Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
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] => [2,3,1] => [3,2,1] => [[[.,.],.],.]
[1,0,1,1,0,0] => [2,1,3] => [2,1,3] => [[.,.],[.,.]]
[1,1,0,0,1,0] => [1,3,2] => [1,3,2] => [.,[[.,.],.]]
[1,1,0,1,0,0] => [3,1,2] => [2,3,1] => [[.,[.,.]],.]
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [4,2,3,1] => [[[.,.],[.,.]],.]
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [2,1,4,3] => [[.,.],[[.,.],.]]
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [3,2,4,1] => [[[.,.],[.,.]],.]
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [1,4,3,2] => [.,[[[.,.],.],.]]
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [3,4,1,2] => [[.,[.,.]],[.,.]]
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [2,4,3,1] => [[.,[[.,.],.]],.]
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [2,3,1,4] => [[.,[.,.]],[.,.]]
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,3,4,2] => [.,[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [2,3,4,1] => [[.,[.,[.,.]]],.]
[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] => [2,3,4,5,1] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [4,2,3,5,1] => [[[.,.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [3,2,5,4,1] => [[[.,.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [2,1,4,5,3] => [[.,.],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [3,2,4,5,1] => [[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.]
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [2,3,1,5,4] => [[.,[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [3,4,1,5,2] => [[.,[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [1,3,5,4,2] => [.,[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [4,3,5,1,2] => [[[.,.],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.]
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
[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] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [5,2,3,4,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [5,2,3,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [4,2,3,6,5,1] => [[[.,.],[.,[[.,.],.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [3,2,1,5,6,4] => [[[.,.],.],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [4,2,3,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [2,1,5,4,6,3] => [[.,.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [4,2,6,1,5,3] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [5,2,6,4,1,3] => [[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [3,2,6,4,5,1] => [[[.,.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [3,2,5,4,1,6] => [[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [3,2,4,1,6,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [4,2,5,1,6,3] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [3,2,5,4,6,1] => [[[.,.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [2,1,4,6,5,3] => [[.,.],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [3,2,5,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [5,2,4,6,1,3] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [3,2,4,6,5,1] => [[[.,.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
>>> Load all 1915 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => [[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [3,2,4,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [1,5,3,4,6,2] => [.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [1,4,3,6,5,2] => [.,[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,4,3,5,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => [.,[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [1,4,3,5,6,2] => [.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [3,6,1,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [3,5,1,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [3,5,1,4,6,2] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [4,6,3,1,5,2] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [2,4,3,1,6,5] => [[.,[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [4,5,3,1,6,2] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [2,3,1,6,5,4] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [3,4,1,6,5,2] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [3,4,1,5,2,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [2,5,3,6,1,4] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [5,4,3,6,1,2] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [3,4,1,5,6,2] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [1,2,5,4,6,3] => [.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [1,3,6,4,5,2] => [.,[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,3,5,4,2,6] => [.,[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => [.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [1,3,5,4,6,2] => [.,[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [2,4,6,1,5,3] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [4,3,6,1,5,2] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [4,3,5,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [2,5,6,4,1,3] => [[.,[[.,[.,.]],.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [5,3,6,4,1,2] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [4,3,5,1,6,2] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [1,5,4,6,2,3] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [1,3,4,6,5,2] => [.,[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [2,5,4,6,1,3] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [5,3,4,6,1,2] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.]
[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] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [6,2,3,4,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [5,2,3,4,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [4,2,3,1,6,7,5] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [3,2,1,6,5,7,4] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [5,2,3,7,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [5,2,3,6,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [6,2,3,7,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [4,2,3,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [4,2,3,6,5,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [4,2,3,5,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [5,2,3,6,1,7,4] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [4,2,3,6,5,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [4,2,3,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [3,2,1,6,7,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [3,2,1,5,7,6,4] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [3,2,1,5,6,4,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [4,2,3,6,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [6,2,3,5,7,1,4] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [4,2,3,5,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [3,2,1,4,6,7,5] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [3,2,1,5,6,7,4] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [4,2,3,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [2,1,6,4,5,7,3] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,1,6,4,7,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [2,1,5,4,7,6,3] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [2,1,5,4,6,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [2,1,5,4,6,7,3] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [4,2,7,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [4,2,6,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [4,2,5,1,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [4,2,6,1,5,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [4,2,5,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [5,2,7,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [5,2,6,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => [6,2,7,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [3,2,7,4,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [3,2,6,4,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [3,2,5,4,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [5,2,6,4,1,7,3] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [3,2,6,4,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [3,2,5,4,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [3,2,4,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [3,2,4,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [4,2,6,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [4,2,5,1,7,6,3] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [4,2,5,1,6,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [3,2,6,4,7,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [6,2,5,4,7,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [3,2,5,4,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [3,2,5,4,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [3,2,4,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [3,2,4,1,6,7,5] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [4,2,5,1,6,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [3,2,5,4,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [3,2,4,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,1,5,7,3,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,1,6,7,5,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [2,1,4,7,5,6,3] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [2,1,4,6,5,3,7] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [2,1,4,5,3,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [2,1,4,6,5,7,3] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [2,1,4,5,3,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [3,2,5,7,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [3,2,5,6,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [5,2,6,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [5,2,4,7,1,6,3] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [5,2,4,6,1,3,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => [3,2,6,7,5,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => [6,2,4,7,5,1,3] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [3,2,4,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [3,2,4,6,5,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [3,2,4,5,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [3,2,5,6,1,7,4] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [5,2,4,6,1,7,3] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [3,2,4,6,5,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [3,2,4,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [2,1,3,5,7,6,4] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [2,1,4,6,7,3,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [2,1,6,5,7,3,4] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [2,1,4,5,7,6,3] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [2,1,4,5,6,3,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [3,2,4,6,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [3,2,6,5,7,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [6,2,4,5,7,1,3] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [3,2,4,5,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [2,1,4,5,6,7,3] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [3,2,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [1,6,3,4,5,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [1,6,3,4,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [1,5,3,4,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [1,5,3,4,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [1,5,3,4,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [1,5,3,7,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [1,5,3,6,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [1,6,3,7,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [1,4,3,7,5,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [1,4,3,6,5,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [1,4,3,5,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [1,5,3,6,2,7,4] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [1,4,3,6,5,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [1,4,3,5,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [1,3,2,5,7,6,4] => [.,[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [1,4,3,6,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [1,6,3,5,7,2,4] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [1,4,3,5,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [1,4,3,5,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [1,4,3,5,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [3,7,1,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [3,6,1,4,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [3,5,1,4,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [3,6,1,4,5,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [3,5,1,4,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [3,4,1,2,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [3,6,1,4,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [3,5,1,4,7,6,2] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [3,5,1,4,6,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [3,4,1,2,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [3,5,1,4,6,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [4,7,3,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [4,6,3,1,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [4,5,3,1,2,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [4,6,3,1,5,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [5,7,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [2,7,3,4,5,6,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [2,6,3,4,5,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [2,5,3,4,1,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [5,6,3,4,1,7,2] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [2,6,3,4,5,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [2,5,3,4,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [2,4,3,1,7,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [2,4,3,1,6,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [4,6,3,1,7,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [4,5,3,1,7,6,2] => [[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [4,5,3,1,6,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [2,6,3,4,7,1,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [6,5,3,4,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [2,5,3,4,7,6,1] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [2,5,3,4,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [2,4,3,1,5,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [2,4,3,1,6,7,5] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [4,5,3,1,6,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [2,5,3,4,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [2,4,3,1,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [2,3,1,7,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [2,3,1,6,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [2,3,1,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [2,3,1,6,5,7,4] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [2,3,1,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [3,5,1,7,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [3,6,1,7,5,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [3,4,1,7,5,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [3,4,1,6,5,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [3,4,1,5,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [3,5,1,6,2,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [3,4,1,6,5,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [3,4,1,5,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [2,5,3,7,1,6,4] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [2,5,3,6,1,4,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [5,6,3,7,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [5,4,3,7,1,6,2] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [5,4,3,6,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => [2,6,3,7,5,1,4] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => [6,4,3,7,5,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [2,4,3,7,5,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [2,4,3,6,5,1,7] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [2,4,3,5,1,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [2,5,3,6,1,7,4] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [5,4,3,6,1,7,2] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [2,4,3,6,5,7,1] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [2,4,3,5,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [2,3,1,4,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [2,3,1,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [2,3,1,6,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [2,3,1,5,7,6,4] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [2,3,1,5,6,4,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [3,4,1,6,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [3,6,1,5,7,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [3,4,1,5,7,6,2] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [3,4,1,5,6,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [2,4,3,6,7,1,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [2,6,3,5,7,1,4] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [6,4,3,5,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [2,4,3,5,7,6,1] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [2,4,3,5,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [2,3,1,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [2,3,1,4,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [2,3,1,5,6,7,4] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [3,4,1,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [2,4,3,5,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [1,2,6,4,5,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [1,2,6,4,7,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [1,2,5,4,7,6,3] => [.,[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [1,2,5,4,6,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [1,2,5,4,6,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [1,4,7,2,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [1,4,6,2,5,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [1,4,6,2,5,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [1,5,7,4,2,6,3] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [1,5,6,4,2,3,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [1,6,7,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [1,3,7,4,5,6,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [1,3,6,4,5,2,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [1,3,5,4,2,7,6] => [.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [1,5,6,4,2,7,3] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [1,3,6,4,5,7,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [1,3,5,4,2,6,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [1,3,4,2,7,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [1,4,5,2,7,6,3] => [.