Processing math: 100%

Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ 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] => [2,3,1] => [[.,[.,.]],.]
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [[.,.],[.,.]]
[1,1,0,1,0,0] => [2,3,1] => [3,1,2] => [[.,.],[.,.]]
[1,1,1,0,0,0] => [3,2,1] => [3,2,1] => [[[.,.],.],.]
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [2,3,4,1] => [[.,[.,[.,.]]],.]
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,3,1,4] => [[.,[.,.]],[.,.]]
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,4,1,3] => [[.,[.,.]],[.,.]]
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [3,4,2,1] => [[[.,[.,.]],.],.]
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [3,2,4,1] => [[[.,.],[.,.]],.]
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1,2,4] => [[.,.],[.,[.,.]]]
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,1,2,3] => [[.,.],[.,[.,.]]]
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,2,3,1] => [[[.,.],[.,.]],.]
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [4,2,1,3] => [[[.,.],.],[.,.]]
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [4,3,1,2] => [[[.,.],.],[.,.]]
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [[[[.,.],.],.],.]
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [3,4,5,2,1] => [[[.,[.,[.,.]]],.],.]
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [3,4,2,5,1] => [[[.,[.,.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,5,2,4,1] => [[[.,[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [3,4,2,1,5] => [[[.,[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [3,5,2,1,4] => [[[.,[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [3,5,4,1,2] => [[.,[[.,.],.]],[.,.]]
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [4,5,3,2,1] => [[[[.,[.,.]],.],.],.]
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [3,2,4,5,1] => [[[.,.],[.,[.,.]]],.]
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,2,5,1,4] => [[[.,.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [4,3,5,2,1] => [[[[.,.],[.,.]],.],.]
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [4,2,3,5,1] => [[[.,.],[.,[.,.]]],.]
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [5,2,3,1,4] => [[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [5,2,4,1,3] => [[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,3,4,2,1] => [[[[.,.],[.,.]],.],.]
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [4,3,2,5,1] => [[[[.,.],.],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [4,2,1,3,5] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [5,2,1,3,4] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [4,3,1,2,5] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [5,3,1,2,4] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [5,4,1,2,3] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [5,4,2,3,1] => [[[[.,.],.],[.,.]],.]
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [5,3,2,1,4] => [[[[.,.],.],.],[.,.]]
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [5,4,2,1,3] => [[[[.,.],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [5,4,3,1,2] => [[[[.,.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [3,4,5,6,2,1] => [[[.,[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [3,4,5,2,6,1] => [[[.,[.,[.,.]]],[.,.]],.]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [3,4,6,2,5,1] => [[[.,[.,[.,.]]],[.,.]],.]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [3,4,5,2,1,6] => [[[.,[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,4,6,2,1,5] => [[[.,[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [3,4,6,5,1,2] => [[.,[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [4,5,6,3,2,1] => [[[[.,[.,[.,.]]],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => [[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [3,4,2,5,1,6] => [[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,4,2,6,1,5] => [[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [4,5,3,6,2,1] => [[[[.,[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,5,2,4,6,1] => [[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [3,6,2,4,5,1] => [[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [3,5,2,4,1,6] => [[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [3,6,2,4,1,5] => [[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [3,6,2,5,1,4] => [[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [4,6,3,5,2,1] => [[[[.,[.,.]],[.,.]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [3,4,2,1,5,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [4,5,3,2,6,1] => [[[[.,[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [3,5,2,1,4,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [3,6,2,1,4,5] => [[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [4,6,3,2,5,1] => [[[[.,[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [3,5,4,1,2,6] => [[.,[[.,.],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [3,6,4,1,2,5] => [[.,[[.,.],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [3,6,5,1,2,4] => [[.,[[.,.],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [4,6,5,2,3,1] => [[[.,[[.,.],.]],[.,.]],.]
>>> Load all 1666 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [4,5,3,2,1,6] => [[[[.,[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [4,6,3,2,1,5] => [[[[.,[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [4,6,5,2,1,3] => [[[.,[[.,.],.]],.],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [4,6,5,3,1,2] => [[[.,[[.,.],.]],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [5,6,4,3,2,1] => [[[[[.,[.,.]],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [3,2,4,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [3,2,4,6,1,5] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [4,3,5,6,2,1] => [[[[.,.],[.,[.,.]]],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [4,3,5,2,6,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [3,2,5,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [3,2,6,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [4,3,6,2,5,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [4,3,5,2,1,6] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [4,3,6,2,1,5] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [4,3,6,5,1,2] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [5,4,6,3,2,1] => [[[[[.,.],[.,.]],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [4,2,3,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [4,2,3,6,1,5] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [5,3,4,6,2,1] => [[[[.,.],[.,[.,.]]],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [5,2,3,4,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [6,2,3,4,1,5] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [6,2,3,5,1,4] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [5,3,4,2,6,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [5,2,3,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [6,2,3,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [6,3,4,2,5,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [5,2,4,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [6,2,4,1,3,5] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [6,2,5,1,3,4] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [6,3,5,2,4,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,3,4,2,1,6] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [6,3,4,2,1,5] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [6,3,5,2,1,4] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [6,3,5,4,1,2] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,4,5,3,2,1] => [[[[[.,.],[.,.]],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [4,3,2,5,6,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [4,3,2,5,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [4,3,2,6,1,5] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [5,4,3,6,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [5,3,2,4,6,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [6,2,1,3,4,5] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [6,3,2,4,1,5] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [6,3,2,5,1,4] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,4,3,5,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [5,4,2,3,6,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [5,3,1,2,4,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [6,3,1,2,4,5] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [6,4,2,3,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [5,4,1,2,3,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [6,4,1,2,3,5] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [6,5,1,2,3,4] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [5,4,2,3,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [6,4,2,3,1,5] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [6,5,2,3,1,4] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [6,5,2,4,1,3] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [5,4,3,2,6,1] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [5,3,2,1,4,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [6,3,2,1,4,5] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [5,4,2,1,3,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [6,4,2,1,3,5] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [6,5,2,1,3,4] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [6,5,3,2,4,1] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [5,4,3,1,2,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [6,4,3,1,2,5] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [6,5,3,1,2,4] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [6,5,4,2,3,1] => [[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [6,4,3,2,1,5] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [6,5,3,2,1,4] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [6,5,4,2,1,3] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [6,5,4,3,1,2] => [[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [2,3,4,5,7,1,6] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [3,4,5,6,7,2,1] => [[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [3,4,5,6,2,7,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [2,3,4,6,1,5,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [2,3,4,7,1,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [3,4,5,7,2,6,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [3,4,5,6,2,1,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [3,4,5,7,2,1,6] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [3,4,5,7,6,1,2] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => [[[[.,[.,[.,[.,.]]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [3,4,5,2,6,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [3,4,5,2,6,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [3,4,5,2,7,1,6] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [4,5,6,3,7,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [2,3,5,1,4,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [3,4,6,2,5,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [2,3,6,1,4,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [2,3,7,1,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [3,4,7,2,5,6,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [3,4,6,2,5,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [3,4,7,2,5,1,6] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [3,4,7,2,6,1,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [4,5,7,3,6,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [3,4,5,2,1,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [4,5,6,3,2,7,1] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [3,4,6,2,1,5,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [3,4,7,2,1,5,6] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [4,5,7,3,2,6,1] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [3,4,6,5,1,2,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [3,4,7,5,1,2,6] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [3,4,7,6,1,2,5] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [4,5,7,6,2,3,1] => [[[.,[.,[[.,.],.]]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [4,5,6,3,2,1,7] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [4,5,7,3,2,1,6] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [4,5,7,6,2,1,3] => [[[.,[.,[[.,.],.]]],.],[.,.