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,5,7,4,8,3,2] => [1,8,2,7,6,5,4,3] => [.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [1,8,2,3,6,5,4,7] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [1,7,2,3,4,6,5,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,5,4,3,8,2] => [1,8,7,3,4,6,5,2] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,6,7,5,4,8,3,2] => [1,8,2,7,4,6,5,3] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [1,8,2,3,7,6,5,4] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [1,8,2,3,4,6,7,5] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [1,8,2,3,4,6,5,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [1,7,2,3,4,5,6,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [1,8,7,3,4,5,6,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [1,8,2,7,4,5,6,3] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [1,8,2,3,7,5,6,4] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [1,8,2,3,4,7,6,5] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [1,8,2,3,4,5,7,6] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [2,1,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,4,6,8,7,5] => [2,1,3,4,8,6,5,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [2,1,3,4,8,5,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [2,1,3,8,5,7,6,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,7,8,6,4] => [2,1,3,8,5,4,7,6] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,7,6,4] => [2,1,3,8,5,4,6,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,5,4,7,8] => [2,1,3,6,4,5,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [2,1,3,6,4,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,5,7,8,4] => [2,1,3,8,6,5,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [2,1,3,8,6,5,4,7] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,6,7,5,8,4] => [2,1,3,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [2,1,3,8,4,6,7,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,7,5,4] => [2,1,3,8,4,6,5,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,7,6,5,8,4] => [2,1,3,8,7,5,6,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,7,6,8,5,4] => [2,1,3,8,4,7,6,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [2,1,3,8,4,5,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [2,1,3,8,4,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [2,1,4,3,5,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [2,1,4,3,8,6,5,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [2,1,4,3,8,5,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,5,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3,7,8,6] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,6,8,3] => [2,1,8,4,5,7,6,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [2,1,8,4,5,3,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [2,1,8,4,5,3,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [2,1,6,4,3,5,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [2,1,6,4,3,5,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,5,7,8,3] => [2,1,8,4,6,5,7,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [2,1,8,4,7,6,5,3] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [2,1,8,4,3,6,5,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [2,1,8,4,7,5,6,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,7,6,8,5,3] => [2,1,8,4,3,7,6,5] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [2,1,8,4,3,5,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [2,1,5,3,4,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,1,5,3,4,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [2,1,8,5,4,6,7,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [2,1,8,5,4,6,3,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [2,1,8,5,4,7,6,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [2,1,8,5,4,3,7,6] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [2,1,8,5,4,3,6,7] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [2,1,6,3,5,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,5,6,4,7,3,8] => [2,1,7,6,5,4,3,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [2,1,8,6,5,4,7,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [2,1,8,6,5,4,3,7] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [2,1,8,7,5,6,4,3] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [2,1,8,3,5,6,7,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [2,1,8,7,5,4,6,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [2,1,8,3,5,7,6,4] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [2,1,8,3,5,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,1,6,3,4,5,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,5,4,7,8,3] => [2,1,8,6,4,5,7,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [2,1,8,3,6,5,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [2,1,8,3,7,6,5,4] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [2,1,8,3,4,6,7,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [2,1,7,3,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [2,1,8,3,7,5,6,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [2,1,8,3,4,7,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,8,3,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [3,2,1,4,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [3,2,1,4,8,5,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [3,2,1,4,8,5,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [3,2,1,7,5,6,4,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,7,4] => [3,2,1,8,5,6,4,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [3,2,1,8,5,7,6,4] => [[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [3,2,1,8,5,4,7,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,3,1,5,8,7,6,4] => [3,2,1,8,5,4,6,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [3,2,1,6,4,5,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [3,2,1,7,6,5,4,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,5,7,8,4] => [3,2,1,8,6,5,7,4] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [3,2,1,8,6,5,4,7] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,5,4,8] => [3,2,1,7,4,6,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => [3,2,1,8,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [3,2,1,8,4,6,7,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => [3,2,1,8,4,6,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,7,6,5,4,8] => [3,2,1,7,4,5,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [3,2,1,8,7,5,6,4] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [3,2,1,8,4,7,6,5] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [3,2,1,8,4,5,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,2,1,8,4,5,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [4,2,3,1,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [4,2,3,1,5,8,6,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [4,2,3,1,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [4,2,3,1,7,6,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,2,3,1,8,7,6,5] => [[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [4,2,3,1,8,5,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,3,1,8,5,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,2,3,4,1,8,6,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [8,2,3,4,5,7,6,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [8,2,3,4,5,1,7,6] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [7,2,3,4,6,5,1,8] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [7,2,3,4,1,6,5,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [8,2,3,4,7,6,5,1] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [8,2,3,4,1,6,7,5] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [8,2,3,4,1,5,7,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [5,2,3,1,4,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [5,2,3,1,4,8,6,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [6,2,3,5,4,1,7,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [7,2,3,5,4,6,1,8] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [8,2,3,5,4,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,3,5,4,7,6,1,8] => [7,2,3,5,4,1,6,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [8,2,3,5,4,7,6,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => [6,2,3,1,5,4,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => [7,2,3,6,5,4,1,8] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [8,2,3,6,5,4,7,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [7,2,3,1,5,6,4,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [8,2,3,7,5,6,4,1] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [8,2,3,1,5,6,7,4] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [8,2,3,1,5,6,4,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => [8,2,3,1,5,7,6,4] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [8,2,3,1,5,4,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [6,2,3,1,4,5,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [6,2,3,1,4,5,