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [1,4,5,2,6,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [1,3,6,4,7,2,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [1,6,5,4,7,2,3] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [1,3,5,4,7,6,2] => [.,[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [1,3,5,4,6,2,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,3,4,2,6,7,5] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [1,4,5,2,6,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [1,3,5,4,6,7,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [2,4,7,1,5,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [2,4,6,1,5,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [2,4,5,1,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [2,4,6,1,5,7,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [2,4,5,1,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [4,5,7,1,2,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [4,6,7,1,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [4,3,7,1,5,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [4,3,6,1,5,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [4,3,5,1,2,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [4,5,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [4,3,6,1,5,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [4,3,5,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [2,5,7,4,1,6,3] => [[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [2,5,6,4,1,3,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [5,3,7,4,1,6,2] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [5,3,6,4,1,2,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [2,6,7,4,5,1,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [6,3,7,4,5,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [2,3,7,4,5,6,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [2,3,6,4,5,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [2,3,5,4,1,7,6] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [2,5,6,4,1,7,3] => [[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [5,3,6,4,1,7,2] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [2,3,6,4,5,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [2,3,5,4,1,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [2,3,4,1,7,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [2,3,4,1,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [2,4,6,1,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [2,4,5,1,7,6,3] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [2,4,5,1,6,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [4,3,6,1,7,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [4,6,5,1,7,2,3] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [4,3,5,1,7,6,2] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [4,3,5,1,6,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [2,3,6,4,7,1,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [2,6,5,4,7,1,3] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [6,3,5,4,7,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [2,3,5,4,7,6,1] => [[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [2,3,5,4,6,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [2,3,4,1,6,7,5] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [2,4,5,1,6,7,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [4,3,5,1,6,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [2,3,5,4,6,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [1,2,6,7,5,3,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [1,2,4,7,5,6,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [1,2,4,6,5,3,7] => [.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [1,2,4,5,3,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [1,2,4,6,5,7,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [1,3,5,7,2,6,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [1,3,5,6,2,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [1,5,4,7,2,6,3] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [1,5,4,6,2,3,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [1,3,6,7,5,2,4] => [.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [1,6,4,7,5,2,3] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [1,3,4,7,5,6,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [1,3,4,6,5,2,7] => [.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [1,3,4,5,2,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,3,5,6,2,7,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [1,5,4,6,2,7,3] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [1,3,4,6,5,7,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [2,3,5,7,1,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [2,3,5,6,1,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [2,5,6,7,1,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [2,5,4,7,1,6,3] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [2,5,4,6,1,3,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [5,3,6,7,1,2,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [5,6,4,7,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [5,3,4,7,1,6,2] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [5,3,4,6,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [2,3,6,7,5,1,4] => [[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [2,6,4,7,5,1,3] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [6,3,4,7,5,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [2,3,4,7,5,6,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [2,3,4,6,5,1,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [2,3,5,6,1,7,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [2,5,4,6,1,7,3] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [5,3,4,6,1,7,2] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [2,3,4,6,5,7,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [1,2,3,5,7,6,4] => [.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [1,2,4,6,7,3,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [1,2,6,5,7,3,4] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [1,2,4,5,7,6,3] => [.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [1,3,4,6,7,2,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,3,6,5,7,2,4] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [1,6,4,5,7,2,3] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [1,3,4,5,7,6,2] => [.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [2,3,4,6,7,1,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [2,3,6,5,7,1,4] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [2,6,4,5,7,1,3] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [6,3,4,5,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [2,3,4,5,7,6,1] => [[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => [.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[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] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => [7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,7,1,8,6] => [7,2,3,4,5,8,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => [6,2,3,4,5,8,7,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,7] => [5,2,3,4,1,7,8,6] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => [6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,1,6,7,5,8] => [4,2,3,1,7,6,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,8,5,7] => [4,2,3,1,7,6,8,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8] => [4,2,3,1,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,6,1,7,8,5] => [6,2,3,4,8,1,7,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,4,6,7,1,8,5] => [7,2,3,4,8,6,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,1,5] => [5,2,3,4,8,6,7,1] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,4,6,7,1,5,8] => [5,2,3,4,7,6,1,8] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,8,7] => [5,2,3,4,6,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,8,5,7] => [6,2,3,4,7,1,8,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,4,1,5,7,8,6] => [4,2,3,1,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => [4,2,3,1,7,8,5,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => [4,2,3,1,6,8,7,5] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,4,7,1,5,8,6] => [5,2,3,4,7,8,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,4,7,1,8,5,6] => [7,2,3,4,6,8,1,5] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,4,1,5,8,6,7] => [4,2,3,1,5,7,8,6] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [4,2,3,1,6,7,8,5] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,5,6,7,4,8] => [3,2,1,7,5,6,4,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,5,6,8,4,7] => [3,2,1,7,5,6,8,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,5,6,4,7,8] => [3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,7,8,4,6] => [3,2,1,6,5,8,7,4] => [[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6,8] => [3,2,1,6,5,7,4,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,5,8,4,6,7] => [3,2,1,6,5,7,8,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,4] => [5,2,3,8,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,5,1,6,7,4,8] => [5,2,3,7,1,6,4,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,5,1,6,4,8,7] => [5,2,3,6,1,4,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,5,1,6,8,4,7] => [5,2,3,7,1,6,8,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,5,6,1,7,8,4] => [6,2,3,8,5,1,7,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,5,6,1,7,4,8] => [6,2,3,7,5,1,4,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,5,6,7,1,8,4] => [7,2,3,8,5,6,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,1,4] => [4,2,3,8,5,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,8,1,4,7] => [4,2,3,7,5,6,8,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,7,8,6] => [4,2,3,5,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,7,4,8,6] => [5,2,3,7,1,8,4,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,7,8,1,4,6] => [4,2,3,6,5,8,7,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [5,2,3,6,1,7,8,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,1,4,6,7,8] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,1,4,6,8,5,7] => [3,2,1,4,7,6,8,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,3,1,6,4,7,8,5] => [3,2,1,6,8,4,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [3,2,1,6,7,4,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,6,7,4,8,5] => [3,2,1,7,8,6,4,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,4,5] => [3,2,1,5,8,6,7,4] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,6,7,4,5,8] => [3,2,1,5,7,6,4,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => [3,2,1,6,7,4,8,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,4,5,7] => [3,2,1,5,7,6,8,4] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,1,6,4,5,7,8] => [3,2,1,5,6,4,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,6,1,7,4,8,5] => [6,2,3,7,8,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,1,7,8,4,5] => [6,2,3,5,8,1,7,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,8,7] => [4,2,3,5,6,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,6,1,4,5,7,8] => [4,2,3,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [3,2,1,4,6,8,7,5] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,7,4,5,8,6] => [3,2,1,5,7,8