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [4,5,7,6,3,1,2] => [[[.,[.,[[.,.],.]]],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [5,6,7,4,3,2,1] => [[[[[.,[.,[.,.]]],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [3,4,2,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [3,4,2,5,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [3,4,2,5,7,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [4,5,3,6,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [3,4,2,5,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [4,5,3,6,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [3,4,2,6,1,5,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [3,4,2,7,1,5,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [4,5,3,7,2,6,1] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [4,5,3,6,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [4,5,3,7,2,1,6] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [4,5,3,7,6,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [5,6,4,7,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [3,5,2,4,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [3,5,2,4,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [3,5,2,4,7,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [4,6,3,5,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [2,5,1,3,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [3,6,2,4,5,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [2,6,1,3,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [2,7,1,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [3,7,2,4,5,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [3,6,2,4,5,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [3,7,2,4,5,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [3,7,2,4,6,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [4,7,3,5,6,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [3,5,2,4,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [4,6,3,5,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [3,6,2,4,1,5,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [3,7,2,4,1,5,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [4,7,3,5,2,6,1] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [3,6,2,5,1,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [3,7,2,5,1,4,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [3,7,2,6,1,4,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [4,7,3,6,2,5,1] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [4,6,3,5,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [4,7,3,5,2,1,6] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [4,7,3,6,2,1,5] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [4,7,3,6,5,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [5,7,4,6,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [3,4,2,1,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [4,5,3,2,6,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [4,5,3,2,6,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [4,5,3,2,7,1,6] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [5,6,4,3,7,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [3,5,2,1,4,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [4,6,3,2,5,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [3,6,2,1,4,5,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [3,7,2,1,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [4,7,3,2,5,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [4,6,3,2,5,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [4,7,3,2,5,1,6] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [4,7,3,2,6,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [5,7,4,3,6,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [3,5,4,1,2,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [4,6,5,2,3,7,1] => [[[.,[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [3,6,4,1,2,5,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [3,7,4,1,2,5,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [4,7,5,2,3,6,1] => [[[.,[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [3,6,5,1,2,4,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [3,7,5,1,2,4,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [3,7,6,1,2,4,5] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [4,7,6,2,3,5,1] => [[[.,[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [4,6,5,2,3,1,7] => [[[.,[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [4,7,5,2,3,1,6] => [[[.,[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [4,7,6,2,3,1,5] => [[[.,[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [4,7,6,2,5,1,3] => [[[.,[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [5,7,6,3,4,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [4,5,3,2,1,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [5,6,4,3,2,7,1] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [4,6,3,2,1,5,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [4,7,3,2,1,5,6] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [5,7,4,3,2,6,1] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [4,6,5,2,1,3,7] => [[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [4,7,5,2,1,3,6] => [[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [4,7,6,2,1,3,5] => [[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [5,7,6,3,2,4,1] => [[[[.,[[.,.],.]],.],[.,.]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [4,6,5,3,1,2,7] => [[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [4,7,5,3,1,2,6] => [[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [4,7,6,3,1,2,5] => [[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [4,7,6,5,1,2,3] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [5,7,6,4,2,3,1] => [[[[.,[[.,.],.]],.],[.,.]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [5,6,4,3,2,1,7] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [5,7,4,3,2,1,6] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [5,7,6,3,2,1,4] => [[[[.,[[.,.],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [5,7,6,4,2,1,3] => [[[[.,[[.,.],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [5,7,6,4,3,1,2] => [[[[.,[[.,.],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [6,7,5,4,3,2,1] => [[[[[[.,[.,.]],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [3,2,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [3,2,4,5,7,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [4,3,5,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [3,2,4,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [4,3,5,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [3,2,4,6,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [3,2,4,7,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [4,3,5,7,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [4,3,5,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [4,3,5,7,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [4,3,5,7,6,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [5,4,6,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [3,2,4,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [4,3,5,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [4,3,5,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [4,3,5,2,7,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [5,4,6,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [3,2,5,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [4,3,6,2,5,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [3,2,6,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [3,2,7,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [4,3,7,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [4,3,6,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [4,3,7,2,5,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [4,3,7,2,6,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [5,4,7,3,6,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [4,3,5,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [5,4,6,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [4,3,6,2,1,5,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [4,3,7,2,1,5,6] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [5,4,7,3,2,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [4,3,6,5,1,2,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [4,3,7,5,1,2,6] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [4,3,7,6,1,2,5] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [5,4,7,6,2,3,1] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [5,4,6,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [5,4,7,3,2,1,6] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [5,4,7,6,2,1,3] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [5,4,7,6,3,1,2] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [6,5,7,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [4,2,3,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [4,2,3,5,7,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [5,3,4,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [4,2,3,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [5,3,4,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [4,2,3,6,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [4,2,3,7,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [5,3,4,7,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [5,3,4,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [5,3,4,7,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [5,3,4,7,6,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [6,4,5,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [5,2,3,4,7,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [6,3,4,5,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [7,2,3,4,6,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [7,3,4,5,6,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [6,3,4,5,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [7,3,4,5,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [6,2,3,5,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [7,2,3,5,1,4,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [7,2,3,6,1,4,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [7,3,4,6,2,5,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,3,4,5,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [7,3,4,5,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [7,3,4,6,2,1,5] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [7,3,4,6,5,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,4,5,6,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [5,3,4,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [5,3,4,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [5,3,4,2,7,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [6,4,5,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [5,2,3,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [6,3,4,2,5,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [6,2,3,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [7,2,3,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [7,3,4,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [6,3,4,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [7,3,4,2,5,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [7,3,4,2,6,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [7,4,5,3,6,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [5,2,4,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [6,3,5,2,4,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [6,2,4,1,3,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [7,2,4,1,3,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [7,3,5,2,4,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [6,2,5,1,3,4,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [7,2,5,1,3,4,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [7,2,6,1,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [7,3,6,2,4,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [6,3,5,2,4,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [7,3,5,2,4,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [7,3,6,2,4,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [7,3,6,2,5,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [7,4,6,3,5,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,3,4,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [6,4,5,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [6,3,4,2,1,5,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [7,3,4,2,1,5,6] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [7,4,5,3,2,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [6,3,5,2,1,4,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [7,3,5,2,1,4,6] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [7,3,6,2,1,4,5] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [7,4,6,3,2,5,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [6,3,5,4,1,2,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [7,3,5,4,1,2,6] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [7,3,6,4,1,2,5] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [7,3,6,5,1,2,4] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [7,4,6,5,2,3,1] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,4,5,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [7,4,5,3,2,1,6] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [7,4,6,3,2,1,5] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [7,4,6,5,2,1,3] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [7,4,6,5,3,1,2] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,5,6,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [4,3,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [4,3,2,5,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [4,3,2,5,7,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [5,4,3,6,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [4,3,2,5,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [5,4,3,6,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [4,3,2,6,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [4,3,2,7,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [5,4,3,7,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [5,4,3,6,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [5,4,3,7,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [5,4,3,7,6,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [4,2,1,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [5,3,2,4,7,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [6,4,3,5,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [5,2,1,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [6,2,1,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [7,2,1,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [7,3,2,4,6,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [7,4,3,5,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [6,4,3,5,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [6,3,2,4,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [7,3,2,4,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [7,4,3,5,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [6,3,2,5,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [7,3,2,5,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [7,3,2,6,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [7,4,3,6,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,4,3,5,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [7,4,3,5,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [7,4,3,6,2,1,5] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [7,4,3,6,5,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,5,4,6,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [4,3,1,2,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [5,4,2,3,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [5,4,2,3,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [5,4,2,3,7,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [6,5,3,4,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [5,3,1,2,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [6,4,2,3,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [6,3,1,2,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [7,3,1,2,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [7,4,2,3,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [6,4,2,3,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [7,4,2,3,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [7,4,2,3,6,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [5,4,1,2,3,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [6,5,2,3,4,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [6,4,1,2,3,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [7,4,1,2,3,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [7,5,2,3,4,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [6,5,1,2,3,4,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [7,5,1,2,3,4,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [7,6,1,2,3,4,5] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [7,6,2,3,4,5,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [6,5,2,3,4,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [7,5,2,3,4,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [7,6,2,3,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [7,6,2,3,5,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [5,4,2,3,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [6,4,2,3,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [7,4,2,3,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [6,5,2,3,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [7,5,2,3,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [7,6,2,3,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [7,6,3,4,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [6,5,2,4,1,3,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [7,5,2,4,1,3,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [7,6,2,4,1,3,5] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [7,6,2,5,1,3,4] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [7,6,3,5,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [7,6,3,4,2,1,5] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [7,6,3,5,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [7,6,3,5,4,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [5,4,3,2,7,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [6,5,4,3,7,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [5,3,2,1,4,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [6,3,2,1,4,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [7,3,2,1,4,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [7,4,3,2,6,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [5,4,2,1,3,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [6,5,3,2,4,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [6,4,2,1,3,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [7,4,2,1,3,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [7,5,3,2,4,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [6,5,2,1,3,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [7,5,2,1,3,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [7,6,2,1,3,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [7,6,3,2,4,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [6,5,3,2,4,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [7,5,3,2,4,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [7,6,3,2,4,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [7,6,3,2,5,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [5,4,3,1,2,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [6,5,4,2,3,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [6,4,3,1,2,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [7,4,3,1,2,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [7,5,4,2,3,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [6,5,3,1,2,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [7,5,3,1,2,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [7,6,3,1,2,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [7,6,4,2,3,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [6,5,4,1,2,3,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [7,5,4,1,2,3,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [7,6,4,1,2,3,5] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [7,6,5,1,2,3,4] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [7,6,5,2,3,4,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [6,5,4,2,3,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [7,5,4,2,3,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [7,6,4,2,3,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [7,6,5,2,3,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [7,6,5,2,4,1,3] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [6,5,3,2,1,4,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [7,5,3,2,1,4,6] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [7,6,3,2,1,4,5] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [7,6,4,3,2,5,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [6,5,4,2,1,3,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [7,5,4,2,1,3,6] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [7,6,4,2,1,3,5] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [7,6,5,2,1,3,4] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [7,6,5,3,2,4,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [6,5,4,3,1,2,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [7,5,4,3,1,2,6] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [7,6,4,3,1,2,5] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [7,6,5,3,1,2,4] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [7,6,5,4,1,2,3] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [7,6,5,4,2,3,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [7,6,5,4,2,1,3] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [7,6,5,4,3,1,2] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [2,3,4,5,6,7,1,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [3,4,5,6,7,8,2,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [3,4,5,6,7,2,8,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [2,3,4,5,7,1,6,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [2,3,4,5,8,1,6,7] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [3,4,5,6,8,2,7,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [3,4,5,6,7,2,1,8] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [3,4,5,6,8,7,1,2] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [4,5,6,7,8,3,2,1] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [3,4,5,6,2,7,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [3,4,5,6,2,7,1,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [3,4,5,6,2,8,1,7] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [4,5,6,7,3,8,2,1] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [2,3,4,6,1,5,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [3,4,5,7,2,6,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [2,3,4,7,1,5,6,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [2,3,4,8,1,5,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [3,4,5,8,2,6,7,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [3,4,5,8,2,7,1,6] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [3,4,5,6,2,1,7,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [4,5,6,7,3,2,8,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [3,4,5,7,2,1,6,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [3,4,5,8,2,1,6,7] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [4,5,6,8,3,2,7,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [3,4,5,8,7,1,2,6] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [4,5,6,7,3,2,1,8] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [4,5,6,8,3,2,1,7] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [4,5,6,8,7,2,1,3] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [5,6,7,8,4,3,2,1] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [2,3,4,1,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [3,4,5,2,6,7,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [3,4,5,2,6,1,7,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [4,5,6,3,7,2,8,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [3,4,5,2,7,1,6,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [4,5,6,3,8,2,7,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [4,5,6,3,8,2,1,7] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [4,5,6,3,8,7,1,2] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [5,6,7,4,8,3,2,1] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [2,3,5,1,4,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [3,4,6,2,5,7,1,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [4,5,7,3,6,8,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [2,3,6,1,4,5,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [2,3,7,1,4,5,6,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [2,3,8,1,4,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [3,4,8,2,5,6,7,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [4,5,