Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
[1,0] => [1] => [1] => [.,.]
[1,0,1,0] => [2,1] => [2,1] => [[.,.],.]
[1,1,0,0] => [1,2] => [1,2] => [.,[.,.]]
[1,0,1,0,1,0] => [3,2,1] => [3,1,2] => [[.,.],[.,.]]
[1,0,1,1,0,0] => [2,3,1] => [3,2,1] => [[[.,.],.],.]
[1,1,0,0,1,0] => [3,1,2] => [2,3,1] => [[.,[.,.]],.]
[1,1,0,1,0,0] => [2,1,3] => [2,1,3] => [[.,.],[.,.]]
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,1,2,3] => [[.,.],[.,[.,.]]]
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [4,1,3,2] => [[.,.],[[.,.],.]]
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [4,3,1,2] => [[[.,.],.],[.,.]]
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [4,3,2,1] => [[[[.,.],.],.],.]
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [4,2,3,1] => [[[.,.],[.,.]],.]
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [2,4,1,3] => [[.,[.,.]],[.,.]]
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,4,3,1] => [[.,[[.,.],.]],.]
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [3,1,4,2] => [[.,.],[[.,.],.]]
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [3,1,2,4] => [[.,.],[.,[.,.]]]
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [2,3,4,1] => [[.,[.,[.,.]]],.]
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [2,3,1,4] => [[.,[.,.]],[.,.]]
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [5,1,2,4,3] => [[.,.],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [5,1,4,2,3] => [[.,.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [5,1,4,3,2] => [[.,.],[[[.,.],.],.]]
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [5,1,3,4,2] => [[.,.],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [5,3,1,2,4] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [5,3,1,4,2] => [[[.,.],.],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [5,4,2,1,3] => [[[[.,.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [5,4,2,3,1] => [[[[.,.],.],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [5,3,4,1,2] => [[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [5,3,4,2,1] => [[[[.,.],[.,.]],.],.]
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [2,5,1,4,3] => [[.,[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [2,5,4,1,3] => [[.,[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [2,5,4,3,1] => [[.,[[[.,.],.],.]],.]
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.]
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [3,1,5,2,4] => [[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [3,1,5,4,2] => [[.,.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [4,1,2,5,3] => [[.,.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [4,1,3,2,5] => [[.,.],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [4,3,1,5,2] => [[[.,.],.],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [4,3,1,2,5] => [[[.,.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [2,4,1,5,3] => [[.,[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [3,1,4,5,2] => [[.,.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [3,1,4,2,5] => [[.,.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [6,1,2,3,5,4] => [[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [6,1,2,5,3,4] => [[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [6,1,2,5,4,3] => [[.,.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [6,1,2,4,5,3] => [[.,.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [6,1,4,2,3,5] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [6,1,4,2,5,3] => [[.,.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [6,1,5,3,2,4] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [6,1,5,3,4,2] => [[.,.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [6,1,5,4,3,2] => [[.,.],[[[[.,.],.],.],.]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [6,1,4,5,2,3] => [[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [6,1,4,5,3,2] => [[.,.],[[[.,[.,.]],.],.]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [6,1,4,3,5,2] => [[.,.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [6,1,3,4,5,2] => [[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [6,3,1,2,4,5] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [6,3,1,2,5,4] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [6,3,1,5,2,4] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [6,3,1,5,4,2] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [6,3,1,4,5,2] => [[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [6,4,2,1,3,5] => [[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [6,4,2,1,5,3] => [[[[.,.],.],.],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [6,5,2,3,1,4] => [[[[.,.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [6,5,2,4,3,1] => [[[[.,.],.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [6,5,4,2,1,3] => [[[[[.,.],.],.],.],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [6,5,4,2,3,1] => [[[[[.,.],.],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [6,3,4,1,2,5] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [6,3,4,1,5,2] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [6,3,5,2,1,4] => [[[[.,.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [6,3,5,2,4,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [6,3,5,4,2,1] => [[[[.,.],[[.,.],.]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [6,4,2,5,1,3] => [[[[.,.],.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [6,4,2,5,3,1] => [[[[.,.],.],[[.,.],.]],.]
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [6,4,2,3,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.]
>>> Load all 1813 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [6,3,4,5,1,2] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.]
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [6,3,4,2,5,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [2,6,1,3,5,4] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [2,6,1,5,3,4] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [2,6,1,5,4,3] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [2,6,1,4,5,3] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [2,6,4,1,3,5] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [2,6,4,1,5,3] => [[.,[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [2,6,5,3,1,4] => [[.,[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [2,6,5,3,4,1] => [[.,[[[.,.],.],[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [2,6,5,4,3,1] => [[.,[[[[.,.],.],.],.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [2,6,4,5,1,3] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [2,6,4,5,3,1] => [[.,[[[.,.],[.,.]],.]],.]
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [2,6,4,3,5,1] => [[.,[[[.,.],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [3,1,6,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [3,1,6,2,5,4] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [3,1,6,5,2,4] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [3,1,6,5,4,2] => [[.,.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [3,1,6,4,5,2] => [[.,.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [4,1,2,6,3,5] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [4,1,2,6,5,3] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [5,1,2,3,6,4] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [5,1,2,4,3,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [5,1,4,2,6,3] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [5,1,4,2,3,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [5,1,4,3,2,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [5,1,3,4,2,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [4,3,1,6,2,5] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [4,3,1,6,5,2] => [[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [5,3,1,2,6,4] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [5,3,1,2,4,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [5,3,1,4,2,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [5,4,2,1,6,3] => [[[[.,.],.],.],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [5,4,2,1,3,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [5,4,2,3,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [5,3,4,1,6,2] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [5,3,4,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [5,3,4,2,1,6] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [2,3,6,1,5,4] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [2,3,6,5,1,4] => [[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.]
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [2,4,1,6,5,3] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [2,5,1,3,6,4] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [2,5,1,4,3,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [2,5,4,1,6,3] => [[.,[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [2,5,4,1,3,6] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [2,5,4,3,1,6] => [[.,[[[.,.],.],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [3,1,4,6,2,5] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [3,1,4,6,5,2] => [[.,.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [3,1,5,2,6,4] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [3,1,5,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [3,1,5,4,2,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [4,1,2,5,6,3] => [[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [4,1,2,5,3,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [4,1,3,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [4,3,1,5,6,2] => [[[.,.],.],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [4,3,1,5,2,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [4,3,1,2,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [2,4,1,5,6,3] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [2,4,1,5,3,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [3,1,4,5,6,2] => [[.,.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [3,1,4,5,2,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [3,1,4,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [7,1,2,3,4,6,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [7,1,2,3,6,4,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [7,1,2,3,6,5,4] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [7,1,2,3,5,6,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [7,1,2,5,3,4,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [7,1,2,5,3,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [7,1,2,6,4,3,5] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [7,1,2,6,4,5,3] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [7,1,2,6,5,4,3] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [7,1,2,5,6,3,4] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [7,1,2,5,6,4,3] => [[.,.],[.,[[[.,[.,.]],.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [7,1,2,5,4,6,3] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [7,1,2,4,5,6,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [7,1,4,2,3,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [7,1,4,2,3,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [7,1,4,2,6,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [7,1,4,2,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [7,1,4,2,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [7,1,5,3,2,4,6] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [7,1,5,3,2,6,4] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [7,1,6,3,4,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [7,1,6,3,4,5,2] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [7,1,6,3,5,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [7,1,6,5,3,2,4] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [7,1,6,5,3,4,2] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [7,1,6,5,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [7,1,6,4,5,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [7,1,4,5,2,3,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [7,1,4,5,2,6,3] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [7,1,4,6,3,2,5] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [7,1,4,6,3,5,2] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [7,1,4,6,5,3,2] => [[.,.],[[[.,[[.,.],.]],.],.]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [7,1,5,3,6,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [7,1,5,3,6,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [7,1,5,3,4,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [7,1,5,4,3,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [7,1,4,5,6,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [7,1,4,5,6,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [7,1,4,5,3,6,2] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [7,1,4,3,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [7,1,3,4,5,6,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [7,3,1,2,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [7,3,1,2,4,6,5] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [7,3,1,2,6,4,5] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [7,3,1,2,6,5,4] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [7,3,1,2,5,6,4] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [7,3,1,5,2,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [7,3,1,5,2,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [7,3,1,6,4,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [7,3,1,6,4,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [7,3,1,6,5,4,2] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [7,3,1,5,6,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [7,3,1,5,6,4,2] => [[[.,.],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [7,3,1,5,4,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [7,3,1,4,5,6,2] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [7,4,2,1,3,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [7,4,2,1,3,6,5] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [7,4,2,1,6,3,5] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [7,4,2,1,6,5,3] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [7,4,2,1,5,6,3] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [7,5,2,3,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [7,5,2,3,1,6,4] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [7,6,2,3,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [7,6,2,3,4,5,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [7,6,2,3,5,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [7,6,2,5,3,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [7,6,2,5,3,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [7,6,2,5,4,3,1] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [7,6,2,4,5,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [7,5,4,2,1,3,6] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [7,5,4,2,1,6,3] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [7,6,4,2,3,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [7,6,4,2,3,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [7,6,4,2,5,3,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [7,6,5,3,2,4,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [7,6,4,5,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [7,6,4,5,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [7,3,4,1,2,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [7,3,4,1,2,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [7,3,4,1,6,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [7,3,4,1,6,5,2] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [7,3,4,1,5,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [7,3,5,2,1,4,6] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [7,3,5,2,1,6,4] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [7,3,6,2,4,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [7,3,6,2,4,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [7,3,6,2,5,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [7,3,6,5,2,1,4] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [7,3,6,5,2,4,1] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [7,3,6,5,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [7,3,6,4,5,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [7,4,2,5,1,3,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [7,4,2,5,1,6,3] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [7,4,2,6,3,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [7,4,2,6,3,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [7,4,2,6,5,3,1] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [7,5,2,3,6,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [7,5,2,3,6,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [7,5,2,3,4,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [7,5,2,4,3,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [7,5,4,2,6,1,3] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [7,5,4,2,6,3,1] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [7,5,4,2,3,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [7,3,4,5,1,2,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [7,3,4,5,1,6,2] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [7,3,4,6,2,1,5] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [7,3,4,6,2,5,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [7,3,4,6,5,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [7,3,5,2,6,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [7,3,5,2,6,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [7,3,5,2,4,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [7,3,5,4,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [7,4,2,5,6,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [7,4,2,5,6,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [7,4,2,5,3,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [7,4,2,3,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [7,3,4,5,6,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [7,3,4,5,6,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [7,3,4,5,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [7,3,4,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [2,7,1,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [2,7,1,3,4,6,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [2,7,1,3,6,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [2,7,1,3,6,5,4] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [2,7,1,3,5,6,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [2,7,1,5,3,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [2,7,1,5,3,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [2,7,1,6,4,3,5] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [2,7,1,6,4,5,3] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [2,7,1,6,5,4,3] => [[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [2,7,1,5,6,3,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [2,7,1,5,6,4,3] => [[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [2,7,1,5,4,6,3] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [2,7,1,4,5,6,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [2,7,4,1,3,5,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [2,7,4,1,3,6,5] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [2,7,4,1,6,3,5] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [2,7,4,1,6,5,3] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [2,7,4,1,5,6,3] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [2,7,5,3,1,4,6] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [2,7,5,3,1,6,4] => [[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [2,7,6,3,4,1,5] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [2,7,6,3,4,5,1] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [2,7,6,3,5,4,1] => [[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [2,7,6,5,3,1,4] => [[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [2,7,6,5,3,4,1] => [[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [2,7,6,5,4,3,1] => [[.,[[[[[.,.],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [2,7,6,4,5,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [2,7,4,5,1,3,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [2,7,4,5,1,6,3] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [2,7,4,6,3,1,5] => [[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [2,7,4,6,3,5,1] => [[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [2,7,4,6,5,3,1] => [[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [2,7,5,3,6,1,4] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [2,7,5,3,6,4,1] => [[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [2,7,5,3,4,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [2,7,5,4,3,6,1] => [[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [2,7,4,5,6,1,3] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [2,7,4,5,6,3,1] => [[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [2,7,4,5,3,6,1] => [[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [2,7,4,3,5,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [2,7,3,4,5,6,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [3,1,7,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [3,1,7,2,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [3,1,7,2,6,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [3,1,7,2,6,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [3,1,7,2,5,6,4] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [3,1,7,5,2,4,6] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [3,1,7,5,2,6,4] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [3,1,7,6,4,2,5] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [3,1,7,6,4,5,2] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [3,1,7,6,5,4,2] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [3,1,7,5,6,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [3,1,7,5,6,4,2] => [[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [3,1,7,5,4,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [3,1,7,4,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [4,1,2,7,3,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [4,1,2,7,3,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [4,1,2,7,6,3,5] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [4,1,2,7,6,5,3] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [4,1,2,7,5,6,3] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [5,1,2,3,7,4,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [5,1,2,3,7,6,4] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [6,1,2,3,4,7,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [6,1,2,3,5,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [6,1,2,5,3,7,4] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [6,1,2,5,3,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [6,1,2,5,4,3,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [6,1,2,4,5,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [5,1,4,2,7,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [5,1,4,2,7,6,3] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [6,1,4,2,3,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [6,1,4,2,3,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [6,1,4,2,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [6,1,5,3,2,7,4] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [6,1,5,3,2,4,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [6,1,5,3,4,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [6,1,5,4,3,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [6,1,4,5,2,7,3] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [6,1,4,5,2,3,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [6,1,4,5,3,2,7] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [6,1,4,3,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [6,1,3,4,5,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [4,3,1,7,2,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [4,3,1,7,2,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [4,3,1,7,6,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [4,3,1,7,6,5,2] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [4,3,1,7,5,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [5,3,1,2,7,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [5,3,1,2,7,6,4] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [6,3,1,2,4,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [6,3,1,2,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [6,3,1,2,5,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [6,3,1,5,2,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [6,3,1,5,2,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [6,3,1,5,4,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [6,3,1,4,5,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [5,4,2,1,7,3,6] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [5,4,2,1,7,6,3] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [6,4,2,1,3,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [6,4,2,1,3,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [6,4,2,1,5,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [6,5,2,3,1,7,4] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [6,5,2,3,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [6,5,2,3,4,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [6,5,2,4,3,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [6,5,4,2,1,7,3] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [6,5,4,2,1,3,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [6,5,4,2,3,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [5,3,4,1,7,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [5,3,4,1,7,6,2] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [6,3,4,1,2,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [6,3,4,1,2,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [6,3,4,1,5,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [6,3,5,2,1,7,4] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [6,3,5,2,1,4,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [6,3,5,2,4,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [6,3,5,4,2,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [6,4,2,5,1,7,3] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [6,4,2,5,1,3,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [6,4,2,5,3,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [6,4,2,3,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [6,3,4,5,1,7,2] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [6,3,4,5,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [6,3,4,5,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [6,3,4,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [2,3,7,1,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [2,3,7,1,4,6,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [2,3,7,1,6,4,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [2,3,7,1,6,5,4] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [2,3,7,1,5,6,4] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [2,3,7,5,1,4,6] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [2,3,7,5,1,6,4] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [2,3,7,6,4,1,5] => [[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [2,3,7,6,4,5,1] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [2,3,7,6,5,4,1] => [[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [2,3,7,5,6,1,4] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [2,3,7,5,6,4,1] => [[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [2,3,7,5,4,6,1] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [2,3,7,4,5,6,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [2,4,1,7,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [2,4,1,7,3,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [2,4,1,7,6,3,5] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [2,4,1,7,6,5,3] => [[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [2,4,1,7,5,6,3] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [2,5,1,3,7,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [2,5,1,3,7,6,4] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [2,6,1,3,4,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [2,6,1,3,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [2,6,1,3,5,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [2,6,1,5,3,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [2,6,1,5,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [2,6,1,5,4,3,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [2,6,1,4,5,3,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [2,5,4,1,7,3,6] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [2,5,4,1,7,6,3] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [2,6,4,1,3,7,5] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [2,6,4,1,3,5,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [2,6,4,1,5,3,7] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [2,6,5,3,1,7,4] => [[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [2,6,5,3,1,4,7] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [2,6,5,3,4,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [2,6,5,4,3,1,7] => [[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [2,6,4,5,1,7,3] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [2,6,4,5,1,3,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [2,6,4,5,3,1,7] => [[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [2,6,4,3,5,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [2,6,3,4,5,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [3,1,4,7,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [3,1,4,7,2,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [3,1,4,7,6,2,5] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [3,1,4,7,6,5,2] => [[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [3,1,4,7,5,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [3,1,5,2,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [3,1,5,2,7,6,4] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [3,1,6,2,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [3,1,6,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [3,1,6,2,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [3,1,6,5,2,7,4] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [3,1,6,5,2,4,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [3,1,6,5,4,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [3,1,6,4,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [4,1,2,5,7,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [4,1,2,5,7,6,3] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [4,1,2,6,3,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [4,1,2,6,3,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [4,1,2,6,5,3,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [5,1,2,3,6,7,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [5,1,2,3,6,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [5,1,2,4,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [5,1,4,2,6,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [5,1,4,2,6,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [5,1,4,2,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [5,1,4,3,2,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [5,1,3,4,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [4,3,1,5,7,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [4,3,1,5,7,6,2] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [4,3,1,6,2,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [4,3,1,6,2,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [4,3,1,6,5,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [5,3,1,2,6,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [5,3,1,2,6,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [5,3,1,2,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [5,3,1,4,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [5,4,2,1,6,7,3] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [5,4,2,1,6,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [5,4,2,1,3,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [5,4,2,3,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [5,3,4,1,6,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [5,3,4,1,6,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [5,3,4,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [5,3,4,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [2,3,4,7,1,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [2,3,4,7,1,6,5] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [2,3,4,7,6,1,5] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [2,3,4,7,6,5,1] => [[.,[.,[.,[[[.,.],.],.]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [2,3,4,7,5,6,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [2,3,5,1,7,4,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [2,3,5,1,7,6,4] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [2,3,6,1,4,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [2,3,6,1,4,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [2,3,6,1,5,4,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [2,3,6,5,1,7,4] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [2,3,6,5,1,4,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [2,3,6,5,4,1,7] => [[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [2,3,6,4,5,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [2,4,1,5,7,3,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [2,4,1,5,7,6,3] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [2,4,1,6,3,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [2,4,1,6,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [2,4,1,6,5,3,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [2,5,1,3,6,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [2,5,1,3,6,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [2,5,1,3,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [2,5,1,4,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [2,5,4,1,6,7,3] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [2,5,4,1,6,3,7] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [2,5,4,1,3,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [2,5,4,3,1,6,7] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [2,5,3,4,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [3,1,4,5,7,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [3,1,4,5,7,6,2] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [3,1,4,6,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [3,1,4,6,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [3,1,4,6,5,2,7] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [3,1,5,2,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [3,1,5,2,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [3,1,5,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [3,1,5,4,2,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [4,1,2,5,6,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [4,1,2,5,6,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [4,1,2,5,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [4,1,3,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [4,3,1,5,6,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [4,3,1,5,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [4,3,1,5,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [4,3,1,2,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [2,3,4,5,7,1,6] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [2,3,4,5,7,6,1] => [[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [2,3,4,6,1,7,5] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [2,3,4,6,1,5,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [2,3,4,6,5,1,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [2,3,5,1,6,7,4] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [2,3,5,1,6,4,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [2,3,5,1,4,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [2,3,5,4,1,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [2,4,1,5,6,7,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [2,4,1,5,6,3,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [2,4,1,5,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [2,4,1,3,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [2,4,3,1,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [3,1,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [3,1,4,5,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [3,1,4,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [3,1,4,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [8,1,2,3,4,5,7,6] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [8,1,2,3,4,7,5,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [8,1,2,3,4,7,6,5] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [8,1,2,3,4,6,7,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [8,1,2,3,6,4,5,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [8,1,2,3,6,4,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [8,1,2,3,7,5,4,6] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [8,1,2,3,7,5,6,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [8,1,2,3,7,6,5,4] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [8,1,2,3,6,7,4,5] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [8,1,2,3,6,7,5,4] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [8,1,2,3,6,5,7,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [8,1,2,3,5,6,7,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [8,1,2,5,3,4,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [8,1,2,5,3,4,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [8,1,2,5,3,7,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => [8,1,2,5,3,7,6,4] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,2,1] => [8,1,2,5,3,6,7,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,3,2,1] => [8,1,2,6,4,3,7,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [8,1,2,7,4,5,3,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [8,1,2,7,4,5,6,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [8,1,2,7,4,6,5,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [8,1,2,7,6,4,5,3] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [8,1,2,7,6,5,4,3] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [8,1,2,5,6,3,4,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,2,1] => [8,1,2,5,6,3,7,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [8,1,2,5,7,4,6,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [8,1,2,6,4,7,5,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [8,1,2,6,4,5,7,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [8,1,2,5,6,7,3,4] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [8,1,2,5,6,7,4,3] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [8,1,2,4,5,6,7,3] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [8,1,4,2,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [8,1,4,2,3,5,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [8,1,4,2,3,7,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [8,1,4,2,3,7,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,2,1] => [8,1,4,2,3,6,7,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [8,1,4,2,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [8,1,4,2,6,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,2,1] => [8,1,4,2,7,5,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [8,1,4,2,7,5,6,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [8,1,4,2,6,7,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,2,1] => [8,1,4,2,6,7,5,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [8,1,4,2,6,5,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [8,1,4,2,5,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [8,1,5,3,2,4,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => [8,1,5,3,2,4,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => [8,1,5,3,2,7,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [8,1,5,3,2,6,7,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [8,1,6,3,4,2,5,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [8,1,6,3,4,2,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [8,1,7,3,4,5,2,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [8,1,7,3,4,5,6,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,7,2,1] => [8,1,7,3,6,4,2,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => [8,1,7,3,6,4,5,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [8,1,7,3,6,5,4,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [8,1,7,3,5,6,4,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [8,1,7,5,3,6,4,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,2,1] => [8,1,7,6,4,3,2,5] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => [8,1,7,6,4,3,5,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [8,1,7,6,4,5,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,2,1] => [8,1,7,6,5,4,3,2] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [8,1,7,5,6,4,3,2] => [[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [8,1,4,5,2,3,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [8,1,4,5,2,3,7,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [8,1,4,5,2,7,3,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [8,1,4,5,2,6,7,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [8,1,4,7,3,5,6,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,8,2,1] => [8,1,4,7,3,6,5,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,7,2,1] => [8,1,4,7,6,3,2,5] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,8,2,1] => [8,1,4,7,6,5,3,2] => [[.,.],[[[.,[[[.,.],.],.]],.],.]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [8,1,5,3,6,2,4,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,2,1] => [8,1,5,3,6,2,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [8,1,5,3,7,4,2,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [8,1,5,3,7,4,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [8,1,6,3,4,7,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [8,1,6,3,4,5,7,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,2,1] => [8,1,6,3,5,4,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [8,1,4,5,6,2,3,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [8,1,4,5,6,2,7,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,7,2,1] => [8,1,4,5,7,3,2,6] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [8,1,4,5,7,3,6,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [8,1,4,6,3,7,2,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [8,1,4,6,3,7,5,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => [8,1,4,6,3,5,7,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,2,1] => [8,1,5,3,6,4,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,2,1] => [8,1,5,4,3,6,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [8,1,4,5,6,7,2,3] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [8,1,4,5,6,7,3,2] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [8,1,4,5,6,3,7,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [8,1,4,5,3,6,7,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [8,1,4,3,5,6,7,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [8,1,3,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [8,3,1,2,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [8,3,1,2,4,5,7,6] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [8,3,1,2,4,7,5,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [8,3,1,2,4,7,6,5] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [8,3,1,2,6,4,5,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,3,1] => [8,3,1,2,6,4,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [8,3,1,2,7,6,5,4] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [8,3,1,2,6,7,4,5] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [8,3,1,2,5,6,7,4] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [8,3,1,5,2,4,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [8,3,1,5,2,7,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [8,3,1,5,2,7,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [8,3,1,5,2,6,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [8,3,1,6,4,2,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => [8,3,1,7,4,5,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [8,3,1,7,6,4,2,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [8,3,1,7,6,4,5,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [8,3,1,7,6,5,4,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,3,1] => [8,3,1,7,5,6,4,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [8,3,1,5,6,2,7,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