,4,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [3,2,1,7,6,8,4,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,7,8,4,5,6] => [3,2,1,5,6,8,7,4] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [4,2,3,5,6,8,7,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6,8] => [4,2,3,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [3,2,1,4,5,7,8,6] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,1,4,8,5,6,7] => [3,2,1,4,6,7,8,5] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,1,8,4,5,6,7] => [3,2,1,5,6,7,8,4] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [4,2,3,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3,7,8,6] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,7,3,8,6] => [2,1,7,4,5,8,3,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4,5,7,8,3,6] => [2,1,6,4,5,8,7,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4,5,8,3,6,7] => [2,1,6,4,5,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,6,8,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,6,3,7,8,5] => [2,1,6,4,8,3,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,7,3,8,5] => [2,1,7,4,8,6,3,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,6,7,8,3,5] => [2,1,5,4,8,6,7,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,8,7] => [2,1,5,4,6,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,8,5,7] => [2,1,6,4,7,3,8,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,8,3,5,7] => [2,1,5,4,7,6,8,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [2,1,4,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [2,1,4,3,6,8,7,5] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,4,7,3,8,5,6] => [2,1,7,4,6,8,3,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,4,7,8,3,5,6] => [2,1,5,4,6,8,7,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,4,7,3,5,6,8] => [2,1,5,4,6,7,3,8] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => [2,1,4,3,5,7,8,6] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,8,3,5,6,7] => [2,1,5,4,6,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,3] => [4,2,8,1,5,6,7,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,5,6,7,3,8] => [4,2,7,1,5,6,3,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,5,6,3,8,7] => [4,2,6,1,5,3,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,5,6,8,3,7] => [4,2,7,1,5,6,8,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,5,6,3,7,8] => [4,2,6,1,5,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,5,3,7,8,6] => [4,2,5,1,3,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => [4,2,5,1,3,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,4,1,5,7,3,8,6] => [4,2,7,1,5,8,3,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,3,6,8,7] => [4,2,5,1,3,6,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => [4,2,5,1,3,7,8,6] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,4,1,5,8,3,6,7] => [4,2,6,1,5,7,8,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,3,6,7,8] => [4,2,5,1,3,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,4,5,1,6,7,8,3] => [5,2,8,4,1,6,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,4,5,1,6,7,3,8] => [5,2,7,4,1,6,3,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,4,5,1,6,3,8,7] => [5,2,6,4,1,3,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,4,5,1,6,8,3,7] => [5,2,7,4,1,6,8,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,4,5,1,6,3,7,8] => [5,2,6,4,1,3,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,6,1,7,8,3] => [6,2,8,4,5,1,7,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,6,1,7,3,8] => [6,2,7,4,5,1,3,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,1,8,3] => [7,2,8,4,5,6,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,1,3] => [3,2,8,4,5,6,7,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,7,1,3,8] => [3,2,7,4,5,6,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,6,1,3,8,7] => [3,2,6,4,5,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,6,1,8,3,7] => [6,2,7,4,5,1,8,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [3,2,6,4,5,1,7,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,4,5,1,3,7,8,6] => [3,2,5,4,1,8,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6,8] => [3,2,5,4,1,7,6,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,4,5,1,7,3,8,6] => [5,2,7,4,1,8,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,4,5,1,7,8,3,6] => [5,2,6,4,1,8,7,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6,8] => [5,2,6,4,1,7,3,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,7,1,3,8,6] => [3,2,7,4,5,8,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,7,1,8,3,6] => [7,2,6,4,5,8,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [5,2,6,4,1,7,8,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => [3,2,5,4,1,6,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,6,7,8,5] => [3,2,4,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,6,7,5,8] => [3,2,4,1,7,6,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7] => [3,2,4,1,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,8,5,7] => [3,2,4,1,7,6,8,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,6,5,7,8] => [3,2,4,1,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => [4,2,6,1,8,3,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => [4,2,6,1,7,3,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,6,7,3,8,5] => [4,2,7,1,8,6,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,7,8,3,5] => [4,2,5,1,8,6,7,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,8,7] => [4,2,5,1,6,3,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [4,2,6,1,7,3,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,8,3,5,7] => [4,2,5,1,7,6,8,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,6,3,5,7,8] => [4,2,5,1,6,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,6,1,3,7,8,5] => [3,2,6,4,8,1,7,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,6,1,3,7,5,8] => [3,2,6,4,7,1,5,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => [6,2,7,4,8,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,6,7,1,3,8,5] => [3,2,7,4,8,6,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,6,7,1,8,3,5] => [7,2,5,4,8,6,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,6,7,8,1,3,5] => [3,2,5,4,8,6,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [3,2,5,4,7,6,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => [3,2,5,4,6,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,8,5,7] => [3,2,6,4,7,1,8,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [6,2,5,4,7,1,8,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [3,2,5,4,7,6,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,3,5,7,8,6] => [3,2,4,1,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,4,1,3,5,7,6,8] => [3,2,4,1,5,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,3,7,5,8,6] => [3,2,4,1,7,8,5,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,3,7,8,5,6] => [3,2,4,1,6,8,7,5] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,4,1,3,7,5,6,8] => [3,2,4,1,6,7,5,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,7,3,5,8,6] => [4,2,5,1,7,8,3,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,7,3,8,5,6] => [4,2,7,1,6,8,3,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,7,8,3,5,6] => [4,2,5,1,6,8,7,3] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,4,7,1,3,5,8,6] => [3,2,5,4,7,8,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,4,7,1,3,8,5,6] => [3,2,7,4,6,8,1,5] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [3,2,5,4,6,8,7,1] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1,3,5,6,8,7] => [3,2,4,1,5,6,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,3,5,8,6,7] => [3,2,4,1,5,7,8,6] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,3,8,5,6,7] => [3,2,4,1,6,7,8,5] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1,8,3,5,6,7] => [4,2,5,1,6,7,8,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [3,2,5,4,6,7,8,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8] => [3,2,4,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,6,4,8,7] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,1,3,5,7,4,8,6] => [2,1,3,7,5,8,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,1,3,5,7,8,4,6] => [2,1,3,6,5,8,7,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,1,3,5,4,8,6,7] => [2,1,3,5,4,7,8,6] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [2,1,5,8,3,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [2,1,5,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,1,5,3,6,8,4,7] => [2,1,5,7,3,6,8,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,5,6,3,7,8,4] => [2,1,6,8,5,3,7,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,1,5,6,7,3,8,4] => [2,1,7,8,5,6,3,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => [2,1,4,8,5,6,7,3] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,1,4,6,5,3,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,1,5,6,3,4,7,8] => [2,1,4,6,5,3,7,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => [2,1,5,7,3,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,5,3,7,8,4,6] => [2,1,5,6,3,8,7,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6,8] => [2,1,5,6,3,7,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [2,1,7,6,5,8,3,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,5,7,8,3,4,6] => [2,1,4,6,5,8,7,3] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,5,3,4,6,8,7] => [2,1,4,5,3,6,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,1,5,3,8,4,6,7] => [2,1,5,6,3,7,8,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,5,3,4,6,7,8] => [2,1,4,5,3,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,1,3,6,7,8,4] => [3,2,5,8,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,5,1,3,6,7,4,8] => [3,2,5,7,1,6,4,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,1,3,6,8,4,7] => [3,2,5,7,1,6,8,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,1,3,6,4,7,8] => [3,2,5,6,1,4,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,5,1,6,3,7,8,4] => [5,2,6,8,1,3,7,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,1,6,3,7,4,8] => [5,2,6,7,1,3,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => [5,2,7,8,1,6,3,