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,6,5,7,8,4,1] => [8,2,3,1,6,5,7,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [8,2,3,1,6,5,4,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,5,4,1,8] => [7,2,3,1,4,6,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,5,8,4,1] => [8,2,3,1,7,6,5,4] => [[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,6,8,7,5,4,1] => [8,2,3,1,4,6,5,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [7,2,3,1,4,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [8,2,3,7,4,5,6,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => [8,2,3,1,7,5,6,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,7,8,6,5,4,1] => [8,2,3,1,4,5,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [8,2,3,1,4,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [4,2,1,3,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,4,3,1,5,7,8,6] => [4,2,1,3,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [4,2,1,3,5,8,6,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [4,2,1,3,6,5,7,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [4,2,1,3,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [4,2,1,3,8,6,5,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [4,2,1,3,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [4,2,1,3,8,5,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [4,2,1,3,8,5,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [5,2,4,3,1,6,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [5,2,4,3,1,6,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [5,2,4,3,1,7,6,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [5,2,4,3,1,8,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [6,2,4,3,5,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,7,8,6,1] => [8,2,4,3,5,1,7,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [6,2,4,3,1,5,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [6,2,4,3,1,5,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [7,2,4,3,6,5,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [8,2,4,3,6,5,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [8,2,4,3,6,5,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => [8,2,4,3,7,6,5,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [8,2,4,3,7,5,6,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [5,2,1,4,3,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [5,2,1,4,3,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [5,2,1,4,3,8,6,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => [6,2,5,4,3,1,8,7] => [[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,4,5,3,6,7,1,8] => [7,2,5,4,3,6,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [8,2,5,4,3,6,7,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,4,5,3,7,6,8,1] => [8,2,5,4,3,7,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => [6,2,1,4,5,3,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,3,7,1,8] => [7,2,6,4,5,3,1,8] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [8,2,6,4,5,3,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [7,2,1,4,5,6,3,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [8,2,7,4,5,6,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [8,2,1,4,5,6,7,3] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,4,5,7,6,3,1,8] => [7,2,1,4,5,3,6,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,4,5,7,6,3,8,1] => [8,2,7,4,5,3,6,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => [6,2,1,4,3,5,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [6,2,1,4,3,5,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [8,2,6,4,3,5,1,7] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [8,2,7,4,6,5,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [8,2,1,4,6,5,7,3] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [7,2,1,4,3,6,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [8,2,1,4,3,6,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,4,7,6,5,3,1,8] => [7,2,1,4,3,5,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [8,2,1,4,3,5,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [5,2,1,3,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [5,2,1,3,4,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [6,2,5,3,4,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [7,2,5,3,4,6,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,5,4,3,7,6,1,8] => [7,2,5,3,4,1,6,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => [8,2,5,3,4,1,7,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,4,6,3,1,7,8] => [6,2,1,5,4,3,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,5,4,6,3,1,8,7] => [6,2,1,5,4,3,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [7,2,6,5,4,3,1,8] => [[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,4,6,3,7,8,1] => [8,2,6,5,4,3,7,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [7,2,1,5,4,6,3,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [8,2,7,5,4,6,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => [7,2,1,5,4,3,6,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => [8,2,7,5,4,3,6,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [8,2,1,5,4,3,7,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [7,2,1,6,5,4,3,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,5,6,4,7,3,8,1] => [8,2,7,6,5,4,3,1] => [[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,4,7,8,3,1] => [8,2,1,6,5,4,7,3] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [8,2,1,7,5,6,4,3] => [[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [8,2,1,3,5,6,7,4] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => [7,2,1,3,5,4,6,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,5,4,3,7,1,8] => [7,2,6,3,4,5,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [8,2,6,3,4,5,7,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [8,2,6,3,4,5,1,7] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [8,2,7,3,6,5,4,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,6,5,7,4,8,3,1] => [8,2,1,7,6,5,4,3] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,6,5,7,8,4,3,1] => [8,2,1,3,6,5,7,4] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,5,8,7,4,3,1] => [8,2,1,3,6,5,4,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [8,2,1,3,7,6,5,4] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [8,2,1,3,4,6,5,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [7,2,1,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [8,2,7,3,4,5,6,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [8,2,1,3,4,5,7,6] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [8,2,1,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [3,1,2,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [3,1,2,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [3,1,2,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,2,1,4,6,5,8,7] => [3,1,2,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [3,1,2,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [3,1,2,4,8,6,5,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [3,1,2,4,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [3,1,2,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [3,1,2,4,8,5,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [3,1,2,4,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,5,4,6,8,7] => [3,1,2,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [3,1,2,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [3,1,2,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [3,1,2,8,5,6,4,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [3,1,2,7,5,4,6,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [3,1,2,8,5,4,7,6] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [3,1,2,6,4,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [3,1,2,8,6,5,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,1,2,8,6,5,4,7] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [3,1,2,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => [3,1,2,8,4,6,7,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [3,1,2,7,4,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [3,1,2,8,7,5,6,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [3,1,2,8,4,5,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [3,1,2,8,4,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [4,3,2,1,5,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [4,3,2,1,5,8,6,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [4,3,2,1,7,6,5,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [4,3,2,1,8,6,7,5] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [4,3,2,1,8,6,5,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [4,3,2,1,7,5,6,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [4,3,2,1,8,5,7,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [4,3,2,1,8,5,6,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,2,4,5,1,7,6,8] => [5,3,2,4,1,7,6,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,2,4,5,1,7,8,6] => [5,3,2,4,1,8,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [8,3,2,4,5,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [8,3,2,4,6,5,1,7] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,6,7,5,8,1] => [8,3,2,4,7,6,5,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,2,4,7,6,8,5,1] => [8,3,2,4,1,7,6,5] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [5,3,2,1,4,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [5,3,2,1,4,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [5,3,2,1,4,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [5,3,2,1,4,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [5,3,2,1,4,8,6,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,5,4,6,1,7,8] => [6,3,2,5,4,1,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,5,4,6,7,1,8] => [7,3,2,5,4,6,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [7,3,2,5,4,1,6,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [8,3,2,5,4,7,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => [7,3,2,1,5,6,4,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [8,3,2,7,5,6,4,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [8,3,2,1,5,6,7,4] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,5,6,8,7,4,1] => [8,3,2,1,5,6,4,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,5,7,6,4,1,8] => [7,3,2,1,5,4,6,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [8,3,2,1,5,4,7,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [6,3,2,1,4,5,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [8,3,2,6,4,5,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [8,3,2,7,6,5,4,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,6,5,7,8,4,1] => [8,3,2,1,6,5,7,4] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,6,5,8,7,4,1] => [8,3,2,1,6,5,4,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [7,3,2,1,4,6,5,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [8,3,2,7,4,6,5,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,6,7,5,8,4,1] => [8,3,2,1,7,6,5,4] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [8,3,2,1,4,6,5,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [7,3,2,1,4,5,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,7,6,8,5,4,1] => [8,3,2,1,4,7,6,5] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [8,3,2,1,4,5,7,6] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [4,1,3,2,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,4,2,1,5,7,6,8] => [4,1,3,2,5,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [4,1,3,2,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [4,1,3,2,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [4,1,3,2,8,6,5,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [4,1,3,2,8,5,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [4,1,3,2,8,5,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,4,2,5,1,6,8,7] => [5,4,3,2,1,6,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [5,4,3,2,1,7,6,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [5,4,3,2,1,8,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [5,4,3,2,1,8,6,7] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [6,4,3,2,5,1,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => [8,4,3,2,5,7,6,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [8,4,3,2,5,1,7,6] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,4,2,6,5,1,7,8] => [6,4,3,2,1,5,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [6,4,3,2,1,5,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [7,4,3,2,6,5,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [8,4,3,2,6,5,7,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => [7,4,3,2,1,6,5,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [8,4,3,2,7,6,5,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,4,2,7,6,5,1,8] => [7,4,3,2,1,5,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,2,7,6,5,8,1] => [8,4,3,2,7,5,6,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [8,4,3,2,1,5,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [5,1,3,4,2,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,2,1,6,8,7] => [5,1,3,4,2,6,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,5,2,1,7,6,8] => [5,1,3,4,2,7,6,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [5,1,3,4,2,8,6,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [6,5,3,4,2,1,8,7] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [8,5,3,4,2,6,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [8,5,3,4,2,7,6,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [6,1,3,4,5,2,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [8,6,3,4,5,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [7,1,3,4,5,6,2,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [8,1,3,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [8,1,3,4,5,7,6,2] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [8,1,3,4,5,2,6,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => [6,1,3,4,2,5,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [8,7,3,4,6,5,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,4,6,5,8,7,2,1] => [8,1,3,4,6,5,2,7] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [8,7,3,4,2,6,5,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [8,1,3,4,2,6,7,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,7,5,2,1] => [8,1,3,4,2,6,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,4,7,6,8,5,2,1] => [8,1,3,4,2,7,6,5] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [5,1,3,2,4,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [5,1,3,2,4,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [5,1,3,2,4,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,4,2,6,1,8,7] => [6,5,3,2,4,1,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => [7,5,3,2,4,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,4,2,6,8,7,1] => [8,5,3,2,4,6,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [7,5,3,2,4,1,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => [8,5,3,2,4,1,7,6] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [7,6,3,5,4,2,1,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,4,6,2,7,8,1] => [8,6,3,5,4,2,7,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => [8,7,3,5,4,6,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,5,4,6,8,7,2,1] => [8,1,3,5,4,6,2,7] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [8,7,3,5,4,2,6,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [8,1,3,5,4,7,6,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,5,4,8,7,6,2,1] => [8,1,3,5,4,2,6,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [6,1,3,2,5,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [7,6,3,2,5,4,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,4,2,7,8,1] => [8,6,3,2,5,4,7,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,4,7,2,1,8] => [7,1,3,6,5,4,2,8] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [8,7,3,6,5,4,2,1] => [[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,5,6,4,8,7,2,1] => [8,1,3,6,5,4,2,7] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,4,2,1,8] => [7,1,3,2,5,6,4,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [8,7,3,2,5,6,4,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [8,1,3,7,5,6,4,2] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [8,1,3,2,5,6,7,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [8,1,3,2,5,6,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [7,1,3,2,5,4,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [8,1,3,2,5,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [8,1,3,2,5,4,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,5,4,2,7,1,8] => [7,6,3,2,4,5,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,5,4,2,8,7,1] => [8,6,3,2,4,5,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,5,4,7,2,1,8] => [7,1,3,6,4,5,2,8] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [8,7,3,6,4,5,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,5,4,8,7,2,1] => [8,1,3,6,4,5,2,7] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,6,5,7,4,8,2,1] => [8,1,3,7,6,5,4,2] => [[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,5,7,8,4,2,1] => [8,1,3,2,6,5,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,6,5,8,7,4,2,1] => [8,1,3,2,6,5,4,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,6,7,5,4,2,8,1] => [8,7,3,2,4,6,5,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,5,4,8,2,1] => [8,1,3,7,4,6,5,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,6,7,5,8,4,2,1] => [8,1,3,2,7,6,5,4] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,5,4,2,1] => [8,1,3,2,4,6,7,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [8,1,3,2,4,6,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,7,6,5,4,2,1,8] => [7,1,3,2,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [8,1,3,7,4,5,6,2] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [8,1,3,2,7,5,6,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [8,1,3,2,4,7,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [8,1,3,2,4,5,