8,3,6,7,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [3,4,7,2,5,1,6,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [3,4,8,2,7,1,5,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [4,5,8,3,7,2,6,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,6,8,5,3] => [4,5,8,3,7,2,1,6] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [4,5,8,3,7,6,1,2] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [5,6,8,4,7,3,2,1] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [3,4,5,2,1,6,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [4,5,6,3,2,7,8,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [4,5,6,3,2,8,1,7] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [5,6,7,4,3,8,2,1] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [3,4,8,2,1,5,6,7] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [4,5,8,3,2,6,1,7] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,7,8,6,3] => [4,5,8,3,2,7,1,6] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [3,4,6,5,1,2,7,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [3,4,8,6,1,2,5,7] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [3,4,8,7,1,2,5,6] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [4,5,8,7,2,3,6,1] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [4,5,8,7,2,3,1,6] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [4,5,6,3,2,1,7,8] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [4,5,8,3,2,1,6,7] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [5,6,8,4,3,2,7,1] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [4,5,8,7,6,1,2,3] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [5,6,7,4,3,2,1,8] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [5,6,8,4,3,2,1,7] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [5,6,8,7,3,2,1,4] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [5,6,8,7,4,2,1,3] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [5,6,8,7,4,3,1,2] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [6,7,8,5,4,3,2,1] => [[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [3,4,2,5,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [3,4,2,5,6,7,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [3,4,2,5,6,8,1,7] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [3,4,2,5,6,1,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [4,5,3,6,7,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [4,5,3,6,8,2,7,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [5,6,4,7,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [3,4,2,5,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [4,5,3,6,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [4,5,3,6,2,8,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [3,4,2,7,1,5,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [3,4,2,8,1,5,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [4,5,3,7,2,6,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [4,5,3,8,2,6,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [4,5,3,8,2,7,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [5,6,4,8,3,7,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [4,5,3,8,2,1,6,7] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [4,5,3,8,6,1,2,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [5,6,4,7,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [5,6,4,8,3,2,1,7] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [5,6,4,8,7,2,1,3] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [6,7,5,8,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [2,4,1,3,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [3,5,2,4,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [3,5,2,4,6,8,1,7] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [4,6,3,5,7,8,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [4,6,3,5,7,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [3,5,2,4,7,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [4,6,3,5,8,2,7,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [4,6,3,5,8,2,1,7] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [4,6,3,5,8,7,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [5,7,4,6,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [2,5,1,3,4,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [2,6,1,3,4,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [2,7,1,3,4,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [2,8,1,3,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [3,8,2,4,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [3,7,2,4,5,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [3,8,2,4,7,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [3,5,2,4,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [4,6,3,5,2,7,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [4,6,3,5,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [4,6,3,5,2,8,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [4,7,3,5,2,6,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [4,8,3,5,2,6,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,4,7,8,6,2] => [4,8,3,5,2,7,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [3,6,2,5,1,4,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [3,7,2,5,1,4,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => [3,7,2,6,1,4,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [3,8,2,7,1,4,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [4,7,3,6,2,5,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,6,4,8,2] => [4,8,3,6,2,5,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,6,8,4,2] => [4,8,3,7,2,5,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [4,8,3,7,2,6,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [5,8,4,7,3,6,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [4,7,3,5,2,1,6,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [5,8,4,6,3,2,7,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [4,8,3,6,2,1,5,7] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [4,8,3,7,2,1,5,6] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => [4,7,3,6,5,1,2,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [4,8,3,7,5,1,2,6] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [4,8,3,7,6,1,2,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,7,5,4,2] => [5,8,4,7,6,2,3,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [5,7,4,6,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [5,8,4,7,6,3,1,2] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [6,8,5,7,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [3,4,2,1,5,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [4,5,3,2,6,7,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [4,5,3,2,8,1,6,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [5,6,4,3,8,2,7,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [5,6,4,3,7,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [6,7,5,4,8,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [3,5,2,1,4,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [3,8,2,1,4,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [5,8,4,3,6,7,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [4,6,3,2,5,1,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [4,7,3,2,5,1,6,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [5,8,4,3,6,2,7,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,3,6,7,5,8,2] => [4,8,3,2,6,1,5,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => [4,8,3,2,7,1,5,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,6,8,7,5,2] => [5,8,4,3,7,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [5,8,4,3,7,2,1,6] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [5,8,4,3,7,6,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [6,8,5,4,7,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => [3,5,4,1,2,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,3,7,2,8] => [3,7,5,1,2,4,6,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [3,7,6,1,2,4,5,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [3,8,6,1,2,4,5,7] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [3,8,7,1,2,4,5,6] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [5,8,7,3,4,6,2,1] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,5,8,7,3,2] => [5,8,7,3,4,2,6,1] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [4,8,7,2,5,1,3,6] => [[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [4,8,7,2,6,1,3,5] => [[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [5,8,7,3,6,2,4,1] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [5,7,6,3,4,2,1,8] => [[[[.,[[.,.],.]],[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [6,8,7,4,5,3,2,1] => [[[[[.,[[.,.],.]],[.,.]],.],.],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [4,5,3,2,1,6,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [5,6,4,3,2,7,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [5,6,4,3,2,8,1,7] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [6,7,5,4,3,8,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [4,7,3,2,1,5,6,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [4,8,3,2,1,5,6,7] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [5,8,4,3,2,6,7,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [6,8,5,4,3,7,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,4,6,3,2,7,8] => [4,6,5,2,1,3,7,8] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [4,7,5,2,1,3,6,8] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [4,8,5,2,1,3,6,7] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [4,8,6,2,1,3,5,7] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [4,8,7,2,1,3,5,6] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,4,6,8,7,3,2] => [5,8,7,3,2,4,6,1] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,4,7,6,3,2,8] => [5,7,6,3,2,4,1,8] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,4,7,8,6,3,2] => [5,8,7,3,2,6,1,4] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => [4,8,6,5,1,2,3,7] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [4,8,7,6,1,2,3,5] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => [5,8,7,6,2,3,1,4] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [5,6,4,3,2,1,7,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [6,7,5,4,3,2,8,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [5,8,4,3,2,1,6,7] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [6,8,5,4,3,2,7,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => [5,8,7,3,2,1,4,6] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,5,7,4,3,2,8] => [5,7,6,4,2,1,3,8] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [5,8,6,4,2,1,3,7] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [5,8,7,6,2,1,3,4] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [6,8,7,5,3,2,4,1] => [[[[[.,[[.,.],.]],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [5,8,7,6,3,1,2,4] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [5,8,7,6,4,1,2,3] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [6,7,5,4,3,2,1,8] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [6,8,5,4,3,2,1,7] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [6,8,7,4,3,2,1,5] => [[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [6,8,7,5,3,2,1,4] => [[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [6,8,7,5,4,2,1,3] => [[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [6,8,7,5,4,3,1,2] => [[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [7,8,6,5,4,3,2,1] => [[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [3,2,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [3,2,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [3,2,4,5,6,8,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [4,3,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [3,2,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [3,2,4,5,8,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [4,3,5,6,8,7,1,2] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [5,4,6,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [3,2,4,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [4,3,5,6,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [4,3,5,6,2,8,1,7] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [5,4,6,7,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [4,3,5,7,2,6,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [3,2,4,8,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [6,5,7,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [3,2,4,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [4,3,5,