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,1,6,7,8,3,4] => [5,2,4,8,1,6,7,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,5,1,6,3,4,8,7] => [5,2,4,6,1,3,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,5,6,1,3,7,8,4] => [3,2,6,8,5,1,7,4] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,5,6,1,3,7,4,8] => [3,2,6,7,5,1,4,8] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,5,6,1,7,3,8,4] => [6,2,7,8,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,5,6,7,1,3,8,4] => [3,2,7,8,5,6,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,1,3,4] => [3,2,4,8,5,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [3,2,4,7,5,6,8,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,7,8,6] => [3,2,4,5,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,7,4,8,6] => [3,2,5,7,1,8,4,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,7,8,4,6] => [3,2,5,6,1,8,7,4] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,5,1,7,3,4,8,6] => [5,2,4,7,1,8,3,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,5,7,1,3,4,8,6] => [3,2,4,7,5,8,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,5,7,1,3,8,4,6] => [3,2,7,6,5,8,1,4] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [3,2,4,6,5,8,7,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,5,1,3,8,4,6,7] => [3,2,5,6,1,7,8,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,4,6,7,8] => [3,2,4,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,1,3,6,7,4,8,5] => [2,1,3,7,8,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,6,7,8,4,5] => [2,1,3,5,8,6,7,4] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,6,4,5,8,7] => [2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,1,3,6,4,8,5,7] => [2,1,3,6,7,4,8,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [2,1,4,6,8,3,7,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [2,1,6,7,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,6,3,7,8,4,5] => [2,1,6,5,8,3,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,6,7,3,4,8,5] => [2,1,4,7,8,6,3,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,1,6,7,3,8,4,5] => [2,1,7,5,8,6,3,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => [2,1,4,5,8,6,7,3] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [2,1,4,5,6,3,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,1,6,3,4,8,5,7] => [2,1,4,6,7,3,8,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,1,6,3,8,4,5,7] => [2,1,6,5,7,3,8,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,6,1,3,7,4,8,5] => [3,2,6,7,8,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,1,3,7,8,4,5] => [3,2,6,5,8,1,7,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,6,1,3,7,4,5,8] => [3,2,6,5,7,1,4,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,6,1,7,3,4,8,5] => [6,2,4,7,8,1,3,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => [3,2,4,7,8,6,1,5] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,6,7,1,3,8,4,5] => [3,2,7,5,8,6,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [3,2,4,5,8,6,7,1] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,6,1,3,8,4,5,7] => [3,2,6,5,7,1,8,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,6,1,8,3,4,5,7] => [6,2,4,5,7,1,8,3] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [3,2,4,5,7,6,8,1] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,6,1,3,4,5,7,8] => [3,2,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,4,7,5,8,6] => [2,1,3,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,1,7,3,8,4,5,6] => [2,1,7,5,6,8,3,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,7,8,3,4,5,6] => [2,1,4,5,6,8,7,3] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6,8] => [2,1,4,5,6,7,3,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,7,1,3,4,5,8,6] => [3,2,4,5,7,8,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,7,1,8,3,4,5,6] => [7,2,4,5,6,8,1,3] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [3,2,4,5,6,8,7,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => [3,2,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => [2,1,3,5,6,7,8,4] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [2,1,4,5,6,7,8,3] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [3,2,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,8,2,7] => [1,7,3,4,5,6,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,2,7,8,6] => [1,5,3,4,2,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,5,7,2,8,6] => [1,7,3,4,5,8,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,7,8,2,6] => [1,6,3,4,5,8,7,2] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,5,2,8,6,7] => [1,5,3,4,2,7,8,6] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,5] => [1,4,3,2,8,6,7,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,6,2,7,8,5] => [1,6,3,4,8,2,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,6,7,2,8,5] => [1,7,3,4,8,6,2,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,8,7] => [1,5,3,4,6,2,8,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,4,2,5,7,8,6] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,4,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,2,7,5,8,6] => [1,4,3,2,7,8,5,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,4,2,7,8,5,6] => [1,4,3,2,6,8,7,5] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,4,2,7,5,6,8] => [1,4,3,2,6,7,5,8] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,4,7,2,5,8,6] => [1,5,3,4,7,8,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [1,5,3,4,6,7,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,3,4,2,5,8,6,7] => [1,4,3,2,5,7,8,6] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [1,4,3,2,6,7,8,5] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [1,5,3,4,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,6,4,8,7] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,5,6,8,4,7] => [1,3,2,7,5,6,8,4] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,7,4,8,6] => [1,3,2,7,5,8,4,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,7,8,4,6] => [1,3,2,6,5,8,7,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6,8] => [1,3,2,6,5,7,4,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => [1,3,2,6,5,7,8,4] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,5,2,6,7,8,4] => [1,5,3,8,2,6,7,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,5,2,6,7,4,8] => [1,5,3,7,2,6,4,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,5,2,6,4,7,8] => [1,5,3,6,2,4,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,5,6,2,7,8,4] => [1,6,3,8,5,2,7,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,5,6,2,7,4,8] => [1,6,3,7,5,2,4,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,5,6,7,2,8,4] => [1,7,3,8,5,6,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,2,4] => [1,4,3,8,5,6,7,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [1,4,3,6,5,2,7,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6,8] => [1,4,3,5,2,7,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,7,4,8,6] => [1,5,3,7,2,8,4,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,7,8,4,6] => [1,5,3,6,2,8,7,4] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6,8] => [1,5,3,6,2,7,4,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,7,2,4,8,6] => [1,4,3,7,5,8,2,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,7,2,8,4,6] => [1,7,3,6,5,8,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,7,8,2,4,6] => [1,4,3,6,5,8,7,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [1,4,3,6,5,7,2,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [1,5,3,6,2,7,8,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [1,4,3,6,5,7,8,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,2,4,6,7,8] => [1,4,3,5,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,2,4,6,7,5,8] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,4,6,8,5,7] => [1,3,2,4,7,6,8,5] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,2,6,4,7,8,5] => [1,3,2,6,8,4,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [1,3,2,6,7,4,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,2,6,7,4,5,8] => [1,3,2,5,7,6,4,8] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => [1,3,2,6,7,4,8,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [1,3,2,5,6,4,7,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,2,7,4,8,5] => [1,6,3,7,8,2,4,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,6,7,2,4,8,5] => [1,4,3,7,8,6,2,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,6,7,2,8,4,5] => [1,7,3,5,8,6,2,4] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,6,7,8,2,4,5] => [1,4,3,5,8,6,7,2] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,6,7,2,4,5,8] => [1,4,3,5,7,6,2,8] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,6,2,4,8,5,7] => [1,4,3,6,7,2,8,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,6,2,8,4,5,7] => [1,6,3,5,7,2,8,4] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,6,2,4,5,7,8] => [1,4,3,5,6,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,3,2,4,7,5,8,6] => [1,3,2,4,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,4,7,8,5,6] => [1,3,2,4,6,8,7,5] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,3,2,4,7,5,6,8] => [1,3,2,4,6,7,5,8] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,3,2,7,4,5,8,6] => [1,3,2,5,7,8,4,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,3,2,7,6,8,4,5] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,3,2,7,8,4,5,6] => [1,3,2,5,6,8,7,4] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [1,3,2,5,6,7,4,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,2,4,5,8,6] => [1,4,3,5,7,8,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,7,2,4,8,5,6] => [1,4,3,7,6,8,2,5] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [1,7,3,5,6,8,2,4] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6,8] => [1,4,3,5,6,7,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,7,8,6] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [1,3,2,4,6,7,8,5] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [1,3,2,5,6,7,8,4] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [1,4,3,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => [3,8,1,4,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,2,8] => [3,7,1,4,5,6,