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [8,1,3,2,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [4,1,2,3,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [4,1,2,3,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [4,1,2,3,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [4,1,2,3,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [4,1,2,3,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [4,1,2,3,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [4,1,2,3,7,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [4,1,2,3,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [4,1,2,3,8,6,5,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [4,1,2,3,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [4,1,2,3,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [4,1,2,3,8,5,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [4,1,2,3,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [5,4,2,3,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,3,2,5,1,6,8,7] => [5,4,2,3,1,6,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [5,4,2,3,1,8,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [5,4,2,3,1,8,6,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [6,4,2,3,5,1,8,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [7,4,2,3,5,6,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [8,4,2,3,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [7,4,2,3,5,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [8,4,2,3,5,7,6,1] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [8,4,2,3,5,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,6,7,5,8,1] => [8,4,2,3,7,6,5,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,6,7,8,5,1] => [8,4,2,3,1,6,7,5] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [8,4,2,3,1,6,5,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [8,4,2,3,7,5,6,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [8,4,2,3,1,5,7,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [8,4,2,3,1,5,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [5,1,4,3,2,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [5,1,4,3,2,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,3,5,2,1,7,8,6] => [5,1,4,3,2,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,3,5,2,6,7,1,8] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,3,5,2,6,8,7,1] => [8,5,4,3,2,6,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [7,5,4,3,2,1,6,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [8,5,4,3,2,7,6,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => [8,5,4,3,2,1,6,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [6,1,4,3,5,2,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => [8,7,4,3,5,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [8,1,4,3,5,6,7,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,3,5,6,8,7,2,1] => [8,1,4,3,5,6,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,3,5,7,6,2,8,1] => [8,7,4,3,5,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [8,1,4,3,5,7,6,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => [8,1,4,3,5,2,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,3,5,8,7,6,2,1] => [8,1,4,3,5,2,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [8,7,4,3,6,5,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [8,1,4,3,6,5,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [8,1,4,3,6,5,2,7] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,3,6,7,5,8,2,1] => [8,1,4,3,7,6,5,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [8,1,4,3,2,6,7,5] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,3,6,8,7,5,2,1] => [8,1,4,3,2,6,5,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [7,1,4,3,2,5,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [8,7,4,3,2,5,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => [8,1,4,3,7,5,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,7,6,8,5,2,1] => [8,1,4,3,2,7,6,5] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [8,1,4,3,2,5,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [8,1,4,3,2,5,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [5,1,2,4,3,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => [5,1,2,4,3,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,5,3,2,6,8,7,1] => [8,5,2,4,3,6,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [7,5,2,4,3,1,6,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,5,3,2,7,8,6,1] => [8,5,2,4,3,1,7,6] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,3,2,8,7,6,1] => [8,5,2,4,3,1,6,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [6,1,5,4,3,2,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,5,3,6,2,7,8,1] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,3,6,7,8,2,1] => [8,1,5,4,3,6,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [8,1,5,4,3,6,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [8,1,5,4,3,7,6,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [8,1,5,4,3,2,7,6] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,3,8,7,6,2,1] => [8,1,5,4,3,2,6,7] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [6,1,2,4,5,3,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [8,6,2,4,5,3,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => [8,6,2,4,5,3,1,7] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [8,1,6,4,5,3,2,7] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [7,1,2,4,5,6,3,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [8,7,2,4,5,6,3,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [8,1,2,4,5,6,7,3] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [8,1,2,4,5,6,3,7] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,5,7,6,3,2,8,1] => [8,7,2,4,5,3,6,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,6,3,2,1] => [8,1,2,4,5,3,7,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [8,1,2,4,5,3,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [6,1,2,4,3,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [8,6,2,4,3,5,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [8,7,6,4,3,5,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,6,5,3,7,8,2,1] => [8,1,6,4,3,5,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,5,3,8,7,2,1] => [8,1,6,4,3,5,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [8,7,2,4,6,5,3,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,6,5,7,3,8,2,1] => [8,1,7,4,6,5,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [8,1,2,4,6,5,7,3] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [8,1,2,4,6,5,3,7] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [8,7,2,4,3,6,5,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,6,7,5,3,8,2,1] => [8,1,7,4,3,6,5,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [8,1,2,4,7,6,5,3] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [8,1,2,4,3,6,5,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [7,1,2,4,3,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [8,7,2,4,3,5,6,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [8,1,7,4,3,5,6,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [8,1,2,4,7,5,6,3] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [8,1,2,4,3,7,6,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [8,1,2,4,3,5,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [8,1,2,4,3,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [5,1,2,3,4,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [5,1,2,3,4,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [5,1,2,3,4,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [6,5,2,3,4,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [8,5,2,3,4,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [7,5,2,3,4,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [8,5,2,3,4,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [6,1,5,3,4,2,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [7,6,5,3,4,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [8,6,5,3,4,2,1,7] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,4,3,6,7,2,8,1] => [8,7,5,3,4,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,4,3,6,8,7,2,1] => [8,1,5,3,4,6,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,4,3,7,6,2,8,1] => [8,7,5,3,4,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [8,1,5,3,4,2,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [8,1,5,3,4,2,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [6,1,2,5,4,3,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => [7,6,2,5,4,3,1,8] => [[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [8,6,2,5,4,3,7,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [7,1,6,5,4,3,2,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,4,6,3,8,7,2,1] => [8,1,6,5,4,3,2,7] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [7,1,2,5,4,6,3,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,4,6,8,7,3,2,1] => [8,1,2,5,4,6,3,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,4,7,6,3,2,8,1] => [8,7,2,5,4,3,6,