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [4,3,5,2,6,8,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [4,3,5,2,6,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [5,4,6,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [4,3,5,2,7,1,6,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [4,3,5,2,8,1,6,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [5,4,6,3,8,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [5,4,6,3,8,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [5,4,6,3,8,7,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [6,5,7,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [3,2,5,1,4,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [4,3,6,2,5,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [5,4,7,3,6,8,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [4,3,7,2,5,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [3,2,8,1,4,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [4,3,8,2,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [4,3,6,2,5,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [5,4,7,3,6,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [5,4,8,3,6,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,5,3,8] => [4,3,7,2,6,1,5,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [4,3,8,2,6,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [4,3,8,2,7,1,5,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [5,4,8,3,7,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [5,4,8,3,6,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,7,6,8,5,3] => [5,4,8,3,7,2,1,6] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [5,4,8,3,7,6,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [4,3,5,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [5,4,7,3,2,6,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [4,3,7,2,1,5,6,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [4,3,8,2,1,5,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [5,4,8,3,2,6,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [5,4,8,3,2,6,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [5,4,8,3,2,7,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [6,5,8,4,3,7,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [4,3,6,5,1,2,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [5,4,7,6,2,3,8,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [5,4,8,6,2,3,7,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [4,3,8,6,1,2,5,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [4,3,8,7,1,2,5,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,7,4,3] => [5,4,8,7,2,3,6,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [5,4,8,6,2,3,1,7] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [5,4,8,7,2,3,1,6] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [5,4,8,7,2,6,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [6,5,8,7,3,4,2,1] => [[[[[.,.],[[.,.],.]],[.,.]],.],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [6,5,7,4,3,2,8,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [5,4,8,6,2,1,3,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [5,4,8,7,2,1,3,6] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [6,5,8,7,3,2,4,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,5,4,3,8] => [5,4,7,6,3,1,2,8] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => [5,4,8,6,3,1,2,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [5,4,8,7,3,1,2,6] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [5,4,8,7,6,1,2,3] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,7,5,4,3] => [6,5,8,7,4,2,3,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [6,5,7,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [6,5,8,4,3,2,1,7] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [6,5,8,7,3,2,1,4] => [[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [6,5,8,7,4,2,1,3] => [[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [6,5,8,7,4,3,1,2] => [[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [7,6,8,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [4,2,3,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [4,2,3,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [4,2,3,5,6,8,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [4,2,3,5,8,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [6,4,5,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [5,3,4,6,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [4,2,3,8,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [6,4,5,7,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [6,4,5,8,3,2,7,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [5,3,4,8,7,1,2,6] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [6,4,5,8,7,3,1,2] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [7,5,6,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [5,2,3,4,6,8,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [6,3,4,5,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [6,3,4,5,7,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [5,2,3,4,7,1,6,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [5,2,3,4,8,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [6,3,4,5,8,2,7,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [6,3,4,5,8,2,1,7] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [6,3,4,5,8,7,1,2] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [7,4,5,6,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [6,2,3,4,5,8,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [7,3,4,5,6,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [8,2,3,4,5,7,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [8,3,4,5,6,7,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [8,2,3,4,6,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [8,2,3,4,7,1,5,6] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [8,3,4,5,6,2,1,7] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [8,3,4,5,7,2,1,6] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [8,3,4,5,7,6,1,2] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [8,4,5,6,7,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [6,3,4,5,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [6,3,4,5,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [7,4,5,6,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,7,8,6,1] => [8,3,4,5,2,7,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [8,2,3,5,1,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [8,2,3,6,1,4,5,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [8,2,3,7,1,4,5,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [8,3,4,7,2,5,6,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [8,3,4,7,2,6,1,5] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,7,6,4,1] => [8,4,5,7,3,6,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [6,3,4,5,2,1,7,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [7,4,5,6,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [8,3,4,5,2,1,6,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,5,7,4,1,8] => [7,3,4,6,2,1,5,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [8,4,5,7,3,2,6,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => [8,3,4,7,6,1,2,5] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [7,4,5,6,3,2,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [8,4,5,6,3,2,1,7] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [8,5,6,7,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [6,4,5,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [6,4,5,3,8,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [6,4,5,3,8,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [6,4,5,3,8,7,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [7,5,6,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [5,2,3,1,4,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [7,2,3,1,4,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [8,2,3,1,4,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [8,3,4,2,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [7,4,5,3,6,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [8,4,5,3,6,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [8,4,5,3,7,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [8,4,5,3,6,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [8,5,6,4,7,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => [6,3,5,2,4,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [6,3,5,2,4,8,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [8,2,4,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => [8,3,5,2,4,7,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [8,3,6,2,4,5,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => [8,3,7,2,4,5,6,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => [8,3,7,2,4,6,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => [6,3,5,2,4,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [7,4,6,3,5,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => [8,3,5,2,4,1,6,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [8,4,6,3,5,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [8,3,6,2,4,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [8,3,7,2,4,1,5,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [8,4,7,3,5,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [8,3,7,2,6,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [8,4,7,3,6,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,4,7,6,5,8,3,1] => [8,4,7,3,5,2,1,6] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [8,4,7,3,6,5,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [8,5,7,4,6,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [5,3,4,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [6,4,5,3,2,8,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [7,5,6,4,3,8,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [8,3,4,2,1,5,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [8,4,5,3,2,6,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [7,3,5,2,1,4,6,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,4,6,3,7,8,1] => [8,3,5,2,1,4,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [7,3,6,2,1,4,5,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [8,3,6,2,1,4,5,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => [8,3,7,2,1,4,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [8,4,7,3,2,5,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [8,4,7,3,2,6,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => [8,5,7,4,3,6,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,4,7,8,3,1] => [8,3,7,4,1,2,5,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [8,4,7,5,2,3,6,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [8,3,6,5,1,2,4,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [8,3,7,5,1,2,4,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [8,3,7,6,1,2,4,5] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [8,4,5,3,2,1,6,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [8,4,7,3,2,1,5,6] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [8,5,7,4,3,2,6,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,6,5,7,8,4,3,1] => [8,4,7,6,2,1,3,5] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [8,4,7,6,3,1,2,5] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [8,4,7,6,5,1,2,3] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [8,5,7,6,4,2,3,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [7,5,6,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [8,5,6,4,3,2,1,7] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [8,5,7,4,3,2,1,6] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => [8,5,7,6,4,2,1,3] => [[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [8,5,7,6,4,3,1,2] => [[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [8,6,7,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [4,3,2,5,6,8,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [5,4,3,6,7,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [5,4,3,6,7,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [5,4,3,6,8,7,1,2] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [6,5,4,7,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [5,4,3,6,2,7,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [4,3,2,6,1,5,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => [4,3,2,7,1,5,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [4,3,2,8,1,5,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [5,4,3,7,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [5,4,3,8,2,7,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [6,5,4,8,3,7,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => [5,4,3,7,2,1,6,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [5,4,3,8,2,1,6,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [6,5,4,8,3,2,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [6,5,4,8,7,2,3,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [6,5,4,7,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [6,5,4,8,3,2,1,7] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => [6,5,4,8,7,2,1,3] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [6,5,4,8,7,3,1,2] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [4,2,1,3,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [5,3,2,4,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [5,3,2,4,6,8,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [6,4,3,5,7,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [5,3,2,4,7,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [6,4,3,5,8,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [6,4,3,5,8,2,1,7] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [6,4,3,5,8,7,1,2] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [7,5,4,6,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [5,2,1,3,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [7,2,1,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [8,2,1,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [8,3,2,4,5,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => [8,3,2,4,5,7,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [8,4,3,5,6,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => [7,3,2,4,6,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [8,4,3,5,6,2,1,7] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [6,4,3,5,2,8,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [7,5,4,6,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [7,4,3,5,2,6,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [7,4,3,5,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [8,4,3,5,2,6,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [7,4,3,6,2,5,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => [8,3,2,5,1,4,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => [7,3,2,6,1,4,5,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [8,3,2,6,1,4,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [8,3,2,7,1,4,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [8,4,3,6,2,5,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [8,4,3,7,2,6,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [7,4,3,5,2,1,6,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [8,5,4,6,3,2,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,6,5,7,4,1,8] => [7,4,3,6,2,1,5,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [8,4,3,6,2,1,5,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [8,4,3,6,5,1,2,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,6,7,5,8,4,1] => [8,4,3,7,5,1,2,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [7,5,4,6,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [8,5,4,7,6,3,1,2] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [8,6,5,7,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [4,3,1,2,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,2,1,5,6,8,7] => [5,4,2,3,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,2,1,5,8,7,6] => [6,5,3,4,7,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [6,5,3,4,7,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [5,4,2,3,8,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [6,5,3,4,8,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [6,5,3,4,8,2,1,7] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [6,5,3,4,8,7,1,2] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [7,6,4,5,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [5,3,1,2,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [6,4,2,3,5,7,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [6,4,2,3,5,8,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [7,5,3,4,6,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [7,3,1,2,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [8,3,1,2,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [8,4,2,3,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,2,5,7,6,1,8] => [7,4,2,3,5,6,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [8,4,2,3,5,7,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => [8,5,3,4,6,7,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [7,5,3,4,6,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [7,4,2,3,5,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [8,4,2,3,5,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [8,4,2,3,6,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [8,6,4,5,7,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [5,4,1,2,3,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,2,1,6,8,7] => [6,5,2,3,4,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,2,1,7,8,6] => [6,5,2,3,4,8,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [7,6,3,4,5,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [6,4,1,2,3,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [7,5,2,3,4,6,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [7,4,1,2,3,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [8,4,1,2,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [8,5,2,3,4,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [6,5,1,2,3,4,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,2,1,8,7] => [7,6,2,3,4,5,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [7,5,1,2,3,4,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [8,5,1,2,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [8,6,2,3,4,5,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [7,6,1,2,3,4,5,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [8,6,1,2,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [8,7,1,2,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [8,7,2,3,4,5,6,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [8,7,2,3,4,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [8,7,2,3,4,6,1,5] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => [7,6,3,4,5,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,5,2,7,1,8] => [7,5,2,3,4,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,5,2,7,8,1] => [8,5,2,3,4,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [8,6,2,3,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,5,7,8,2,1] => [8,7,2,3,4,1,5,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [8,6,2,3,5,1,4,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [8,7,2,3,6,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => [8,7,3,4,5,2,1,6] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [5,4,2,3,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [6,5,3,4,2,7,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [6,5,3,4,2,8,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [7,6,4,5,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => [8,4,2,3,1,5,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => [8,5,3,4,2,7,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [7,5,2,3,1,4,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,4,6,7,8,2,1] => [8,7,2,3,1,4,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [8,7,3,4,2,5,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [8,6,2,4,1,3,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,4,7,8,2,1] => [8,7,2,4,1,3,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [8,6,2,5,1,3,4,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [8,7,2,5,1,3,4,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [8,7,2,6,1,3,4,5] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [7,6,3,5,2,4,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [8,6,3,5,2,4,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => [8,7,3,5,2,4,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => [8,7,3,6,2,4,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [8,7,3,6,2,5,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [8,7,4,6,3,5,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [7,6,4,5,3,2,8,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,5,4,7,2,1,8] => [7,6,3,4,2,1,5,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [8,6,3,4,2,1,5,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,5,4,7,8,2,1] => [8,7,3,4,2,1,5,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [8,7,4,6,5,2,3,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [8,7,4,5,3,2,1,6] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [8,7,4,6,3,2,1,5] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [8,7,4,6,5,2,1,3] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [8,7,4,6,5,3,1,2] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [8,7,5,6,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [5,4,3,2,6,8,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [5,4,3,2,7,1,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [5,4,3,2,8,1,6,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [6,5,4,3,8,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [6,5,4,3,8,2,1,7] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [6,5,4,3,8,7,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [5,3,2,1,4,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [7,5,4,3,6,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [7,4,3,2,5,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [7,3,2,1,4,5,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,3,2,5,7,8,6,1] => [8,4,3,2,5,7,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [7,5,4,3,6,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [8,5,4,3,7,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [8,5,4,3,7,6,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [5,4,2,1,3,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [6,5,3,2,4,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => [7,6,4,3,5,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [6,4,2,1,3,5,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [7,5,3,2,4,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [8,4,2,1,3,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [7,5,3,2,4,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [8,5,3,2,4,6,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => [8,6,4,3,5,7,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [7,6,3,2,4,5,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [8,5,2,1,3,4,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [8,7,2,1,3,4,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,3,5,7,6,2,1,8] => [7,6,3,2,4,5,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => [8,7,3,2,4,6,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [7,6,4,3,5,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,3,6,5,7,2,1,8] => [7,6,3,2,4,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [8,6,3,2,4,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [8,7,3,2,4,1,5,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [8,7,4,3,5,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,6,7,5,2,8,1] => [8,6,3,2,5,1,4,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [8,7,3,2,6,1,4,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [8,7,4,3,6,5,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [8,7,5,4,6,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [5,4,3,1,2,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => [6,5,4,2,3,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [7,6,5,3,4,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,5,3,2,6,1,7,8] => [6,4,3,1,2,5,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,3,2,6,1,8,7] => [7,5,4,2,3,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,5,3,2,6,8,7,1] => [8,5,4,2,3,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [7,6,4,2,3,5,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [7,5,3,1,2,4,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [8,6,4,2,3,5,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,5,3,7,6,2,1,8] => [7,6,4,2,3,5,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,3,7,6,2,8,1] => [8,6,4,2,3,5,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [8,7,4,2,3,6,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [6,5,4,1,2,3,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [7,6,5,2,3,4,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [8,5,4,1,2,3,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [8,6,4,1,2,3,5,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,5,6,3,7,8,2,1] => [8,7,4,1,2,3,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [7,6,5,1,2,3,4,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [8,6,5,1,2,3,4,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [8,7,5,1,2,3,4,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [8,7,6,1,2,3,4,5] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [8,7,6,2,3,4,5,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => [7,6,5,2,3,4,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [8,7,6,2,3,4,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [8,7,6,3,4,5,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [7,6,5,3,4,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [8,6,4,2,3,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,5,7,3,2,1,8] => [7,6,5,2,3,1,4,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [8,6,5,2,3,1,4,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [8,7,6,2,3,1,4,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [8,7,6,3,4,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [8,6,5,2,4,1,3,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [8,7,6,2,4,1,3,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,5,3,2,1] => [8,7,6,2,5,1,3,4] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [8,7,6,3,5,2,4,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [7,6,5,3,4,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [8,6,5,3,4,2,1,7] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [8,7,5,3,4,2,1,6] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [8,7,6,3,4,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [8,7,6,3,5,2,1,4] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [8,7,6,3,5,4,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [6,5,4,3,2,8,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [6,4,3,2,1,5,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [7,5,4,3,2,6,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [7,4,3,2,1,5,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [8,4,3,2,1,5,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [8,5,4,3,2,6,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [8,5,4,3,2,7,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [8,6,5,4,3,7,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [7,5,3,2,1,4,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => [8,5,3,2,1,4,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,4,3,6,7,2,1,8] => [7,6,3,2,1,4,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,4,3,6,7,2,8,1] => [8,6,3,2,1,4,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [8,7,3,2,1,4,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,4,3,6,8,7,2,1] => [8,7,4,3,2,5,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [8,7,4,3,2,6,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [6,5,4,2,1,3,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [7,6,5,3,2,4,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [8,5,4,2,1,3,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [8,6,5,3,2,4,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [7,6,4,2,1,3,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [8,6,4,2,1,3,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [7,6,5,2,1,3,4,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [8,7,5,2,1,3,4,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [8,7,6,2,1,3,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [7,6,5,3,2,4,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [8,7,5,3,2,4,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => [8,7,6,3,2,4,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => [8,7,6,3,2,5,1,4] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [6,5,4,3,1,2,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [7,6,5,4,2,3,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,4,3,2,7,1,8] => [7,5,4,3,1,2,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [7,6,4,3,1,2,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [8,7,5,4,2,3,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [8,7,6,3,1,2,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [7,6,5,4,1,2,3,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,4,3,2,8,1] => [8,6,5,4,1,2,3,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [8,7,5,4,1,2,3,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [8,7,6,4,1,2,3,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [8,7,6,5,1,2,3,4] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [8,7,6,5,2,3,4,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [7,6,5,4,2,3,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [8,6,5,4,2,3,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [8,7,6,4,2,3,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [8,7,6,5,2,3,1,4] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [8,7,6,5,2,4,1,3] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [8,7,6,5,3,4,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [7,5,4,3,2,1,6,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [8,5,4,3,2,1,6,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [7,6,4,3,2,1,5,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [8,6,4,3,2,1,5,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [8,7,4,3,2,1,5,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [7,6,5,3,2,1,4,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [8,6,5,3,2,1,4,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [8,7,5,3,2,1,4,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [8,7,6,3,2,1,4,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,5,4,8,7,3,2,1] => [8,7,6,4,3,2,5,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [7,6,5,4,2,1,3,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [8,6,5,4,2,1,3,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [8,7,6,4,2,1,3,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [8,7,6,5,2,1,3,4] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [8,7,6,5,3,2,4,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [7,6,5,4,3,1,2,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [8,6,5,4,3,1,2,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,5,4,3,8,2,1] => [8,7,5,4,3,1,2,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [8,7,6,4,3,1,2,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [8,7,6,5,3,1,2,4] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [8,7,6,5,4,1,2,3] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [8,7,6,5,4,2,3,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [8,7,5,4,3,2,1,6] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [8,7,6,4,3,2,1,5] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [8,7,6,5,4,2,1,3] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [8,7,6,5,4,3,1,2] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [8,9,7,6,5,4,3,2,1] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,6,5,4,3,2,1,9] => [8,7,6,5,4,3,1,2,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,1,2,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,6,8,5,4,3,2,1,9] => [8,7,6,5,4,2,1,3,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,7,5,4,3,2,1,9] => [8,7,6,5,4,2,3,1,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [10,11,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1,12] => [11,10,9,8,7,6,5,4,3,2,1,12] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [8,7,9,6,5,4,3,2,1,10] => [9,8,7,6,5,4,2,1,3,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,6,5,8,4,3,2,1,9] => [8,7,6,5,3,2,1,4,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,5,4,3,2,1,9] => [8,7,6,5,4,1,2,3,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [8,7,6,9,5,4,3,2,1,10] => [9,8,7,6,5,3,2,1,4,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,8,7,6,5,3,2,1,9] => [8,7,6,4,5,3,2,1,9] => [[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,9,8,7,6,4,3,2,1,10] => [9,8,7,6,4,5,3,2,1,10] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,6,5,4,3,8,2,1,9] => [8,7,5,4,3,2,1,6,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [8,7,6,5,4,9,3,2,1,10] => [9,8,7,5,4,3,2,1,6,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => [8,6,5,4,3,2,1,7,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [8,6,7,5,4,3,2,1,9] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [8,7,6,5,4,3,2,9,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [8,7,9,6,5,4,3,2,1] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [8,7,6,5,4,3,9,2,1,10] => [9,8,6,5,4,3,2,1,7,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [7,8,6,5,4,3,2,1,9] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [6,7,5,4,3,2,1,9,8] => [8,7,6,5,4,2,3,9,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [7,8,9,6,5,4,3,2,1] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => [9,7,6,5,4,3,2,1,8,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [9,8,7,6,5,4,3,2,10,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [9,8,10,7,6,5,4,3,2,1] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [8,9,7,6,5,4,3,2,1,10] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [8,9,10,7,6,5,4,3,2,1] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[] => [] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [9,2,3,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [9,3,4,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,1] => [9,2,3,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,5,8,7,6,9,1] => [9,3,4,5,6,7,2,1,8] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,1] => [9,2,3,4,5,1,6,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [9,6,7,8,5,4,3,2,1] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [9,2,3,1,4,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [9,6,7,5,4,3,2,1,8] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [9,7,8,6,5,4,3,2,1] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [9,2,1,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [9,3,1,2,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,9,1] => [9,4,1,2,3,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,7,2,8,9,1] => [9,6,1,2,3,4,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,2,9,1] => [9,7,1,2,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [9,8,1,2,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [3,8,7,6,5,4,9,2,1] => [9,8,5,6,4,3,2,1,7] => [[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,6,3,7,8,9,2,1] => [9,8,4,1,2,3,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [9,8,7,1,2,3,4,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,8,7,6,5,9,3,2,1] => [9,8,7,4,5,3,2,1,6] => [[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,9,8,7,6,5,3,2,1] => [9,8,7,5,6,4,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => [9,7,5,3,1,2,4,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [9,8,7,6,1,2,3,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,8,7,6,9,4,3,2,1] => [9,8,7,6,3,4,2,1,5] => [[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => [9,8,7,6,4,5,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => [9,5,4,3,2,1,6,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [9,8,7,6,5,1,2,3,4] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,8,5,4,3,2,1] => [9,8,7,6,5,2,3,4,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,8,7,9,5,4,3,2,1] => [9,8,7,6,5,2,3,1,4] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,9,8,7,5,4,3,2,1] => [9,8,7,6,5,3,4,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => [9,6,5,4,3,2,1,7,8] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,6,5,4,3,2,9,8,1] => [9,7,6,5,4,3,2,8,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,6,8,9,5,4,3,2,1] => [9,8,7,6,5,2,1,3,4] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,6,9,8,5,4,3,2,1] => [9,8,7,6,5,3,2,4,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,6,5,4,3,2,9,1] => [9,7,6,5,4,3,1,2,8] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => [9,8,7,6,5,4,1,2,3] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [9,8,7,6,5,4,2,3,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [9,7,6,5,4,3,2,1,8] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1] => [9,8,6,5,4,3,2,1,7] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,7,6,5,4,9,3,2,1] => [9,8,7,5,4,3,2,1,6] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,7,6,5,9,4,3,2,1] => [9,8,7,6,4,3,2,1,5] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