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,5,6,2,8,7] => [3,6,1,4,5,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,8,2,7] => [3,7,1,4,5,6,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,4,5,6,2,7,8] => [3,6,1,4,5,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,5,2,7,8,6] => [3,5,1,4,2,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6,8] => [3,5,1,4,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4,5,8,2,6,7] => [3,6,1,4,5,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,2,6,7,8] => [3,5,1,4,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [3,4,1,2,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,4,2,6,7,5,8] => [3,4,1,2,7,6,5,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [3,4,1,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => [3,4,1,2,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,1,4,2,6,5,7,8] => [3,4,1,2,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,1,4,6,2,7,5,8] => [3,6,1,4,7,2,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,8,7] => [3,5,1,4,6,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,8,5,7] => [3,6,1,4,7,2,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,4,6,8,2,5,7] => [3,5,1,4,7,6,8,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,4,6,2,5,7,8] => [3,5,1,4,6,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => [3,4,1,2,5,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,2,5,7,6,8] => [3,4,1,2,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [3,4,1,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,4,2,7,8,5,6] => [3,4,1,2,6,8,7,5] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,4,2,7,5,6,8] => [3,4,1,2,6,7,5,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,4,7,2,8,5,6] => [3,7,1,4,6,8,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,1,4,7,2,5,6,8] => [3,5,1,4,6,7,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,2,5,6,8,7] => [3,4,1,2,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,2,5,8,6,7] => [3,4,1,2,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => [3,4,1,2,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,4,8,2,5,6,7] => [3,5,1,4,6,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [4,8,3,1,5,6,7,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,5,6,7,2,8] => [4,7,3,1,5,6,2,8] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,4,1,5,6,2,8,7] => [4,6,3,1,5,2,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,4,1,5,6,2,7,8] => [4,6,3,1,5,2,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,4,1,5,2,7,8,6] => [4,5,3,1,2,8,7,6] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,7,8,2,6] => [4,6,3,1,5,8,7,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,4,1,5,2,6,8,7] => [4,5,3,1,2,6,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => [5,8,3,4,1,6,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,5,1,6,7,2,8] => [5,7,3,4,1,6,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,1,6,2,8,7] => [5,6,3,4,1,2,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,1,6,2,7,8] => [5,6,3,4,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,8,2] => [6,8,3,4,5,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,8] => [6,7,3,4,5,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => [7,8,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,1,2] => [2,8,3,4,5,6,7,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,1,2,8] => [2,7,3,4,5,6,1,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [2,6,3,4,5,1,7,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,5,1,2,7,8,6] => [2,5,3,4,1,8,7,6] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6,8] => [5,6,3,4,1,7,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => [2,7,3,4,5,8,1,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,5,7,1,8,2,6] => [7,6,3,4,5,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,5,7,8,1,2,6] => [2,6,3,4,5,8,7,1] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,5,1,8,2,6,7] => [5,6,3,4,1,7,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [2,6,3,4,5,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [2,5,3,4,1,6,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [2,4,3,1,6,5,8,7] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,8,5,7] => [2,4,3,1,7,6,8,5] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,6,5,7,8] => [2,4,3,1,6,5,7,8] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,4,1,6,2,7,8,5] => [4,6,3,1,8,2,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,6,2,7,5,8] => [4,6,3,1,7,2,5,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,4,1,6,7,2,8,5] => [4,7,3,1,8,6,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,4,1,6,7,2,5,8] => [4,5,3,1,7,6,2,8] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,8,5,7] => [4,6,3,1,7,2,8,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,4,6,1,2,7,5,8] => [2,6,3,4,7,1,5,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => [6,7,3,4,8,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,4,6,1,7,8,2,5] => [6,5,3,4,8,1,7,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,1,2,5] => [2,5,3,4,8,6,7,1] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [2,5,3,4,7,6,8,1] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,4,1,2,5,7,8,6] => [2,4,3,1,5,8,7,6] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,4,1,2,7,5,8,6] => [2,4,3,1,7,8,5,6] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => [2,4,3,1,6,8,7,5] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,4,1,7,2,5,8,6] => [4,5,3,1,7,8,2,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,7,2,8,5,6] => [4,7,3,1,6,8,2,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,4,1,7,8,2,5,6] => [4,5,3,1,6,8,7,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [7,5,3,4,6,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [2,5,3,4,6,8,7,1] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1,2,8,5,6,7] => [2,4,3,1,6,7,8,5] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1,8,2,5,6,7] => [4,5,3,1,6,7,8,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => [2,5,3,4,6,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [2,4,3,1,5,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,4] => [2,3,1,8,5,6,7,4] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,5,6,7,4,8] => [2,3,1,7,5,6,4,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,5,6,4,7,8] => [2,3,1,6,5,4,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,7,4,8,6] => [2,3,1,7,5,8,4,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,7,8,4,6] => [2,3,1,6,5,8,7,4] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6,8] => [2,3,1,6,5,7,4,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,5,4,6,7,8] => [2,3,1,5,4,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [3,5,1,6,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,5,2,6,8,4,7] => [3,5,1,7,2,6,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,4,7,8] => [3,5,1,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,5,6,2,7,8,4] => [3,6,1,8,5,2,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,5,6,7,2,8,4] => [3,7,1,8,5,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,2,4] => [3,4,1,8,5,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,5,6,7,2,4,8] => [3,4,1,7,5,6,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,5,6,2,8,4,7] => [3,6,1,7,5,2,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,5,6,8,2,4,7] => [3,4,1,7,5,6,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,8,6] => [3,4,1,5,2,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6,8] => [3,4,1,5,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,7,8,4,6] => [3,5,1,6,2,8,7,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6,8] => [3,5,1,6,2,7,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,7,2,4,8,6] => [3,4,1,7,5,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,7,2,8,4,6] => [3,7,1,6,5,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,7,8,2,4,6] => [3,4,1,6,5,8,7,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6,8] => [3,4,1,6,5,7,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => [3,5,1,6,2,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,5,8,2,4,6,7] => [3,4,1,6,5,7,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,5,2,4,6,7,8] => [3,4,1,5,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,5,1,2,6,7,8,4] => [2,5,3,8,1,6,7,4] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [2,5,3,7,1,6,4,8] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,1,2,6,8,4,7] => [2,5,3,7,1,6,8,4] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,5,1,6,2,7,8,4] => [5,6,3,8,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => [5,6,3,7,1,2,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,5,1,6,7,2,8,4] => [5,7,3,8,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [5,4,3,6,1,2,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,5,1,6,8,2,4,7] => [5,4,3,7,1,6,8,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,5,1,6,2,4,7,8] => [5,4,3,6,1,2,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,5,6,1,2,7,8,4] => [2,6,3,8,5,1,7,4] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => [6,7,3,8,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,5,6,1,7,8,2,4] => [6,4,3,8,5,1,7,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,5,6,1,7,2,4,8] => [6,4,3,7,5,1,2,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,5,6,7,1,2,8,4] => [2,7,3,8,5,6,1,4] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,1,2,4] => [2,4,3,8,5,6,7,1] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,5,6,1,2,4,8,7] => [2,4,3,6,5,1,8,7] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [6,4,3,7,5,1,8,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [2,4,3,7,5,6,8,1] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,5,6,1,2,4,7,8] => [2,4,3,6,5,1,7,8] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,7,8,6] => [2,4,3,5,1,8,7,6] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [2,4,3,5,1,7,6,8] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,7,8,4,6] => [2,5,3,6,1,8,7,4] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6,8] => [2,5,3,6,1,7,4,8] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