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,4,8,7,6,3,2,1] => [8,1,2,5,4,3,6,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [6,1,2,3,5,4,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,4,3,2,7,1,8] => [7,6,2,3,5,4,1,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,6,4,3,2,8,7,1] => [8,6,2,3,5,4,1,7] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [7,1,6,3,5,4,2,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,4,3,7,2,8,1] => [8,7,6,3,5,4,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,4,3,7,8,2,1] => [8,1,6,3,5,4,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => [7,1,2,6,5,4,3,8] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,6,4,7,3,8,2,1] => [8,1,7,6,5,4,3,2] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [8,1,2,6,5,4,3,7] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [7,1,2,3,5,6,4,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [8,1,7,3,5,6,4,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [8,1,2,3,5,6,7,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [8,1,2,3,5,6,4,7] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [7,1,2,3,5,4,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [8,7,2,3,5,4,6,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [8,1,7,3,5,4,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [8,1,2,3,5,7,6,4] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [8,1,2,3,5,4,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [8,1,2,3,5,4,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [6,1,2,3,4,5,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [7,6,2,3,4,5,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [8,6,2,3,4,5,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [8,7,6,3,4,5,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [8,1,6,3,4,5,7,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [8,1,6,3,4,5,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [7,1,2,6,4,5,3,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [8,7,2,6,4,5,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [8,1,7,6,4,5,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [8,1,2,6,4,5,7,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,5,4,8,7,3,2,1] => [8,1,2,6,4,5,3,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [7,1,2,3,6,5,4,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [8,7,2,3,6,5,4,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [8,1,7,3,6,5,4,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [8,1,2,7,6,5,4,3] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [8,1,2,3,6,5,7,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [8,1,2,3,6,5,4,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [7,1,2,3,4,6,5,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [8,1,2,7,4,6,5,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [8,1,2,3,7,6,5,4] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [8,1,2,3,4,6,7,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [8,1,2,3,4,6,5,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [8,7,2,3,4,5,6,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [8,1,7,3,4,5,6,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [8,1,2,7,4,5,6,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [8,1,2,3,7,5,6,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [8,1,2,3,4,7,6,5] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [8,1,2,3,4,5,7,6] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,1,2,3,4,5,6,7,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [1,9,2,3,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,1,2,3,4,5,6,7,8,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,6,5,4,3,2,1,9] => [8,1,2,3,4,5,7,6,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [1,9,2,3,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [1,10,2,3,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,1,2,3,4,5,6,7,8,9,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,7,6,5,4,3,2,1,10] => [9,1,2,3,4,5,6,8,7,10] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,6,8,5,4,3,2,1,9] => [8,1,2,3,4,7,6,5,9] => [[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,7,5,4,3,2,1,9] => [8,1,2,3,4,6,5,7,9] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,7,9,6,5,4,3,2] => [1,9,2,3,4,5,8,7,6] => [.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => [1,9,2,3,4,5,7,6,8] => [.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [1,10,2,3,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [1,11,2,3,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,10,11,9,8,7,6,5,4,3,2] => [1,11,2,3,4,5,6,7,8,10,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [8,2,1,3,4,5,6,7,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [7,1,2,3,4,5,6,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [2,1,9,3,4,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [1,9,3,2,4,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [7,1,2,3,4,5,6,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [1,8,2,3,4,5,6,7,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [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] => [2,9,8,7,6,5,4,3,1,10] => [9,2,1,3,4,5,6,7,8,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [8,1,2,3,4,5,6,7,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,8,9,7,6,5,4,3] => [1,2,9,3,4,5,6,8,7] => [.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,3,4,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [8,1,2,3,4,5,6,7,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [1,9,2,3,4,5,6,7,8,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [1,2,10,3,4,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[] => [] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [9,2,3,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [9,2,3,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,9,8,7,6,1] => [9,2,3,4,5,1,6,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [9,2,3,1,4,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [9,2,1,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [9,3,2,4,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [9,4,3,2,5,6,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [9,1,3,4,5,6,7,8,2] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,8,7,6,5,4,2,1] => [9,1,3,2,4,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => [9,1,2,3,5,4,6,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => [9,1,2,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [9,1,2,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [9,8,2,3,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1] => [9,1,8,3,4,5,6,7,2] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,7,6,5,4,9,3,2,1] => [9,1,2,8,4,5,6,7,3] => [[.,.],[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,7,6,5,9,4,3,2,1] => [9,1,2,3,8,5,6,7,4] => [[.,.],[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,7,6,9,5,4,3,2,1] => [9,1,2,3,4,8,6,7,5] => [[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => [9,1,2,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [9,1,2,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [9,1,2,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,3,4,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,9,7,8] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,9,8,7,6] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7] => [.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [1,2,3,4,9,7,6,8,5] => [.,[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6] => [.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [1,2,3,9,6,5,7,8,4] => [.,[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5] => [.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [1,2,9,5,4,6,7,8,3] => [.,[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4] => [.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [1,9,4,3,5,6,7,8,2] => [.,[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3] => [.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,3,4,5,6,7,8,9,2] => [.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,10,8,9] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,7,6] => [1,2,3,4,5,9,6,8,7] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,9,6,7,8] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [10,3,2,4,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [1,2,3,4,5,6,7,8,11,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [1,2,3,4,5,6,10,7,8,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [1,2,3,4,9,5,6,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [1,2,3,4,5,10,6,7,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,8,3,9,2] => [1,9,8,4,5,6,7,3,2] => [.,[[[[[.,.],.],[.,[.,[.,.]]]],.],.]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [1,2,3,9,4,5,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [1,2,3,4,10,5,6,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,6,5,8,7,9] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => [1,3,2,4,5,6,9,7,8] => [.