,3,1] => [8,3,1,5,4,6,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [8,3,1,4,5,6,7,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [8,4,2,1,3,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => [8,4,2,1,3,5,7,6] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [8,4,2,1,3,7,5,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [8,4,2,1,3,7,6,5] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [8,4,2,1,3,6,7,5] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [8,4,2,1,6,3,5,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [8,4,2,1,7,5,3,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [8,4,2,1,7,5,6,3] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [8,4,2,1,7,6,5,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,4,1] => [8,4,2,1,6,7,5,3] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [8,4,2,1,5,6,7,3] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [8,5,2,3,1,7,6,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => [8,5,2,3,1,6,7,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [8,6,2,3,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [8,6,2,3,4,1,7,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [8,7,2,3,4,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [8,7,2,3,4,5,6,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [8,7,2,3,6,5,4,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => [8,7,2,6,4,5,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [8,7,2,5,6,4,3,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [8,7,2,4,5,6,3,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [8,5,4,2,1,3,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [8,5,4,2,1,3,7,6] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [8,5,4,2,1,7,3,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [8,5,4,2,1,7,6,3] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [8,5,4,2,1,6,7,3] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [8,6,4,2,3,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [8,6,4,2,3,1,7,5] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [8,7,4,2,6,3,1,5] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [8,7,4,2,6,3,5,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [8,7,4,2,6,5,3,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [8,6,5,3,2,1,4,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => [8,6,5,3,2,1,7,4] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [8,7,5,3,2,4,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [8,7,5,3,2,4,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,8,1] => [8,7,5,3,2,6,4,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => [8,7,6,3,4,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [8,7,6,3,4,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [8,7,6,3,4,5,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,8,1] => [8,7,6,3,5,4,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [8,7,6,5,3,2,4,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [8,7,6,5,3,4,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [8,7,4,5,2,3,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,2,7,1] => [8,7,4,6,3,2,1,5] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [8,7,4,6,3,2,5,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [8,7,4,6,3,5,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => [8,7,4,6,5,3,2,1] => [[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [8,7,5,3,6,4,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => [8,7,5,3,4,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [8,7,4,5,6,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => [8,7,4,3,5,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [8,3,4,1,2,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [8,3,4,1,2,7,5,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [8,3,4,1,2,6,7,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [8,3,4,1,6,2,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [8,3,4,1,7,5,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [8,3,4,1,6,7,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [8,3,4,1,5,6,7,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,5,1] => [8,3,5,2,1,4,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,3,5,1] => [8,3,5,2,1,4,7,6] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,5,1] => [8,3,5,2,1,7,4,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [8,3,5,2,1,6,7,4] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => [8,3,6,2,4,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,3,6,1] => [8,3,6,2,4,1,7,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [8,3,7,2,4,5,6,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => [8,3,7,2,6,4,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [8,3,7,2,6,4,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [8,3,7,2,6,5,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,6,1] => [8,3,6,5,2,1,7,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => [8,3,7,5,2,4,6,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [8,3,7,5,2,6,4,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,2,3,7,1] => [8,3,7,6,4,2,1,5] => [[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [8,3,7,6,5,4,2,1] => [[[[.,.],[[[[.,.],.],.],.]],.],.]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [8,3,7,5,6,4,2,1] => [[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [8,3,7,5,4,6,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [8,3,7,4,5,6,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [8,4,2,5,1,3,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [8,4,2,5,1,3,7,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [8,4,2,5,1,6,7,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [8,4,2,7,3,5,6,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [8,5,2,3,6,1,4,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [8,5,2,3,6,1,7,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => [8,5,2,3,7,4,1,6] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,8,1] => [8,5,2,3,7,4,6,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [8,6,2,3,4,7,1,5] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [8,6,2,3,4,5,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,2,7,8,1] => [8,6,2,5,3,4,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => [8,6,2,5,4,3,7,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [8,6,2,4,5,3,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,6,1] => [8,5,4,2,6,1,3,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => [8,5,4,2,6,1,7,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,5,8,1] => [8,5,4,2,7,3,6,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [8,6,4,2,3,7,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => [8,6,4,2,3,5,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,7,8,1] => [8,6,5,3,2,4,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,8,1] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [8,6,4,5,2,7,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [8,6,3,4,5,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [8,3,4,5,1,2,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [8,3,4,5,1,7,2,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [8,3,4,5,1,6,7,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [8,3,4,7,2,5,6,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => [8,3,4,7,6,2,5,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => [8,3,5,2,6,1,7,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [8,3,5,2,7,4,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [8,3,5,2,7,4,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [8,3,6,2,4,7,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => [8,3,6,2,4,5,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => [8,3,6,5,2,7,1,4] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [8,3,6,4,5,2,7,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [8,4,2,5,6,1,7,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [8,4,2,5,7,3,6,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [8,4,2,5,7,6,3,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [8,4,2,6,3,7,5,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [8,5,2,3,6,7,4,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [8,5,4,2,6,7,1,3] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [8,5,4,2,3,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [8,5,3,4,2,6,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [8,3,4,5,6,1,2,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [8,3,4,5,6,1,7,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [8,3,4,5,7,2,1,6] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [8,3,4,5,7,6,2,1] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [8,3,5,4,2,6,7,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [8,4,2,5,6,7,1,3] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [8,4,2,5,6,7,3,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,8,1] => [8,4,2,5,6,3,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [8,4,2,5,3,6,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [8,4,2,3,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [8,3,4,5,6,7,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [8,3,4,5,6,7,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [8,3,4,5,2,6,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [8,3,4,2,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [2,8,1,3,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [2,8,1,3,4,5,7,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [2,8,1,3,4,7,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [2,8,1,3,4,6,7,5] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [2,8,1,3,6,4,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [2,8,1,3,6,4,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [2,8,1,3,7,5,4,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [2,8,1,3,7,5,6,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [2,8,1,3,7,6,5,4] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,1,2] => [2,8,1,3,6,7,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => [2,8,1,3,6,7,5,4] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [2,8,1,3,6,5,7,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [2,8,1,3,5,6,7,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [2,8,1,5,3,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [2,8,1,5,3,4,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [2,8,1,5,3,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,1,2] => [2,8,1,5,3,7,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [2,8,1,7,6,5,4,3] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,1,2] => [2,8,1,5,6,3,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [2,8,1,5,6,3,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,1,2] => [2,8,1,5,6,4,7,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [2,8,1,5,4,6,7,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [2,8,1,4,5,6,7,3] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [2,8,4,1,3,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [2,8,4,1,3,5,7,6] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,1,2] => [2,8,4,1,3,7,5,6] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [2,8,4,1,3,7,6,5] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [2,8,4,1,3,6,7,5] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [2,8,4,1,6,3,5,7] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [2,8,4,1,6,3,7,5] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [2,8,4,1,7,5,3,6] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [2,8,4,1,6,7,3,5] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [2,8,4,1,6,7,5,3] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [2,8,4,1,6,5,7,3] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [2,8,4,1,5,6,7,3] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,1,2] => [2,8,5,3,1,4,6,7] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,1,2] => [2,8,5,3,1,4,7,6] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,1,2] => [2,8,5,3,1,7,4,6] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,1,2] => [2,8,5,3,1,7,6,4] => [[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [2,8,6,3,4,1,7,5] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [2,8,7,3,4,5,6,1] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,1,2] => [2,8,7,3,4,6,5,1] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => [2,8,6,5,3,1,4,7] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [2,8,7,5,3,6,4,1] => [[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => [2,8,7,6,4,3,1,5] => [[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => [2,8,7,6,4,5,3,1] => [[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [2,8,7,6,5,4,3,1] => [[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,1,2] => [2,8,7,5,6,3,4,1] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,1,2] => [2,8,7,5,6,4,3,1] => [[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => [2,8,7,5,4,6,3,1] => [[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [2,8,7,4,5,6,3,1] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [2,8,4,5,1,3,6,7] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [2,8,4,5,1,7,3,6] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,1,2] => [2,8,4,5,1,7,6,3] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,1,2] => [2,8,4,5,1,6,7,3] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,1,2] => [2,8,4,6,3,1,5,7] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => [2,8,4,7,3,5,6,1] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,8,1,2] => [2,8,4,7,3,6,5,1] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,7,1,2] => [2,8,4,7,6,3,1,5] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,1,2] => [2,8,4,7,6,3,5,1] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,8,1,2] => [2,8,4,7,6,5,3,1] => [[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [2,8,5,3,6,1,7,4] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [2,8,6,3,4,7,1,5] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [2,8,6,3,4,5,7,1] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [2,8,6,3,5,4,7,1] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [2,8,4,5,6,1,3,7] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [2,8,4,5,6,1,7,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [2,8,4,5,7,3,6,1] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => [2,8,4,6,3,7,1,5] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [2,8,4,6,5,3,7,1] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [2,8,5,3,6,7,1,4] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [2,8,5,3,6,4,7,1] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [2,8,5,3,4,6,7,1] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [2,8,5,4,3,6,7,1] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [2,8,4,5,6,7,1,3] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [2,8,4,5,6,7,3,1] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [2,8,4,5,6,3,7,1] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [2,8,4,5,3,6,7,1] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [2,8,4,3,5,6,7,1] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [2,8,3,4,5,6,7,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [3,1,8,2,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [3,1,8,2,4,5,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [3,1,8,2,4,7,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [3,1,8,2,4,7,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [3,1,8,2,6,4,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [3,1,8,2,6,4,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,1,3] => [3,1,8,2,7,5,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [3,1,8,2,7,5,6,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [3,1,8,2,7,6,5,4] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,1,3] => [3,1,8,2,6,7,4,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => [3,1,8,2,6,7,5,4] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => [3,1,8,2,6,5,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [3,1,8,2,5,6,7,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [3,1,8,5,2,4,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,1,3] => [3,1,8,5,2,7,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,1,3] => [3,1,8,5,2,7,6,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,2,1,3] => [3,1,8,6,4,2,7,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,1,3] => [3,1,8,7,6,4,5,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [3,1,8,7,6,5,4,2] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [3,1,8,7,5,6,4,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,1,3] => [3,1,8,5,6,2,4,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,1,3] => [3,1,8,5,6,2,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,1,3] => [3,1,8,5,7,4,2,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => [3,1,8,5,7,4,6,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,2,1,3] => [3,1,8,6,4,7,2,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,1,3] => [3,1,8,6,4,7,5,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [3,1,8,5,6,7,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [3,1,8,5,4,6,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [3,1,8,4,5,6,7,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [4,1,2,8,3,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [4,1,2,8,3,7,5,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [4,1,2,8,3,6,7,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [4,1,2,8,6,3,5,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [4,1,2,8,6,3,7,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [4,1,2,8,7,5,3,6] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [4,1,2,8,7,5,6,3] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [4,1,2,8,7,6,5,3] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [4,1,2,8,6,7,3,5] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [4,1,2,8,5,6,7,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [5,1,2,3,8,4,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [5,1,2,3,8,4,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [5,1,2,3,8,7,4,6] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [5,1,2,3,8,7,6,4] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [5,1,2,3,8,6,7,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [6,1,2,3,4,8,5,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [6,1,2,3,4,8,7,5] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [7,1,2,3,4,5,8,6] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [7,1,2,3,4,6,5,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [7,1,2,3,6,4,8,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [7,1,2,3,6,4,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [7,1,2,3,6,5,4,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [7,1,2,3,5,6,4,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [6,1,2,5,3,8,4,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => [7,1,2,5,3,4,8,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [7,1,2,5,3,4,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,1,7] => [7,1,2,6,4,3,8,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [7,1,2,6,4,3,5,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [7,1,2,6,4,5,3,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [7,1,2,6,5,4,3,8] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [7,1,2,5,6,3,8,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [7,1,2,5,4,6,3,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [7,1,2,4,5,6,3,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [5,1,4,2,8,3,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => [5,1,4,2,8,3,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [5,1,4,2,8,6,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [6,1,4,2,3,8,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [7,1,4,2,3,5,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [7,1,4,2,3,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [7,1,4,2,6,3,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [7,1,4,2,6,3,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => [7,1,4,2,6,5,3,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [7,1,4,2,5,6,3,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,1,6] => [6,1,5,3,2,8,4,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,1,7] => [7,1,5,3,2,4,8,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [7,1,5,3,2,4,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,1,7] => [7,1,6,3,4,2,8,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [7,1,6,3,4,2,5,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [7,1,6,3,5,4,2,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,1,8] => [7,1,6,5,3,2,4,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [7,1,6,5,4,3,2,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [6,1,4,5,2,8,3,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => [6,1,4,5,2,8,7,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [7,1,4,5,2,3,6,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,1,8] => [7,1,4,6,5,3,2,8] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [7,1,5,3,6,2,8,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,1,8] => [7,1,5,3,6,4,2,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [7,1,4,5,6,2,8,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [7,1,3,4,5,6,2,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [4,3,1,8,2,5,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [4,3,1,8,2,7,5,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => [4,3,1,8,2,6,7,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [4,3,1,8,6,2,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [4,3,1,8,6,2,7,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => [4,3,1,8,7,5,2,6] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [4,3,1,8,7,5,6,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [4,3,1,8,7,6,5,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => [4,3,1,8,6,7,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [4,3,1,8,6,7,5,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => [4,3,1,8,6,5,7,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [4,3,1,8,5,6,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [5,3,1,2,8,4,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,3,1,5] => [5,3,1,2,8,4,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,1,5] => [5,3,1,2,8,7,4,6] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [5,3,1,2,8,6,7,4] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,1,6] => [6,3,1,2,4,8,5,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [7,3,1,2,4,5,8,6] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [7,3,1,2,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [7,3,1,2,4,6,5,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [7,3,1,2,6,4,8,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [7,3,1,2,6,4,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [7,3,1,2,5,6,4,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [6,3,1,5,2,8,4,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,1,7] => [7,3,1,5,2,4,8,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [7,3,1,5,2,4,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [7,3,1,5,2,6,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [7,3,1,6,5,4,2,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [7,3,1,5,6,2,8,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [7,3,1,5,6,2,4,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,1,8] => [7,3,1,5,6,4,2,8] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [7,3,1,4,5,6,2,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [5,4,2,1,8,3,6,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [5,4,2,1,8,7,3,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,4,1,5] => [5,4,2,1,8,7,6,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [6,4,2,1,3,8,5,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,4,1,6] => [6,4,2,1,3,8,7,5] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [7,4,2,1,6,5,3,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [7,4,2,1,5,6,3,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [6,5,2,3,1,8,7,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,1,7] => [7,5,2,3,1,4,8,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [7,5,2,3,1,4,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [7,6,2,3,4,1,8,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [7,6,2,3,4,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [7,6,2,3,4,5,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => [7,6,2,3,5,4,1,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,1,7] => [7,6,2,5,3,1,8,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [7,6,2,5,3,1,4,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => [7,6,2,5,4,3,1,8] => [[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [7,5,4,2,1,6,3,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [7,6,4,2,3,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [7,6,4,2,5,3,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [7,6,5,3,2,1,8,4] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [7,6,5,3,2,1,4,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,7,1,8] => [7,6,5,3,2,4,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [7,6,5,3,4,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,1,7] => [7,6,4,5,2,1,8,3] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,6,1,8] => [7,6,4,5,2,1,3,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [7,6,4,5,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [7,6,4,5,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [5,3,4,1,8,2,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,1,5] => [5,3,4,1,8,2,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,3,4,1,6] => [6,3,4,1,2,8,5,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [6,3,4,1,2,8,7,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [7,3,4,1,2,5,8,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [7,3,4,1,2,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [7,3,4,1,2,6,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => [7,3,4,1,6,2,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [7,3,4,1,6,2,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [7,3,4,1,6,5,2,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [7,3,4,1,5,6,2,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,1,6] => [6,3,5,2,1,8,7,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [7,3,5,2,1,4,6,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [7,3,5,2,1,6,4,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [7,3,6,5,2,1,8,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [7,3,6,5,2,1,4,8] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,1,8] => [7,3,6,4,5,2,1,8] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,5,1,6] => [6,4,2,5,1,8,3,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [7,4,2,5,1,3,8,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [7,4,2,5,1,3,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [7,4,2,5,1,6,3,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [7,4,2,6,3,5,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => [7,5,4,2,6,1,8,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,1,8] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [6,3,4,5,1,8,2,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,1,8] => [7,3,4,6,2,1,5,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,1,7] => [7,3,5,2,6,1,8,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [7,3,5,2,6,4,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => [7,3,5,2,4,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => [7,3,5,4,2,6,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => [7,4,2,5,6,3,1,8] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,1,8] => [7,4,2,5,3,6,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [7,4,2,3,5,6,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [7,3,4,5,6,1,8,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [2,3,8,1,4,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [2,3,8,1,4,5,7,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [2,3,8,1,4,6,7,5] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [2,3,8,1,6,4,7,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [2,3,8,1,7,6,5,4] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [2,3,8,1,6,7,4,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [2,3,8,1,6,7,5,4] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [2,3,8,1,5,6,7,4] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [2,3,8,5,1,4,6,7] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,1,2,3] => [2,3,8,5,1,4,7,6] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [2,3,8,5,1,7,4,6] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [2,3,8,5,1,6,7,4] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [2,3,8,6,4,1,5,7] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [2,3,8,6,4,1,7,5] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => [2,3,8,7,4,5,1,6] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [2,3,8,7,4,5,6,1] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [2,3,8,7,6,5,4,1] => [[.,[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [2,3,8,5,6,1,4,7] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [2,3,8,5,6,1,7,4] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [2,3,8,5,7,6,4,1] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [2,3,8,6,4,5,7,1] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => [2,3,8,6,5,4,7,1] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [2,3,8,5,6,7,1,4] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,1,2,3] => [2,3,8,5,6,7,4,1] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,1,2,3] => [2,3,8,5,6,4,7,1] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [2,3,8,5,4,6,7,1] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [2,3,8,4,5,6,7,1] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [2,4,1,8,3,5,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => [2,4,1,8,3,5,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [2,4,1,8,3,7,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [2,4,1,8,6,3,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [2,4,1,8,6,3,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [2,4,1,8,7,6,5,3] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,1,2,4] => [2,4,1,8,6,7,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [2,4,1,8,6,7,5,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [2,4,1,8,5,6,7,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [2,5,1,3,8,4,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,1,2,5] => [2,5,1,3,8,4,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,1,2,5] => [2,5,1,3,8,7,4,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [2,5,1,3,8,6,7,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [2,6,1,3,4,8,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [2,7,1,3,4,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [2,7,1,3,4,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [2,7,1,3,6,4,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,1,2,8] => [2,7,1,3,6,5,4,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,1,2,8] => [2,7,1,3,5,6,4,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [2,7,1,5,3,4,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => [2,7,1,5,3,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [2,5,4,1,8,3,6,7] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [2,5,4,1,8,3,7,6] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [2,5,4,1,8,7,3,6] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,1,2,5] => [2,5,4,1,8,7,6,3] => [[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [2,5,4,1,8,6,7,3] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [2,6,4,1,3,8,5,7] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,1,2,6] => [2,6,4,1,3,8,7,5] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [2,7,4,1,3,5,8,6] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,1,2,8] => [2,7,4,1,3,6,5,8] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [2,7,4,1,6,3,8,5] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [2,7,4,1,6,5,3,8] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,1,2,6] => [2,6,5,3,1,8,7,4] => [[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,1,2,7] => [2,7,5,3,1,4,8,6] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [2,7,6,3,4,1,8,5] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,1,2,8] => [2,7,6,3,5,4,1,8] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,1,2,8] => [2,7,6,5,4,3,1,8] => [[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [2,6,4,5,1,8,7,3] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [2,7,4,5,1,3,8,6] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [2,7,4,6,3,1,8,5] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [2,7,4,6,5,3,1,8] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,1,2,8] => [2,7,5,3,6,4,1,8] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [2,7,4,5,6,1,8,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [2,7,4,5,6,3,1,8] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [2,7,3,4,5,6,1,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [3,1,4,8,2,5,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [3,1,4,8,2,5,7,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,1,3,4] => [3,1,4,8,2,7,5,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [3,1,4,8,2,6,7,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [3,1,4,8,6,2,5,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [3,1,4,8,6,2,7,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [3,1,4,8,7,5,2,6] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [3,1,4,8,7,6,5,2] => [[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => [3,1,4,8,6,7,2,5] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [3,1,4,8,6,5,7,2] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [3,1,4,8,5,6,7,2] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [3,1,5,2,8,4,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => [3,1,5,2,8,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [3,1,5,2,8,7,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,1,3,5] => [3,1,5,2,8,7,6,4] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [3,1,5,2,8,6,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,1,3,6] => [3,1,6,2,4,8,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [3,1,6,2,4,8,7,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [3,1,7,2,4,5,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [3,1,7,2,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [3,1,7,2,6,4,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,1,3,8] => [3,1,7,2,5,6,4,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,1,3,6] => [3,1,6,5,2,8,7,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,1,3,7] => [3,1,7,5,2,4,8,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [3,1,7,5,2,4,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,2,1,3,7] => [3,1,7,6,4,2,8,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,1,3,8] => [3,1,7,6,4,5,2,8] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,1,3,8] => [3,1,7,6,5,4,2,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [3,1,7,5,6,2,4,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [4,1,2,5,8,3,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [4,1,2,5,8,3,7,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [4,1,2,5,8,7,3,6] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [4,1,2,5,8,6,7,3] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [4,1,2,6,3,8,5,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [4,1,2,6,3,8,7,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [4,1,2,7,3,5,8,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [4,1,2,7,3,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [4,1,2,7,6,3,8,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,1,4,8] => [4,1,2,7,5,6,3,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [5,1,2,3,6,8,4,7] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [5,1,2,3,6,8,7,4] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [5,1,2,3,7,4,8,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [5,1,2,3,7,6,4,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [6,1,2,3,4,7,8,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [6,1,2,3,4,7,5,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [6,1,2,3,5,4,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [6,1,2,5,3,7,8,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,2,1,7,8] => [6,1,2,5,3,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [5,1,4,2,6,8,3,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [5,1,4,2,6,8,7,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [5,1,4,2,7,3,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [5,1,4,2,7,3,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [6,1,4,2,3,5,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [6,1,4,5,2,7,8,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [6,1,4,5,2,7,3,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,1,7,8] => [6,1,4,5,3,2,7,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [6,1,3,4,5,2,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [4,3,1,5,8,2,6,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => [4,3,1,5,8,2,7,6] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [4,3,1,5,8,7,6,2] => [[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [4,3,1,5,8,6,7,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,3,1,4,6] => [4,3,1,6,2,8,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [4,3,1,7,2,5,8,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [4,3,1,7,6,2,8,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [4,3,1,7,6,2,5,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [5,3,1,2,7,4,8,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [5,3,1,2,7,4,6,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,1,6,7] => [6,3,1,2,4,7,8,5] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [6,3,1,2,4,7,5,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,1,7,8] => [6,3,1,2,4,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => [6,3,1,5,2,7,8,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [6,3,1,5,4,2,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => [5,4,2,1,6,8,3,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [5,4,2,1,6,8,7,3] => [[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [5,4,2,1,7,3,6,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => [5,4,2,1,7,6,3,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,1,6,7] => [6,4,2,1,3,7,8,5] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,1,7,8] => [6,4,2,1,3,5,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [6,4,2,1,5,3,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [6,5,2,3,4,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,5,1,7,8] => [6,5,4,2,1,3,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [5,3,4,1,6,8,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => [5,3,4,1,7,2,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [6,3,4,1,2,7,8,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [6,3,4,1,2,7,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [6,3,4,1,5,2,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [6,3,5,2,1,7,4,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,1,7,8] => [6,3,5,2,1,4,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,1,7,8] => [6,3,5,2,4,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,1,6,8] => [6,4,2,5,1,7,3,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => [6,4,2,5,3,1,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [6,3,4,5,1,7,8,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [6,3,4,5,2,1,7,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [2,3,4,8,1,5,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [2,3,4,8,1,5,7,6] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [2,3,4,8,1,7,5,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [2,3,4,8,1,7,6,5] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [2,3,4,8,1,6,7,5] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [2,3,4,8,6,1,5,7] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [2,3,4,8,6,1,7,5] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [2,3,4,8,7,5,1,6] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [2,3,4,8,7,5,6,1] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [2,3,4,8,7,6,5,1] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [2,3,4,8,6,7,1,5] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [2,3,4,8,6,7,5,1] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [2,3,4,8,6,5,7,1] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [2,3,4,8,5,6,7,1] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [2,3,5,1,8,4,6,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => [2,3,5,1,8,4,7,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,1,2,3,5] => [2,3,5,1,8,7,4,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [2,3,6,1,4,8,5,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [2,3,6,1,4,8,7,5] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [2,3,7,1,4,5,8,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [2,3,7,1,4,5,6,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [2,3,7,1,6,4,8,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,1,2,3,8] => [2,3,7,1,6,5,4,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [2,3,7,1,5,6,4,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => [2,3,6,5,1,8,4,7] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [2,3,6,5,1,8,7,4] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [2,3,7,5,1,4,8,6] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [2,3,7,6,5,4,1,8] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => [2,3,7,5,6,1,8,4] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,1,2,3,8] => [2,3,7,5,6,4,1,8] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [2,3,7,5,4,6,1,8] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [2,4,1,5,8,3,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [2,4,1,5,8,3,7,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => [2,4,1,5,8,7,3,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [2,4,1,5,8,7,6,3] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [2,4,1,6,3,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,1,2,4,7] => [2,4,1,7,3,5,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [2,4,1,7,6,3,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [2,4,1,7,5,6,3,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,1,2,5,6] => [2,5,1,3,6,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [2,5,1,3,6,8,7,4] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [2,5,1,3,7,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,1,2,5,8] => [2,5,1,3,7,6,4,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,1,2,6,7] => [2,6,1,3,4,7,8,5] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => [2,6,1,3,4,7,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [2,6,1,3,4,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [2,6,1,3,5,4,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,1,2,6,8] => [2,6,1,5,3,7,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => [2,6,1,5,3,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [2,6,1,5,4,3,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,1,2,7,8] => [2,6,1,4,5,3,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [2,5,4,1,6,8,3,7] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => [2,5,4,1,7,3,8,6] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [2,6,4,1,3,7,8,5] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,1,2,6,8] => [2,6,4,1,3,7,5,8] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,1,2,7,8] => [2,6,4,1,3,5,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [2,6,4,1,5,3,7,8] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [2,6,5,3,4,1,7,8] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => [2,6,4,5,1,7,8,3] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,1,2,7,8] => [2,6,4,5,1,3,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,1,2,7,8] => [2,6,4,5,3,1,7,8] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [2,6,3,4,5,1,7,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [3,1,4,5,8,2,6,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [3,1,4,5,8,7,2,6] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [3,1,4,5,8,6,7,2] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [3,1,4,6,2,8,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [3,1,4,6,2,8,7,5] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [3,1,4,7,2,5,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [3,1,4,7,6,2,8,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [3,1,4,7,6,2,5,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [3,1,4,7,5,6,2,8] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [3,1,5,2,6,8,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [3,1,5,2,7,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [3,1,5,2,7,4,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [3,1,6,2,4,7,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [3,1,6,2,5,4,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,1,3,6,7] => [3,1,6,5,2,7,8,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [3,1,6,5,4,2,7,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [4,1,2,5,6,8,3,7] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [4,1,2,5,6,8,7,3] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [4,1,2,5,7,3,8,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [4,1,2,5,7,3,6,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [4,1,2,5,7,6,3,8] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [4,1,2,6,3,7,8,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [4,1,2,6,3,7,5,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [4,1,2,6,5,3,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [5,1,2,3,6,7,8,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [5,1,2,3,6,7,4,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [5,1,2,3,6,4,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [5,1,2,4,3,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [5,1,4,2,6,7,8,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [5,1,4,2,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [5,1,4,3,2,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [5,1,3,4,2,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [4,3,1,5,6,8,7,2] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,1,4,5,7] => [4,3,1,5,7,2,8,6] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => [4,3,1,5,7,2,6,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [5,3,1,2,6,7,8,4] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [5,3,1,2,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [5,3,1,4,2,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,1,5,6,7] => [5,4,2,1,6,7,8,3] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,1,5,6,8] => [5,4,2,1,6,7,3,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,1,5,7,8] => [5,4,2,1,6,3,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [5,4,2,1,3,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [5,4,2,3,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [5,3,4,1,6,7,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,1,5,7,8] => [5,3,4,1,6,2,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [5,3,4,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [2,3,4,5,8,1,6,7] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [2,3,4,5,8,1,7,6] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [2,3,4,5,8,7,1,6] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [2,3,4,5,8,7,6,1] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [2,3,4,5,8,6,7,1] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [2,3,4,6,1,8,5,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [2,3,4,6,1,8,7,5] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [2,3,4,7,1,5,8,6] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [2,3,4,7,1,5,6,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [2,3,4,7,1,6,5,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [2,3,4,7,6,1,8,5] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [2,3,4,7,6,1,5,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [2,3,4,7,6,5,1,8] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [2,3,4,7,5,6,1,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [2,3,5,1,6,8,4,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [2,3,5,1,7,4,8,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [2,3,6,1,4,7,8,5] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [2,3,6,1,4,5,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,6,4,1,2,3,7,8] => [2,3,6,1,5,4,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => [2,3,6,5,1,7,8,4] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [2,3,6,5,1,7,4,8] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,6,1,2,3,7,8] => [2,3,6,5,4,1,7,8] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [2,3,6,4,5,1,7,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [2,4,1,6,3,7,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [2,4,1,6,3,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [6,5,3,1,2,4,7,8] => [2,4,1,6,3,5,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,6,3,1,2,4,7,8] => [2,4,1,6,5,3,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [8,4,3,1,2,5,6,7] => [2,5,1,3,6,7,8,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [2,5,1,3,6,4,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [2,5,1,3,4,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,5,3,1,2,6,7,8] => [2,5,1,4,3,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [2,5,4,1,6,7,8,3] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [2,5,4,1,6,7,3,8] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,4,1,2,5,7,8] => [2,5,4,1,6,3,7,8] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => [2,5,4,1,3,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [2,5,4,3,1,6,7,8] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [2,5,3,4,1,6,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [3,1,4,5,6,8,2,7] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [3,1,4,5,6,8,7,2] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [3,1,4,6,2,7,8,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [3,1,4,6,5,2,7,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [3,1,5,2,6,7,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [4,1,2,5,6,7,8,3] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [4,1,2,5,6,7,3,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,4,5,7,8] => [4,1,2,5,6,3,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [4,1,2,5,3,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [4,1,3,2,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [4,3,1,5,6,7,8,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [4,3,1,2,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [2,3,4,5,6,8,1,7] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [2,3,4,5,6,8,7,1] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [2,3,4,5,7,1,8,6] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [2,3,4,5,7,1,6,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [2,3,4,5,7,6,1,8] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [2,3,4,6,1,7,8,5] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [2,3,4,6,1,7,5,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,2,3,4,7,8] => [2,3,4,6,1,5,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,6,1,2,3,4,7,8] => [2,3,4,6,5,1,7,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [2,3,5,1,6,7,8,4] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [2,3,5,1,4,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [2,3,5,4,1,6,7,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [2,4,1,5,6,7,8,3] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [2,4,1,5,6,7,3,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [2,4,1,5,6,3,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [2,4,1,5,3,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [2,4,1,3,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [2,4,3,1,5,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [3,1,4,5,6,7,8,2] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [3,1,4,5,6,7,2,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [3,1,4,5,2,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [3,1,4,2,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [2,3,4,5,6,7,1,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [2,3,4,5,6,1,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [2,3,4,5,1,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [2,3,4,1,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,9,1] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => [3,1,4,5,6,7,8,9,2] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [9,3,2,4,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => [3,1,4,5,6,7,8,9,10,2] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => [2,4,1,5,6,7,8,9,3] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => [4,3,1,5,6,7,8,9,2] => [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => [9,3,4,2,5,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => [9,4,3,2,5,6,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [10,3,2,4,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [2,3,4,5,6,7,8,9,10,11,12,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => [2,4,1,5,6,7,8,9,10,3] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,1,4,5,6,7,8,9] => [4,3,1,5,6,7,8,9,10,2] => [[[.,.],.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [9,4,1,2,3,5,6,7,8] => [2,3,5,1,6,7,8,9,4] => [[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,1,4,5,6,7,8] => [4,1,2,5,6,7,8,9,3] => [[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,1,5,6,7,8] => [5,3,4,1,6,7,8,9,2] => [[[.,.],[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [11,3,1,2,4,5,6,7,8,9,10] => [2,4,1,5,6,7,8,9,10,11,3] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [10,4,1,2,3,5,6,7,8,9] => [2,3,5,1,6,7,8,9,10,4] => [[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,2,1,4,5,6,7,8,9] => [4,1,2,5,6,7,8,9,10,3] => [[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,1,5,6,7,8,9] => [5,3,4,1,6,7,8,9,10,2] => [[[.,.],[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,1,6,7,8] => [6,3,4,5,1,7,8,9,2] => [[[.,.],[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,1,6,7,8,9] => [6,3,4,5,1,7,8,9,10,2] => [[[.,.],[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [9,6,1,2,3,4,5,7,8] => [2,3,4,5,7,1,8,9,6] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [9,4,3,1,2,5,6,7,8] => [2,5,1,3,6,7,8,9,4] => [[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,1,7,8] => [7,3,4,5,6,1,8,9,2] => [[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [10,6,1,2,3,4,5,7,8,9] => [2,3,4,5,7,1,8,9,10,6] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,1,7,8,9] => [7,3,4,5,6,1,8,9,10,2] => [[[.,.],[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [2,3,4,5,6,8,1,9,7] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [9,4,3,2,1,5,6,7,8] => [5,1,2,3,6,7,8,9,4] => [[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,1,8] => [8,3,4,5,6,7,1,9,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [2,3,4,5,6,7,9,8,1] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [9,3,4,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [2,9,3,4,5,6,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [10,7,1,2,3,4,5,6,8,9] => [2,3,4,5,6,8,1,9,10,7] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [10,4,3,2,1,5,6,7,8,9] => [5,1,2,3,6,7,8,9,10,4] => [[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,1,8,9] => [8,3,4,5,6,7,1,9,10,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,9,1,8] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => [9,3,4,5,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,1,2] => [2,9,4,3,5,6,7,8,1] => [[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [9,1,3,4,5,6,7,8,2] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,1,9] => [9,3,4,5,6,7,8,1,10,2] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,10,9,1] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,1,3,4,5,6,7] => [3,1,4,5,6,7,9,2,8] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [10,3,4,5,6,7,8,9,2,1] => [[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [2,10,3,4,5,6,7,8,9,1] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,10,1,9] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,9,1] => [10,3,4,5,6,7,8,9,1,2] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [10,1,3,4,5,6,7,8,9,2] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[] => [] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [8,1,2,3,4,5,6,7,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [8,1,2,3,4,5,7,6,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => [8,1,2,3,4,7,6,5,9] => [[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => [8,1,2,5,3,4,6,7,9] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => [8,1,2,6,4,3,5,7,9] => [[.,.],[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,1,9] => [8,3,1,2,4,5,6,7,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [2,8,1,3,4,5,6,7,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => [2,8,4,1,6,3,7,5,9] => [[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => [2,8,3,4,5,6,7,1,9] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1,7,9] => [7,1,2,3,4,5,8,6,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [7,1,2,3,4,5,6,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [7,5,4,3,2,1,6,8,9] => [6,1,2,3,4,7,5,8,9] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [6,1,2,3,4,5,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,2,6,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [2,3,4,8,5,6,7,1,9] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => [2,6,4,1,5,3,7,8,9] => [[.,[[.,.],.