,7,6,9,5,4,3,2,1] => [9,8,7,6,5,3,2,1,4] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => [9,8,7,6,5,4,2,1,3] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1,2] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [2,3,4,5,6,7,9,1,8] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [2,3,4,5,6,9,1,7,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [2,3,4,5,9,1,6,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [2,3,4,9,1,5,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [2,3,9,1,4,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [2,9,1,3,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [2,3,4,5,6,7,8,9,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [3,4,5,6,7,8,9,2,1] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [2,3,4,5,6,7,8,10,1,9] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [2,3,4,5,6,7,10,1,8,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [2,3,4,5,6,10,1,7,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [2,3,4,5,10,1,6,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [2,3,4,10,1,5,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [2,3,10,1,4,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [2,10,1,3,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [3,4,5,6,7,8,9,10,2,1] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [2,3,4,5,6,7,8,9,11,1,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [4,5,6,7,8,9,3,2,1] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [10,2,1,3,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [2,11,1,3,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [3,4,5,6,7,8,9,10,11,2,1] => [[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [4,5,6,7,8,9,10,3,2,1] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,10,1] => [10,3,1,2,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => [11,2,1,3,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [2,12,1,3,4,5,6,7,8,9,10,11] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [5,6,7,8,9,4,3,2,1] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,9,10,1] => [10,4,1,2,3,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,10,11,1] => [11,3,1,2,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [5,6,7,8,9,10,4,3,2,1] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,9,10,11,1] => [11,4,1,2,3,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,6,7,2,8,9,10,1] => [10,6,1,2,3,4,5,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [6,7,8,9,5,4,3,2,1] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,7,8,2,9,10,1] => [10,7,1,2,3,4,5,6,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [6,7,8,9,10,5,4,3,2,1] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,2,8,9,10,11,1] => [11,6,1,2,3,4,5,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,2,9,10,11,1] => [11,7,1,2,3,4,5,6,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [2,3,4,5,6,7,8,1,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [2,3,4,5,6,7,1,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [3,4,5,6,7,8,2,9,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [2,3,4,5,6,1,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [4,5,6,3,7,2,8,1,9] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [3,4,2,5,6,7,8,9,1] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [3,4,2,5,1,6,7,8,9] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [5,6,4,7,3,8,2,9,1] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [3,4,2,1,5,6,7,8,9] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [3,2,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [3,2,4,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [5,4,6,3,7,2,8,1,9] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [7,6,8,5,4,3,2,1,9] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => [4,3,2,5,1,6,7,8,9] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [8,7,6,9,5,4,3,2,1] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,3,2,1,6,5,7,8,9] => [5,4,3,2,6,1,7,8,9] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [8,7,6,5,9,4,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => [6,5,4,3,2,7,1,8,9] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [8,7,6,5,4,9,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => [7,6,5,4,3,2,8,1,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [8,7,6,5,4,3,9,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [2,3,4,5,6,7,8,9,1,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [2,3,4,5,6,7,8,1,9,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [7,8,9,10,6,5,4,3,2,1] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [5,6,4,7,3,8,2,9,1,10] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [3,2,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [6,5,7,4,8,3,9,2,10,1] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [9,8,7,10,6,5,4,3,2,1] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [9,8,7,6,10,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [9,8,7,6,5,10,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [9,8,7,6,5,4,10,3,2,1] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => [8,7,6,5,4,3,2,9,1,10] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [9,8,7,6,5,4,3,10,2,1] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [6,1,2,3,4,5,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [7,1,2,3,4,5,6,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,4,6,5,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,5,7,6,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [8,1,2,3,4,5,6,7,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [3,2,4,5,6,7,9,1,8] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,10,9,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,2,3,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,2,1,3] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => [4,2,3,5,6,7,9,1,8] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [4,2,3,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9] => [4,3,1,2,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [10,8,9,7,6,5,4,3,2,1] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [10,8,7,6,5,4,3,2,1,9] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [11,9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,9,7,6,5,4,3,2,10,1] => [10,8,7,6,5,4,3,1,2,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => [10,9,8,7,5,6,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,10,9,8,7,6,5,3,2,1] => [10,9,8,6,7,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [8,6,7,9,5,4,3,2,1] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,2,1,9,8,7,6,5] => [8,7,5,6,9,4,3,2,1] => [[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,5,3,2,1,9,8,7,6] => [8,7,6,4,5,9,3,2,1] => [[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [5,6,4,3,2,1,9,8,7] => [8,7,6,5,3,4,9,2,1] => [[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => [2,3,5,1,4,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => [3,2,5,1,4,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,10,1] => [10,2,3,4,5,1,6,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [8,2,1,3,4,5,6,7,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [3,9,2,4,5,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [8,2,3,4,5,6,7,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [3,2,9,1,4,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [8,3,4,5,6,7,9,2,1] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [10,3,4,5,6,7,8,9,2,1] => [[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [10,9,8,1,2,3,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => [7,6,5,4,3,2,9,1,8] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [10,9,7,6,5,4,3,2,1,8] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,8,7,6,5,4,10,3,2,1] => [10,9,8,6,5,4,3,2,1,7] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,8,7,6,5,10,4,3,2,1] => [10,9,8,7,5,4,3,2,1,6] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,8,7,6,10,5,4,3,2,1] => [10,9,8,7,6,4,3,2,1,5] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,8,7,10,6,5,4,3,2,1] => [10,9,8,7,6,5,3,2,1,4] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,10,1] => [10,2,3,4,5,6,1,7,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [6,4,5,7,3,8,2,9,1,10] => [[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [10,9,1,2,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [11,2,3,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [11,10,1,2,3,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,10,9,8,7,2,1] => [10,9,7,6,5,4,8,3,2,1] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,5,7,9,10,8,6,4,2] => [5,10,4,9,3,8,2,7,1,6] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => [9,7,5,3,1,2,4,6,8,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,11,10,9,8,7,6,5,4,3] => [10,9,11,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,11,10,9,8,7,6,5,4,3,1] => [11,9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [3,4,5,6,7,9,2,8,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => [10,9,8,7,6,5,4,3,2,11,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [10,9,8,7,1,2,3,4,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9] => [6,5,4,3,1,2,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8,9] => [5,4,3,1,2,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [4,2,3,9,1,5,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,1,2,3] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [2,3,4,5,6,7,8,9,10,1,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [2,3,4,5,6,8,1,7,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8,9] => [5,3,1,2,4,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [10,9,8,7,6,1,2,3,4,5] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [10,9,8,7,6,5,1,2,3,4] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [10,1,2,3,4,5,6,7,8,9,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [2,8,1,3,4,5,6,7,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,7,6,5,4,3,2,10,9,1] => [10,8,7,6,5,4,3,2,9,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [9,2,3,4,5,6,7,8,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [7,2,3,4,5,6,9,1,8] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9,10] => [6,5,4,3,1,2,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [5,6,4,3,2,7,1,8,9] => [7,5,4,3,1,2,6,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10] => [7,6,5,4,3,1,2,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10,11] => [7,6,5,4,3,1,2,8,9,10,11] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,9,10,2,11,1] => [11,9,1,2,3,4,5,6,7,8,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => [5,2,3,4,9,1,6,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,2,1,7,8,9,6] => [6,5,4,3,2,9,1,7,8] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,2,8,7,6,5,4,1,9] => [8,6,5,7,4,3,2,1,9] => [[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => [10,7,6,5,4,3,2,1,8,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [5,6,4,7,3,8,2,10,1,9] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,10,1] => [10,8,6,4,2,1,3,5,7,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [7,6,8,5,9,4,10,3,11,2,12,1] => [[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[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] => [12,10,8,6,4,2,1,3,5,7,9,11] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,11,10] => [10,2,3,4,5,6,7,8,9,11,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => [6,2,3,4,5,9,1,7,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,7,8,10,9,1] => [10,3,2,4,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,5,4,3,2,1,9,10,8] => [8,7,6,5,4,3,2,10,1,9] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,3,2,1,8,9,10,7] => [7,6,5,4,3,2,10,1,8,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [6,5,7,4,8,3,10,2,9,1] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7,9] => [4,6,3,5,7,2,8,1,9] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,4,6,3,7,2,8,1,9] => [8,6,4,2,1,3,5,7,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,5,3,6,2,7,1,8,9] => [7,5,3,1,2,4,6,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length 0 to the empty tree, and sending a permutation σ of length n≥1 to a root node with two subtrees L and R by splitting σ at the index σ−1(1), normalizing both sides again to permutations and sending the permutations on the left and on the right of σ−1(1) to the trees L and R, respectively.