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,7,6,5,4,3,2,8,9] => [1,7,2,3,4,5,6,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => [1,7,2,3,4,5,6,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,8,7] => [2,1,3,4,5,6,9,7,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,9,8,7] => [2,1,4,3,6,5,9,7,8] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [2,1,8,3,4,5,6,7,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,7,9,8] => [3,1,2,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => [3,1,2,5,4,7,6,9,8] => [[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [3,1,2,9,4,5,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => [4,1,2,3,6,5,8,7,9] => [[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [4,1,2,3,9,5,6,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => [5,1,2,3,4,7,6,8,9] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [5,1,2,3,4,9,6,7,8] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [6,1,2,3,4,5,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [6,1,2,3,4,5,9,7,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [1,2,3,10,4,5,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [1,3,2,5,4,7,6,10,8,9] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [2,1,6,3,4,5,10,7,8,9] => [[.,.],[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [2,1,8,3,4,5,6,7,10,9] => [[.,.],[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => [3,1,2,5,4,7,6,9,8,10] => [[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [3,1,2,10,4,5,6,7,8,9] => [[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [4,1,2,3,6,5,8,7,10,9] => [[.,.],[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => [4,1,2,3,6,5,10,7,8,9] => [[.,.],[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [4,1,2,3,8,5,6,7,10,9] => [[.,.],[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [4,1,2,3,10,5,6,7,8,9] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [5,1,2,3,4,10,6,7,8,9] => [[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [6,1,2,3,4,5,10,7,8,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [7,1,2,3,4,5,6,10,8,9] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [10,1,2,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [10,2,3,4,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => [10,1,2,3,4,5,6,9,8,7] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,8,7] => [.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [10,2,1,3,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [10,9,2,3,4,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [11,10,2,3,4,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [10,1,2,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => [10,1,2,3,5,4,6,7,8,9] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [7,2,3,4,5,6,1,9,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,4,5,6,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [10,2,3,4,5,6,7,1,8,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => [6,1,2,3,4,5,9,8,7] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [10,1,9,3,4,5,6,7,8,2] => [[.,.],[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,8,7,6,5,4,10,3,2,1] => [10,1,2,9,4,5,6,7,8,3] => [[.,.],[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,8,7,6,5,10,4,3,2,1] => [10,1,2,3,9,5,6,7,8,4] => [[.,.],[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,8,7,6,10,5,4,3,2,1] => [10,1,2,3,4,9,6,7,8,5] => [[.,.],[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,8,7,10,6,5,4,3,2,1] => [10,1,2,3,4,5,9,7,8,6] => [[.,.],[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [3,2,1,5,4,7,6,9,8] => [[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,1,5,4,7,6,9,8,10] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [10,1,3,4,5,6,7,8,9,2] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [11,2,3,4,5,6,7,8,9,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [11,1,3,4,5,6,7,8,9,10,2] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,6,4,7,3,9,10,8,2] => [1,10,7,6,5,4,3,2,9,8] => [.,[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,7,5,8,4,9,3,10,2] => [1,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,7,8,6,9,5,10,4] => [3,2,1,10,9,8,7,6,5,4] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1,8,9,7,10,6] => [5,4,3,2,1,10,9,8,7,6] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,3,6,2,7,1,9,10,8] => [7,6,5,4,3,2,1,10,9,8] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,7,8,6,9,5,10,4,11,3,12,2] => [1,12,11,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,3,1,8,9,7,10,6,11,5,12,4] => [3,2,1,12,11,10,9,8,7,6,5,4] => [[[.,.],.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,4,2,5,1,9,10,8,11,7,12,6] => [5,4,3,2,1,12,11,10,9,8,7,6] => [[[[[.,.],.],.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1,10,11,9,12,8] => [7,6,5,4,3,2,1,12,11,10,9,8] => [[[[[[[.,.],.],.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [5,6,4,7,3,8,2,9,1,11,12,10] => [9,8,7,6,5,4,3,2,1,12,11,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,9,10,8,7,6,5,4,3,1] => [10,2,1,3,4,5,6,7,9,8] => [[[.,.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,11,10,9,8,7,6,5,4,3,1] => [11,2,1,3,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [2,12,11,10,9,8,7,6,5,4,3,1] => [12,2,1,3,4,5,6,7,8,9,10,11] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [1,2,9,4,3,5,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [1,2,3,9,5,4,6,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [1,2,3,4,9,6,5,7,8] => [.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,9,7,6,8] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [10,1,2,3,4,6,7,8,9,5] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [1,3,2,5,4,7,6,9,8,11,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7,10,9] => [4,1,3,2,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7,10,9] => [6,3,2,5,4,1,8,7,10,9] => [[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,7,6,8,1,10,9] => [8,3,2,5,4,7,6,1,10,9] => [[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => [10,3,2,5,4,7,6,9,8,1] => [[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,10,7] => [2,1,4,3,6,5,10,9,8,7] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,6,9,8,10,5] => [2,1,4,3,10,7,6,9,8,5] => [[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,9,8,10,3] => [2,1,10,5,4,7,6,9,8,3] => [[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,9,8] => [.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10,11,12] => [3,1,2,4,5,6,7,8,9,10,11,12] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7,10,9] => [6,5,4,3,2,1,8,7,10,9] => [[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7,10,9] => [2,1,6,5,4,3,8,7,10,9] => [[.,.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,6,5,7,4,8,3,10,9] => [2,1,8,7,6,5,4,3,10,9] => [[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,6,5,7,4,8,1,10,9] => [8,3,2,7,6,5,4,1,10,9] => [[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,6,5,7,2,8,1,10,9] => [8,7,4,3,6,5,2,1,10,9] => [[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,4,6,3,7,2,8,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,6,8,5,10,9] => [2,1,4,3,8,7,6,5,10,9] => [[.,.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,7,6,8,5,10,9] => [4,3,2,1,8,7,6,5,10,9] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,7,6,8,1,10,9] => [8,5,4,3,2,7,6,1,10,9] => [[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,7,6,8,3,10,9] => [2,1,8,5,4,7,6,3,10,9] => [[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,8,7,9,6,10,5] => [2,1,4,3,10,9,8,7,6,5] => [[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,2,4,1,8,7,9,6,10,5] => [4,3,2,1,10,9,8,7,6,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,8,7,9,6,10,1] => [10,5,4,3,2,9,8,7,6,1] => [[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,8,7,9,6,10,3] => [2,1,10,5,4,9,8,7,6,3] => [[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,8,7,9,6,10,1] => [10,3,2,5,4,9,8,7,6,1] => [[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,8,7,9,2,10,1] => [10,9,4,3,6,5,8,7,2,1] => [[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,4,6,3,8,7,9,2,10,1] => [10,9,6,5,4,3,8,7,2,1] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,7,6,8,5,9,2,10,1] => [10,9,4,3,8,7,6,5,2,1] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,7,6,8,3,9,2,10,1] => [10,9,8,5,4,7,6,3,2,1] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,8,7,9,4,10,3] => [2,1,10,9,6,5,8,7,4,3] => [[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,8,7,9,4,10,1] => [10,3,2,9,6,5,8,7,4,1] => [[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,10,1] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,7,6,8,5,9,4,10,3] => [2,1,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,7,6,8,5,9,4,10,1] => [10,3,2,9,8,7,6,5,4,1] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,6,5,9,8,10,7] => [4,3,2,1,6,5,10,9,8,7] => [[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,3,5,2,6,1,9,8,10,7] => [6,5,4,3,2,1,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3,9,8,10,7] => [2,1,6,5,4,3,10,9,8,7] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,5,4,6,1,9,8,10,7] => [6,3,2,5,4,1,10,9,8,7] => [[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,6,5,7,4,9,8,10,3] => [2,1,10,7,6,5,4,9,8,3] => [[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,6,5,7,4,9,8,10,1] => [10,3,2,7,6,5,4,9,8,1] => [[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,6,5,7,2,9,8,10,1] => [10,7,4,3,6,5,2,9,8,1] => [[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,4,6,3,7,2,9,8,10,1] => [10,7,6,5,4,3,2,9,8,1] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,7,6,9,8,10,5] => [4,3,2,1,10,7,6,9,8,5] => [[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,9,8,10,1] => [10,5,4,3,2,7,6,9,8,1] => [[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9,12,11] => [4,3,2,1,6,5,8,7,10,9,12,11] => [[[[.,.],.],.