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1,5,7,8,9] => [5,1,2,3,6,4,7,8,9] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [2,3,6,4,5,1,7,8,9] => [[.,[.,[[.,.],[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1,4,6,7,8,9] => [4,1,2,5,3,6,7,8,9] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,1,5,6,7,8,9] => [4,3,1,2,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6,9] => [2,3,4,5,6,8,1,7,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => [2,3,4,5,6,8,7,1,9] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7,8,9] => [2,3,4,6,5,1,7,8,9] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1,2,3,6,7,8,9] => [2,3,5,1,4,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8,9] => [2,3,5,4,1,6,7,8,9] => [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1,2,4,6,7,8,9] => [2,4,1,5,3,6,7,8,9] => [[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => [3,1,4,5,6,7,8,2,9] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [4,2,1,3,5,6,7,8,9] => [3,1,4,2,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [2,3,4,5,6,7,8,1,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [2,3,4,5,6,7,1,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [2,3,4,5,6,1,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [9,1,2,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => [9,1,2,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [9,1,2,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => [9,1,2,3,4,8,6,7,5] => [[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => [9,1,2,3,8,5,6,7,4] => [[.,.],[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => [9,1,2,8,4,5,6,7,3] => [[.,.],[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => [9,1,8,3,4,5,6,7,2] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [9,8,2,3,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [10,1,2,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [10,1,2,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [9,1,2,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => [10,1,2,3,4,5,6,9,8,7] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => [9,1,2,3,4,7,8,6,5] => [[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [10,1,2,3,4,5,9,7,8,6] => [[.,.],[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [8,7,5,6,9,4,3,2,1] => [9,1,2,3,6,8,5,7,4] => [[.,.],[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [10,1,2,3,4,9,6,7,8,5] => [[.,.],[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,9,3,2,1] => [9,1,2,5,8,4,6,7,3] => [[.,.],[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [10,1,2,3,9,5,6,7,8,4] => [[.,.],[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => [9,1,4,8,3,5,6,7,2] => [[.,.],[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [10,1,2,9,4,5,6,7,8,3] => [[.,.],[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => [9,3,8,2,4,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [10,1,9,3,4,5,6,7,8,2] => [[.,.],[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [10,9,2,3,4,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [9,1,2,3,4,5,6,7,8,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [11,10,2,3,4,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,1,2,3,4,5,6,7,8,9,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [10,1,2,3,4,6,7,8,9,5] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,2,1] => [9,1,2,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,3,2,1] => [9,1,2,5,3,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [9,8,3,4,5,6,7,2,1] => [9,1,4,5,6,7,2,3,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,2,1] => [9,1,4,5,6,7,8,2,3] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,3,1] => [9,3,1,2,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,4,1] => [9,3,4,1,2,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,3,4,5,6,7,1] => [9,3,4,5,6,7,1,2,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => [2,9,1,3,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,1,2] => [2,9,1,3,4,5,8,6,7] => [[.,[.,.]],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => [2,9,4,1,3,5,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => [2,9,4,1,6,3,5,7,8] => [[.,[[.,.],.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => [2,9,4,1,6,3,8,5,7] => [[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => [2,9,4,5,6,7,8,1,3] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => [2,3,9,1,4,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => [2,3,9,5,1,4,6,7,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => [2,3,9,5,1,7,4,8,6] => [[.,[.,[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => [2,3,9,5,6,1,4,7,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => [2,3,9,5,6,1,7,8,4] => [[.,[.,[[.,.],[.,.]]]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [2,3,9,4,5,6,7,8,1] => [[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [2,3,4,9,1,5,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => [2,3,4,9,6,1,5,7,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => [2,3,4,9,6,1,8,5,7] => [[.,[.,[.,[[.,.],.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => [2,3,4,9,6,7,1,5,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => [2,3,4,9,6,7,1,8,5] => [[.,[.,[.,[[.,.],[.,.]]]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => [2,3,4,9,6,7,8,1,5] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [2,3,4,9,5,6,7,8,1] => [[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [2,3,4,5,9,1,6,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => [2,3,4,5,9,7,1,6,8] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => [2,3,4,5,9,7,8,1,6] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [2,3,4,5,9,6,7,8,1] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [2,3,4,5,6,9,1,7,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => [2,3,4,5,6,9,8,1,7] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [2,3,4,5,6,9,7,8,1] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,2,1] => [10,1,4,5,6,7,8,9,2,3] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,3,1] => [10,3,1,2,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [10,9,2,3,4,5,6,7,8,1] => [10,3,4,5,6,7,8,1,2,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => [2,10,1,3,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => [2,10,4,1,3,5,6,7,8,9] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => [2,10,4,1,6,3,5,7,8,9] => [[.,[[.,.],.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => [2,10,4,1,6,3,8,5,7,9] => [[.,[[.,.],.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => [2,10,4,1,6,3,8,5,9,7] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,1,2] => [2,10,4,5,6,7,8,9,1,3] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => [2,3,10,1,4,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => [2,3,10,5,1,4,6,7,8,9] => [[.,[.,[[.,.],.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => [2,3,10,5,1,7,4,9,6,8] => [[.,[.,[[.,.],.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [2,3,10,5,6,1,8,4,9,7] => [[.,[.,[[.,.],[.,.]]]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [2,3,10,4,5,6,7,8,9,1] => [[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => [2,3,4,10,1,5,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => [2,3,4,10,6,1,8,5,9,7] => [[.,[.,[.,[[.,.],.]]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => [2,3,4,10,6,7,1,8,9,5] => [[.,[.,[.,[[.,.],[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [2,3,4,10,6,7,8,1,5,9] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => [2,3,4,10,6,7,8,1,9,5] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [2,3,4,10,5,6,7,8,9,1] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => [2,3,4,5,10,1,6,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => [2,3,4,5,10,7,1,9,6,8] => [[.,[.,[.,[.,[[.,.],.]]]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => [2,3,4,5,10,7,8,9,1,6] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [2,3,4,5,10,6,7,8,9,1] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => [2,3,4,5,6,10,1,7,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => [2,3,4,5,6,10,8,9,1,7] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [2,3,4,5,6,10,7,8,9,1] => [[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,10,1,8,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => [2,3,4,5,6,7,10,9,1,8] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [2,3,4,5,6,7,10,8,9,1] => [[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,1,3] => [3,1,9,2,4,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,3,2,1,6] => [6,1,2,3,4,9,5,7,8] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,2,1,7] => [7,1,2,3,4,5,9,6,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,9,7] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,1,4] => [4,3,1,9,2,5,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,1,4] => [4,1,2,10,3,5,6,7,8,9] => [[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,1,5] => [5,1,2,3,10,4,6,7,8,9] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,6,7,5,4,3,2,1,8] => [8,1,2,3,4,7,5,9,6] => [[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,7,10,8] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,1,2] => [2,11,1,3,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [9,1,2,3,4,5,6,8,7,10] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [2,3,1,4,5,6,7,8,9,10,11] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,1,7,8] => [7,1,2,3,4,5,8,9,6] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [9,8,5,4,3,2,1,6,7] => [6,1,2,3,4,7,9,5,8] => [[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,3,2,1,4,5] => [4,1,2,5,9,3,6,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,1,3,4] => [3,1,4,9,2,5,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [2,3,4,5,6,7,8,9,1,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [2,3,4,5,6,7,8,9,10,1,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [10,8,7,6,9,5,4,3,2,1] => [10,1,2,3,4,9,6,7,5,8] => [[.,.],[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,1,2,8] => [2,8,1,3,4,5,6,9,7] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,1,2,3,4] => [2,3,4,9,6,5,7,8,1] => [[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,9,1,2,3,4,5,6] => [2,3,4,5,6,9,8,7,1] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [2,3,4,5,6,7,8,1,9,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [7,6,8,9,1,2,3,4,5] => [2,3,4,5,9,7,6,8,1] => [[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,1,2,3] => [2,3,9,5,4,6,7,8,1] => [[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => [9,1,2,3,6,4,5,7,8,10] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [9,7,8,5,4,3,2,1,6] => [6,1,2,3,4,9,8,5,7] => [[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [8,1,2,3,4,5,6,7,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [2,4,3,1,5,6,7,8,9,10] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [2,3,6,4,5,1,7,8,9,10] => [[.,[.,[[.,.],[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [2,3,4,8,5,6,7,1,9,10] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [6,5,7,4,8,3,9,2,10,1] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7,6,8,5,9,4,10,2,1,3] => [3,1,10,9,8,7,6,5,4,2] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [10,8,6,4,2,1,3,5,7,9] => [3,1,5,2,7,4,9,6,10,8] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [10,9,11,8,12,4,3,5,2,6,1,7] => [7,6,5,3,2,1,12,11,10,9,8,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,7,6,5,4,3,2,1,8,9] => [8,1,2,3,4,5,6,9,10,7] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,5,4,3,2,1,6,7,8] => [6,1,2,3,4,7,8,9,5] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [10,5,4,3,2,1,6,7,8,9] => [6,1,2,3,4,7,8,9,10,5] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [10,6,5,4,3,2,1,7,8,9] => [7,1,2,3,4,5,8,9,10,6] => [[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,11,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [4,2,1,3,5,6,7,8,9,10] => [3,1,4,2,5,6,7,8,9,10] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,2,1,3,4,5,6] => [3,1,4,5,6,9,2,7,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,9,2,1] => [10,1,9,3,4,5,6,7,2,8] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,3,4,5,6,7,8,9,1,10] => [10,3,4,5,6,7,8,9,1,11,2] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => [11,3,4,5,6,7,8,9,10,2,1] => [[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,9,8,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,8,11,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,8,1] => [9,8,2,3,4,5,6,1,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [2,3,4,5,6,7,9,8,1,10] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,2,1,3,4] => [3,1,4,10,2,5,6,7,8,9] => [[.,.],[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [11,10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,11,1,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [9,8,4,1,2,3,5,6,7] => [2,3,5,1,6,7,9,4,8] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,9,1] => [10,9,2,3,4,5,6,7,1,8] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,3,4,5,6,7,8,9,10,1] => [11,3,4,5,6,7,8,9,10,1,2] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [7,8,2,3,4,5,6,9,1] => [9,3,4,5,6,8,7,2,1] => [[[[.,.],[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,1,2,9] => [2,9,1,3,4,5,6,7,10,8] => [[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,8,2,1] => [9,1,8,3,4,5,6,2,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [10,9,2,1,3,4,5,6,7,8] => [3,1,4,5,6,7,8,10,2,9] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => [2,8,4,5,6,7,1,9,3] => [[.,[[.,.],[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [6,7,5,8,4,9,3,10,1,2] => [2,10,9,8,7,6,5,4,3,1] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,1,2,7,8] => [2,7,1,3,4,5,8,9,6] => [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,3,1,2,4,6,8,10] => [2,4,1,6,3,8,5,9,7,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => [2,8,4,1,6,3,7,5,9,10] => [[.,[[.,.],.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [11,1,3,4,5,6,7,8,9,10,2] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [11,3,4,5,6,7,8,9,10,1,2] => [2,11,4,5,6,7,8,9,10,1,3] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [11,8,9,10,1,2,3,4,5,6,7] => [2,3,4,5,6,7,11,9,10,1,8] => [[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [9,8,10,1,2,3,4,5,6,7] => [2,3,4,5,6,7,10,9,8,1] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1,10] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [6,7,5,8,4,9,3,10,2,11,1,12] => [11,10,9,8,7,6,5,4,3,2,1,12] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => [2,3,9,5,6,1,7,8,4,10] => [[.,[.,[[.,.],[.,.]]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,2,1,3,9] => [3,1,9,2,4,5,6,7,10,8] => [[.,.],[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => [2,4,1,6,3,8,5,9,7] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [10,8,6,5,4,3,2,1,7,9] => [7,1,2,3,4,5,9,6,10,8] => [[.,.],[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [9,8,6,4,2,1,3,5,7] => [3,1,5,2,7,4,9,6,8] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [6,4,5,7,3,8,2,9,1] => [9,8,7,5,6,4,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [6,4,5,7,3,8,2,9,1,10] => [9,8,7,5,6,4,3,2,1,10] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [12,11,10,9,8,7,6,5,4,3,1,2] => [2,12,1,3,4,5,6,7,8,9,10,11] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [10,5,6,4,7,3,8,2,9,1] => [10,9,8,7,6,4,3,2,1,5] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [12,10,9,8,7,6,5,4,3,2,1,11] => [11,1,2,3,4,5,6,7,8,9,12,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [9,8,6,4,2,1,3,5,7,10] => [3,1,5,2,7,4,9,6,8,10] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
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