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7,10,9,12,11] => [6,5,4,3,2,1,8,7,10,9,12,11] => [[[[[[.,.],.],.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7,10,9,12,11] => [2,1,6,5,4,3,8,7,10,9,12,11] => [[.,.],[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7,10,9,12,11] => [6,3,2,5,4,1,8,7,10,9,12,11] => [[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,6,5,7,4,8,3,10,9,12,11] => [2,1,8,7,6,5,4,3,10,9,12,11] => [[.,.],[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,6,5,7,4,8,1,10,9,12,11] => [8,3,2,7,6,5,4,1,10,9,12,11] => [[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,3,6,5,7,2,8,1,10,9,12,11] => [8,7,4,3,6,5,2,1,10,9,12,11] => [[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,4,6,3,7,2,8,1,10,9,12,11] => [8,7,6,5,4,3,2,1,10,9,12,11] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,7,6,8,5,10,9,12,11] => [2,1,4,3,8,7,6,5,10,9,12,11] => [[.,.],[[.,.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,7,6,8,5,10,9,12,11] => [4,3,2,1,8,7,6,5,10,9,12,11] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,3,5,2,7,6,8,1,10,9,12,11] => [8,5,4,3,2,7,6,1,10,9,12,11] => [[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,7,6,8,3,10,9,12,11] => [2,1,8,5,4,7,6,3,10,9,12,11] => [[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,5,4,7,6,8,1,10,9,12,11] => [8,3,2,5,4,7,6,1,10,9,12,11] => [[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,8,7,9,6,10,5,12,11] => [2,1,4,3,10,9,8,7,6,5,12,11] => [[.,.],[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,8,7,9,6,10,5,12,11] => [4,3,2,1,10,9,8,7,6,5,12,11] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,8,7,9,6,10,1,12,11] => [10,5,4,3,2,9,8,7,6,1,12,11] => [[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,8,7,9,6,10,3,12,11] => [2,1,10,5,4,9,8,7,6,3,12,11] => [[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,8,7,9,6,10,1,12,11] => [10,3,2,5,4,9,8,7,6,1,12,11] => [[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,6,5,8,7,9,2,10,1,12,11] => [10,9,4,3,6,5,8,7,2,1,12,11] => [[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,4,6,3,8,7,9,2,10,1,12,11] => [10,9,6,5,4,3,8,7,2,1,12,11] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,7,6,8,5,9,2,10,1,12,11] => [10,9,4,3,8,7,6,5,2,1,12,11] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,4,7,6,8,3,9,2,10,1,12,11] => [10,9,8,5,4,7,6,3,2,1,12,11] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,6,5,8,7,9,4,10,3,12,11] => [2,1,10,9,6,5,8,7,4,3,12,11] => [[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,6,5,8,7,9,4,10,1,12,11] => [10,3,2,9,6,5,8,7,4,1,12,11] => [[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [6,5,7,4,8,3,9,2,10,1,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,7,6,8,5,9,4,10,3,12,11] => [2,1,10,9,8,7,6,5,4,3,12,11] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,7,6,8,5,9,4,10,1,12,11] => [10,3,2,9,8,7,6,5,4,1,12,11] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,6,5,9,8,10,7,12,11] => [2,1,4,3,6,5,10,9,8,7,12,11] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5,9,8,10,7,12,11] => [4,3,2,1,6,5,10,9,8,7,12,11] => [[[[.,.],.],.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,9,8,10,7,12,11] => [6,5,4,3,2,1,10,9,8,7,12,11] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,9,8,10,7,12,11] => [2,1,6,5,4,3,10,9,8,7,12,11] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,9,8,10,7,12,11] => [6,3,2,5,4,1,10,9,8,7,12,11] => [[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,6,5,7,4,9,8,10,3,12,11] => [2,1,10,7,6,5,4,9,8,3,12,11] => [[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,6,5,7,4,9,8,10,1,12,11] => [10,3,2,7,6,5,4,9,8,1,12,11] => [[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,3,6,5,7,2,9,8,10,1,12,11] => [10,7,4,3,6,5,2,9,8,1,12,11] => [[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [5,4,6,3,7,2,9,8,10,1,12,11] => [10,7,6,5,4,3,2,9,8,1,12,11] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,6,9,8,10,5,12,11] => [2,1,4,3,10,7,6,9,8,5,12,11] => [[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,7,6,9,8,10,5,12,11] => [4,3,2,1,10,7,6,9,8,5,12,11] => [[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,7,6,9,8,10,1,12,11] => [10,5,4,3,2,7,6,9,8,1,12,11] => [[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,7,6,9,8,10,3,12,11] => [2,1,10,5,4,7,6,9,8,3,12,11] => [[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,7,6,9,8,10,1,12,11] => [10,3,2,5,4,7,6,9,8,1,12,11] => [[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,6,5,10,9,11,8,12,7] => [2,1,4,3,6,5,12,11,10,9,8,7] => [[.,.],[[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,2,4,1,6,5,10,9,11,8,12,7] => [4,3,2,1,6,5,12,11,10,9,8,7] => [[[[.,.],.],.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1,10,9,11,8,12,7] => [6,5,4,3,2,1,12,11,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,6,3,10,9,11,8,12,7] => [2,1,6,5,4,3,12,11,10,9,8,7] => [[.,.],[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,6,1,10,9,11,8,12,7] => [6,3,2,5,4,1,12,11,10,9,8,7] => [[[[.,.],.],[[.,.],.]],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,10,9,11,8,12,3] => [2,1,12,7,6,5,4,11,10,9,8,3] => [[.,.],[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,10,9,11,8,12,1] => [12,3,2,7,6,5,4,11,10,9,8,1] => [[[[.,.],.],[[[[.,.],.],.],[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,10,9,11,8,12,1] => [12,7,4,3,6,5,2,11,10,9,8,1] => [[[[[[.,.],.],.],[[.,.],.]],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,10,9,11,8,12,1] => [12,7,6,5,4,3,2,11,10,9,8,1] => [[[[[[[[.,.],.],.],.],.],.],[[[[.,.],.],.],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,7,6,10,9,11,8,12,5] => [2,1,4,3,12,7,6,11,10,9,8,5] => [[.,.],[[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,4,1,7,6,10,9,11,8,12,5] => [4,3,2,1,12,7,6,11,10,9,8,5] => [[[[.,.],.],.],[[[[.,.],.],[[[[.,.],.],.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,7,6,10,9,11,8,12,1] => [12,5,4,3,2,7,6,11,10,9,8,1] => [[[[[[.,.],.],.],.],[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,7,6,10,9,11,8,12,3] => [2,1,12,5,4,7,6,11,10,9,8,3] => [[.,.],[[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,7,6,10,9,11,8,12,1] => [12,3,2,5,4,7,6,11,10,9,8,1] => [[[[.,.],.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,8,7,10,9,11,4,12,3] => [2,1,12,11,6,5,8,7,10,9,4,3] => [[.,.],[[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,8,7,10,9,11,4,12,1] => [12,3,2,11,6,5,8,7,10,9,4,1] => [[[[.,.],.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,10,9,11,2,12,1] => [12,11,8,7,6,5,4,3,10,9,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]],.],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,7,6,8,5,10,9,11,4,12,3] => [2,1,12,11,8,7,6,5,10,9,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,7,6,8,5,10,9,11,4,12,1] => [12,3,2,11,8,7,6,5,10,9,4,1] => [[[[.,.],.],[[[[[[.,.],.],.],.],[[.,.],.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,6,5,9,8,10,7,11,4,12,3] => [2,1,12,11,6,5,10,9,8,7,4,3] => [[.,.],[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,6,5,9,8,10,7,11,4,12,1] => [12,3,2,11,6,5,10,9,8,7,4,1] => [[[[.,.],.],[[[[.,.],.],[[[[.,.],.],.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,9,8,10,3,11,2,12,1] => [12,11,10,7,6,5,4,9,8,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.],.],.]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,7,6,9,8,10,5,11,4,12,3] => [2,1,12,11,10,7,6,9,8,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,7,6,9,8,10,5,11,4,12,1] => [12,3,2,11,10,7,6,9,8,5,4,1] => [[[[.,.],.],[[[[[[.,.],.],.],[[.,.],.]],.],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,8,7,10,9,11,2,12,1] => [12,11,4,3,6,5,8,7,10,9,2,1] => [[[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,7,6,8,5,10,9,11,2,12,1] => [12,11,4,3,8,7,6,5,10,9,2,1] => [[[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,4,6,3,8,7,10,9,11,2,12,1] => [12,11,6,5,4,3,8,7,10,9,2,1] => [[[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,4,7,6,8,3,10,9,11,2,12,1] => [12,11,8,5,4,7,6,3,10,9,2,1] => [[[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]],.],.]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,8,7,9,4,10,3,11,2,12,1] => [12,11,10,9,6,5,8,7,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,6,5,9,8,10,7,11,2,12,1] => [12,11,4,3,6,5,10,9,8,7,2,1] => [[[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,7,6,9,8,10,5,11,2,12,1] => [12,11,4,3,10,7,6,9,8,5,2,1] => [[[[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,9,8,10,7,11,2,12,1] => [12,11,6,5,4,3,10,9,8,7,2,1] => [[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,7,6,9,8,10,3,11,2,12,1] => [12,11,10,5,4,7,6,9,8,3,2,1] => [[[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.],.],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,8,7,10,9,11,6,12,5] => [2,1,4,3,12,11,8,7,10,9,6,5] => [[.,.],[[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,4,1,8,7,10,9,11,6,12,5] => [4,3,2,1,12,11,8,7,10,9,6,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],[[.,.],.]],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,8,7,10,9,11,6,12,1] => [12,5,4,3,2,11,8,7,10,9,6,1] => [[[[[[.,.],.],.],.],[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,8,7,10,9,11,6,12,3] => [2,1,12,5,4,11,8,7,10,9,6,3] => [[.,.],[[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,8,7,10,9,11,6,12,1] => [12,3,2,5,4,11,8,7,10,9,6,1] => [[[[.,.],.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,8,7,9,6,10,5,11,4,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,8,7,9,6,10,5,11,4,12,1] => [12,3,2,11,10,9,8,7,6,5,4,1] => [[[[.,.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,8,7,9,6,10,5,11,2,12,1] => [12,11,4,3,10,9,8,7,6,5,2,1] => [[[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]],.],.]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,8,7,9,6,10,3,11,2,12,1] => [12,11,10,5,4,9,8,7,6,3,2,1] => [[[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.],.],.]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,4,3,9,8,10,7,11,6,12,5] => [2,1,4,3,12,11,10,9,8,7,6,5] => [[.,.],[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,4,1,9,8,10,7,11,6,12,5] => [4,3,2,1,12,11,10,9,8,7,6,5] => [[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,5,2,9,8,10,7,11,6,12,1] => [12,5,4,3,2,11,10,9,8,7,6,1] => [[[[[[.,.],.],.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,5,4,9,8,10,7,11,6,12,3] => [2,1,12,5,4,11,10,9,8,7,6,3] => [[.,.],[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,5,4,9,8,10,7,11,6,12,1] => [12,3,2,5,4,11,10,9,8,7,6,1] => [[[[.,.],.],[[.,.],[[[[[[.,.],.],.],.],.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,8,7,11,10,12,9] => [2,1,4,3,6,5,8,7,12,11,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,6,5,8,7,11,10,12,9] => [4,3,2,1,6,5,8,7,12,11,10,9] => [[[[.,.],.],.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [4,3,5,2,6,1,8,7,11,10,12,9] => [6,5,4,3,2,1,8,7,12,11,10,9] => [[[[[[.,.],.],.],.],.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3,8,7,11,10,12,9] => [2,1,6,5,4,3,8,7,12,11,10,9] => [[.,.],[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,2,5,4,6,1,8,7,11,10,12,9] => [6,3,2,5,4,1,8,7,12,11,10,9] => [[[[.,.],.],[[.,.],.]],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3,11,10,12,9] => [2,1,8,7,6,5,4,3,12,11,10,9] => [[.,.],[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1,11,10,12,9] => [8,3,2,7,6,5,4,1,12,11,10,9] => [[[[.,.],.],[[[[.,.],.],.],.]],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1,11,10,12,9] => [8,7,4,3,6,5,2,1,12,11,10,9] => [[[[[[.,.],.],.],[[.,.],.]],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1,11,10,12,9] => [8,7,6,5,4,3,2,1,12,11,10,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5,11,10,12,9] => [2,1,4,3,8,7,6,5,12,11,10,9] => [[.,.],[[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5,11,10,12,9] => [4,3,2,1,8,7,6,5,12,11,10,9] => [[[[.,.],.],.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1,11,10,12,9] => [8,5,4,3,2,7,6,1,12,11,10,9] => [[[[[[.,.],.],.],.],[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3,11,10,12,9] => [2,1,8,5,4,7,6,3,12,11,10,9] => [[.,.],[[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1,11,10,12,9] => [8,3,2,5,4,7,6,1,12,11,10,9] => [[[[.,.],.],[[.,.],[[.,.],.]]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,8,7,9,6,11,10,12,5] => [2,1,4,3,12,9,8,7,6,11,10,5] => [[.,.],[[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,8,7,9,6,11,10,12,5] => [4,3,2,1,12,9,8,7,6,11,10,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,8,7,9,6,11,10,12,1] => [12,5,4,3,2,9,8,7,6,11,10,1] => [[[[[[.,.],.],.],.],[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,8,7,9,6,11,10,12,3] => [2,1,12,5,4,9,8,7,6,11,10,3] => [[.,.],[[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,8,7,9,6,11,10,12,1] => [12,3,2,5,4,9,8,7,6,11,10,1] => [[[[.,.],.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,6,5,8,7,9,2,11,10,12,1] => [12,9,4,3,6,5,8,7,2,11,10,1] => [[[[[[.,.],.],.],[[.,.],[[.,.],.]]],[[.,.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,4,6,3,8,7,9,2,11,10,12,1] => [12,9,6,5,4,3,8,7,2,11,10,1] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,7,6,8,5,9,2,11,10,12,1] => [12,9,4,3,8,7,6,5,2,11,10,1] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],[[.,.],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,4,7,6,8,3,9,2,11,10,12,1] => [12,9,8,5,4,7,6,3,2,11,10,1] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],[[.,.],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,6,5,8,7,9,4,11,10,12,3] => [2,1,12,9,6,5,8,7,4,11,10,3] => [[.,.],[[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,6,5,8,7,9,4,11,10,12,1] => [12,3,2,9,6,5,8,7,4,11,10,1] => [[[[.,.],.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,11,10,12,1] => [12,9,8,7,6,5,4,3,2,11,10,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,7,6,8,5,9,4,11,10,12,3] => [2,1,12,9,8,7,6,5,4,11,10,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,7,6,8,5,9,4,11,10,12,1] => [12,3,2,9,8,7,6,5,4,11,10,1] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,11,10,12,7] => [2,1,4,3,6,5,12,9,8,11,10,7] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,6,5,9,8,11,10,12,7] => [4,3,2,1,6,5,12,9,8,11,10,7] => [[[[.,.],.],.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,6,1,9,8,11,10,12,7] => [6,5,4,3,2,1,12,9,8,11,10,7] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,6,3,9,8,11,10,12,7] => [2,1,6,5,4,3,12,9,8,11,10,7] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1,9,8,11,10,12,7] => [6,3,2,5,4,1,12,9,8,11,10,7] => [[[[.,.],.],[[.,.],.]],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,6,5,7,4,9,8,11,10,12,3] => [2,1,12,7,6,5,4,9,8,11,10,3] => [[.,.],[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,6,5,7,4,9,8,11,10,12,1] => [12,3,2,7,6,5,4,9,8,11,10,1] => [[[[.,.],.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,3,6,5,7,2,9,8,11,10,12,1] => [12,7,4,3,6,5,2,9,8,11,10,1] => [[[[[[.,.],.],.],[[.,.],.]],[[.,.],[[.,.],.]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [5,4,6,3,7,2,9,8,11,10,12,1] => [12,7,6,5,4,3,2,9,8,11,10,1] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,6,9,8,11,10,12,5] => [2,1,4,3,12,7,6,9,8,11,10,5] => [[.,.],[[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,7,6,9,8,11,10,12,5] => [4,3,2,1,12,7,6,9,8,11,10,5] => [[[[.,.],.],.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,9,8,11,10,12,1] => [12,5,4,3,2,7,6,9,8,11,10,1] => [[[[[[.,.],.],.],.],[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,9,8,11,10,12,3] => [2,1,12,5,4,7,6,9,8,11,10,3] => [[.,.],[[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,11,10,12,1] => [12,3,2,5,4,7,6,9,8,11,10,1] => [[[[.,.],.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => [10,1,2,3,4,5,6,7,8,9,12,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,4,6,3,7,2,8,1,9] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,5,7,4,8,3,9,2] => [1,9,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,1,7,8,9,10,6,5,4,3] => [2,1,10,3,4,5,7,8,9,6] => [[.,.],[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,6,5,9,10,8,7] => [4,1,3,2,6,5,10,7,9,8] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [5,6,4,7,3,8,2,10,9,1] => [10,8,7,6,5,4,3,2,1,9] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,5,3,6,2,7,1,8,9] => [7,6,5,4,3,2,1,8,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
Map
to 312-avoiding permutation
Description
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
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 $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ 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 $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
searching the database
Sorry, this map was not found in the database.