,7,2,4,8,6] => [5,4,3,7,1,8,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [5,7,3,6,1,8,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,7,8,2,4,6] => [5,4,3,6,1,8,7,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,7,1,2,4,8,6] => [2,4,3,7,5,8,1,6] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,7,1,2,8,4,6] => [2,7,3,6,5,8,1,4] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,7,1,8,2,4,6] => [7,4,3,6,5,8,1,2] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [2,4,3,6,5,8,7,1] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6,8] => [2,4,3,6,5,7,1,8] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,5,1,2,4,8,6,7] => [2,4,3,5,1,7,8,6] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,5,1,8,2,4,6,7] => [5,4,3,6,1,7,8,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,5,8,1,2,4,6,7] => [2,4,3,6,5,7,8,1] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,5,1,2,4,6,7,8] => [2,4,3,5,1,6,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => [2,3,1,4,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,1,2,4,6,8,5,7] => [2,3,1,4,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,2,6,4,7,8,5] => [2,3,1,6,8,4,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => [2,3,1,7,8,6,4,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [3,1,2,6,8,4,5,7] => [2,3,1,5,7,6,8,4] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,1,2,6,4,5,7,8] => [2,3,1,5,6,4,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,1,6,2,4,7,5,8] => [3,4,1,6,7,2,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [3,6,1,7,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => [3,4,1,5,7,6,2,8] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [3,4,1,5,6,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [3,1,6,2,4,8,5,7] => [3,4,1,6,7,2,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => [3,4,1,5,7,6,8,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,6,2,4,5,7,8] => [3,4,1,5,6,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,6,1,2,4,7,8,5] => [2,4,3,6,8,1,7,5] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [2,4,3,6,7,1,5,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,6,1,2,7,4,8,5] => [2,6,3,7,8,1,4,5] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [3,6,1,2,7,8,4,5] => [2,6,3,5,8,1,7,4] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => [6,4,3,7,8,1,2,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [6,7,3,5,8,1,2,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => [6,4,3,5,8,1,7,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,6,7,1,2,4,8,5] => [2,4,3,7,8,6,1,5] => [[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [3,6,7,1,2,8,4,5] => [2,7,3,5,8,6,1,4] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [2,4,3,5,8,6,7,1] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,8,7] => [2,4,3,5,6,1,8,7] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => [2,3,1,4,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,4,7,5,8,6] => [2,3,1,4,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => [2,3,1,4,6,7,5,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,7,4,5,8,6] => [2,3,1,5,7,8,4,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [3,1,2,7,4,8,5,6] => [2,3,1,7,6,8,4,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,2,7,4,5,6,8] => [2,3,1,5,6,7,4,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,7,2,4,5,8,6] => [3,4,1,5,7,8,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [3,1,7,2,4,8,5,6] => [3,4,1,7,6,8,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [3,1,7,2,8,4,5,6] => [3,7,1,5,6,8,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => [3,4,1,5,6,8,7,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6,8] => [3,4,1,5,6,7,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,7,1,2,4,5,8,6] => [2,4,3,5,7,8,1,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [2,4,3,5,6,8,7,1] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6,8] => [2,4,3,5,6,7,1,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => [2,3,1,4,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [2,3,1,4,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,2,8,4,5,6,7] => [2,3,1,5,6,7,8,4] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [3,4,1,5,6,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [2,4,3,5,6,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,6,8,3,7] => [1,2,7,4,5,6,8,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,5,3,7,8,6] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,7,3,8,6] => [1,2,7,4,5,8,3,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,4,5,3,6,8,7] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,4,5,3,8,6,7] => [1,2,5,4,3,7,8,6] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,4,5,8,3,6,7] => [1,2,6,4,5,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,6,7,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,8,5,7] => [1,2,4,3,7,6,8,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,6,3,7,8,5] => [1,2,6,4,8,3,7,5] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,6,3,7,5,8] => [1,2,6,4,7,3,5,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,6,7,3,8,5] => [1,2,7,4,8,6,3,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,8,5,7] => [1,2,6,4,7,3,8,5] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,8,3,5,7] => [1,2,5,4,7,6,8,3] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,3,7,5,8,6] => [1,2,4,3,7,8,5,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,4,3,7,5,6,8] => [1,2,4,3,6,7,5,8] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,7,3,5,8,6] => [1,2,5,4,7,8,3,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,4,7,8,3,5,6] => [1,2,5,4,6,8,7,3] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [1,2,5,4,6,7,3,8] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => [1,2,4,3,5,7,8,6] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [1,2,4,3,6,7,8,5] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [1,2,5,4,6,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [1,4,8,2,5,6,7,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,4,2,5,6,7,3,8] => [1,4,7,2,5,6,3,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,4,2,5,6,8,3,7] => [1,4,7,2,5,6,8,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,4,2,5,6,3,7,8] => [1,4,6,2,5,3,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [1,4,5,2,3,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => [1,4,7,2,5,8,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,4,5,2,3,7,8,6] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => [1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [1,5,8,4,2,6,7,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,5,2,6,7,3,8] => [1,5,7,4,2,6,3,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,5,2,6,8,3,7] => [1,5,7,4,2,6,8,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,5,6,4,2,3,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,4,5,6,2,7,8,3] => [1,6,8,4,5,2,7,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,4,5,6,2,7,3,8] => [1,6,7,4,5,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,2,8,3] => [1,7,8,4,5,6,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,2,3] => [1,3,8,4,5,6,7,2] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,2,3,8] => [1,3,7,4,5,6,2,8] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,4,5,6,2,3,8,7] => [1,3,6,4,5,2,8,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,4,5,6,2,8,3,7] => [1,6,7,4,5,2,8,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,6,8,2,3,7] => [1,3,7,4,5,6,8,2] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6,8] => [1,3,5,4,2,7,6,8] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => [1,5,7,4,2,8,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,4,5,2,7,8,3,6] => [1,5,6,4,2,8,7,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [1,3,7,4,5,8,2,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,5,2,3,8,6,7] => [1,3,5,4,2,7,8,6] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,4,5,8,2,3,6,7] => [1,3,6,4,5,7,8,2] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,6,7,8,5] => [1,3,4,2,8,6,7,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => [1,3,4,2,6,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,8,5,7] => [1,3,4,2,7,6,8,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,6,3,7,8,5] => [1,4,6,2,8,3,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => [1,4,6,2,7,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,6,7,3,8,5] => [1,4,7,2,8,6,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => [1,4,5,2,8,6,7,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,8,7] => [1,4,5,2,6,3,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,4,6,2,7,3,8,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => [1,4,5,2,6,3,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,4,6,2,3,7,8,5] => [1,3,6,4,8,2,7,5] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,4,6,2,3,7,5,8] => [1,3,6,4,7,2,5,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => [1,6,7,4,8,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,6,2,7,8,3,5] => [1,6,5,4,8,2,7,3] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,7,3,5,8] => [1,6,5,4,7,2,3,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,4,6,7,2,3,8,5] => [1,3,7,4,8,6,2,5] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => [1,7,5,4,8,6,2,3] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [1,3,5,4,7,6,2,8] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,8,5,7] => [1,3,6,4,7,2,8,5] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [1,3,5,4,7,6,8,2] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => [1,3,4,2,5,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,4,2,3,7,5,8,6] => [1,3,4,2,7,8,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,3,7,8,5,6] => [1,3,4,2,6,8,7,5] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => [1,3,4,2,6,7,5,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,4,2,7,3,5,8,6] => [1,4,5,2,7,8,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => [1,4,7,2,6,8,3,5] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => [1,4,5,2,6,8,7,3] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => [1,4,5,2,6,7,3,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,4,7,2,3,5,8,6] => [1,3,5,4,7,8,2,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,7,2,3,8,5,6] => [1,3,7,4,6,8,2,5] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,4,2,3,5,6,8,7] => [1,3,4,2,5,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,3,4,2,5,7,8,6] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [1,3,4,2,6,7,8,5] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [1,4,5,2,6,7,8,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => [1,3,4,2,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => [2,4,8,1,5,6,7,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [2,4,6,1,5,3,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,5,6,8,3,7] => [2,4,7,1,5,6,8,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3,7,8] => [2,4,6,1,5,3,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,5,3,7,8,6] => [2,4,5,1,3,8,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,8] => [2,4,5,1,3,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,5,7,8,3,6] => [2,4,6,1,5,8,7,3] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6,8] => [2,4,6,1,5,7,3,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,5,3,8,6,7] => [2,4,5,1,3,7,8,6] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,5,3,6,7,8] => [2,4,5,1,3,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [4,5,8,1,2,6,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,5,2,6,7,3,8] => [4,5,7,1,2,6,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [4,5,6,1,2,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => [4,5,7,1,2,6,8,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,1,5,2,6,3,7,8] => [4,5,6,1,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,1,5,6,2,7,3,8] => [4,6,7,1,5,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,5,6,7,2,8,3] => [4,7,8,1,5,6,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,2,3] => [4,3,8,1,5,6,7,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,5,6,2,3,8,7] => [4,3,6,1,5,2,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,5,6,8,2,3,7] => [4,3,7,1,5,6,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,1,5,6,2,3,7,8] => [4,3,6,1,5,2,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [4,3,5,1,2,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6,8] => [4,3,5,1,2,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [4,5,7,1,2,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [4,5,6,1,2,8,7,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6,8] => [4,5,6,1,2,7,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,5,7,2,3,8,6] => [4,3,7,1,5,8,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,5,7,2,8,3,6] => [4,7,6,1,5,8,2,3] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,1,5,7,8,2,3,6] => [4,3,6,1,5,8,7,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6,8] => [4,3,6,1,5,7,2,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,1,5,2,8,3,6,7] => [4,5,6,1,2,7,8,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,1,5,8,2,3,6,7] => [4,3,6,1,5,7,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,5,2,3,6,7,8] => [4,3,5,1,2,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [2,5,7,4,1,6,3,8] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [2,5,6,4,1,3,8,7] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,5,1,2,6,8,3,7] => [2,5,7,4,1,6,8,3] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,5,1,6,2,7,8,3] => [5,6,8,4,1,2,7,3] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => [5,6,7,4,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,5,1,6,7,2,8,3] => [5,7,8,4,1,6,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [4,5,1,6,7,2,3,8] => [5,3,7,4,1,6,2,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [4,5,1,6,2,3,8,7] => [5,3,6,4,1,2,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [4,5,1,6,2,8,3,7] => [5,6,7,4,1,2,8,3] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,1,6,2,3,7,8] => [5,3,6,4,1,2,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,1,2,7,8,3] => [2,6,8,4,5,1,7,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,1,2,7,3,8] => [2,6,7,4,5,1,3,8] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,1,7,2,8,3] => [6,7,8,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,6,1,7,8,2,3] => [6,3,8,4,5,1,7,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => [7,3,8,4,5,6,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => [2,3,8,4,5,6,7,1] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [2,3,6,4,5,1,8,7] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,6,1,2,8,3,7] => [2,6,7,4,5,1,8,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [6,3,7,4,5,1,8,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [2,3,7,4,5,6,8,1] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [2,3,6,4,5,1,7,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,7,8,6] => [2,3,5,4,1,8,7,6] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,5,1,2,7,3,8,6] => [2,5,7,4,1,8,3,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6,8] => [2,5,6,4,1,7,3,8] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [4,5,1,7,8,2,3,6] => [5,3,6,4,1,8,7,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6,8] => [5,3,6,4,1,7,2,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [2,7,6,4,5,8,1,3] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [4,5,7,1,8,2,3,6] => [7,3,6,4,5,8,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [2,3,6,4,5,8,7,1] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,5,1,2,3,6,8,7] => [2,3,5,4,1,6,8,7] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,5,1,2,8,3,6,7] => [2,5,6,4,1,7,8,3] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [2,3,6,4,5,7,8,1] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [2,3,5,4,1,6,7,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [2,3,4,1,8,6,7,5] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,6,7,5,8] => [2,3,4,1,7,6,5,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [2,3,4,1,6,5,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,8,5,7] => [2,3,4,1,7,6,8,5] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [2,3,4,1,6,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,6,3,7,8,5] => [2,4,6,1,8,3,7,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,6,7,3,5,8] => [2,4,5,1,7,6,3,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,8,7] => [2,4,5,1,6,3,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => [2,4,6,1,7,3,8,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,6,3,5,7,8] => [2,4,5,1,6,3,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [4,3,6,1,8,2,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,6,2,3,7,5,8] => [4,3,6,1,7,2,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [4,6,7,1,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,6,2,7,3,5,8] => [4,6,5,1,7,2,3,8] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,6,7,8,2,3,5] => [4,3,5,1,8,6,7,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,8,7] => [4,3,5,1,6,2,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,8,5,7] => [4,3,6,1,7,2,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,8,2,3,5,7] => [4,3,5,1,7,6,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,6,2,3,5,7,8] => [4,3,5,1,6,2,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [2,3,6,4,7,1,5,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,6,1,2,7,3,8,5] => [2,6,7,4,8,1,3,5] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,6,1,2,7,8,3,5] => [2,6,5,4,8,1,7,3] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [4,6,1,2,7,3,5,8] => [2,6,5,4,7,1,3,8] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [4,6,1,7,2,3,8,5] => [6,3,7,4,8,1,2,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [4,6,1,7,2,8,3,5] => [6,7,5,4,8,1,2,3] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [4,6,1,7,8,2,3,5] => [6,3,5,4,8,1,7,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => [6,3,5,4,7,1,2,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [7,3,5,4,8,6,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [2,3,5,4,8,6,7,1] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,8,3,5,7] => [2,6,5,4,7,1,8,3] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => [6,3,5,4,7,1,8,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [2,3,5,4,7,6,8,1] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [2,3,4,1,5,8,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [2,3,4,1,5,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => [2,3,4,1,7,8,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,3,7,8,5,6] => [2,3,4,1,6,8,7,5] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [2,3,4,1,6,7,5,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,7,3,5,8,6] => [2,4,5,1,7,8,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [4,1,2,7,3,8,5,6] => [2,4,7,1,6,8,3,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => [2,4,5,1,6,8,7,3] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,7,2,3,5,8,6] => [4,3,5,1,7,8,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [4,1,7,2,3,8,5,6] => [4,3,7,1,6,8,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [4,1,7,2,8,3,5,6] => [4,7,5,1,6,8,2,3] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,1,7,8,2,3,5,6] => [4,3,5,1,6,8,7,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => [7,3,5,4,6,8,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6,8] => [2,3,5,4,6,7,1,8] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [2,3,4,1,5,6,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [2,3,4,1,5,7,8,6] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [2,3,4,1,6,7,8,5] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,8,3,5,6,7] => [2,4,5,1,6,7,8,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [4,3,5,1,6,7,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [2,3,5,4,6,7,8,1] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [2,3,4,1,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,8,4,7] => [1,2,3,7,5,6,8,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,2,3,5,7,4,8,6] => [1,2,3,7,5,8,4,6] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,3,5,7,8,4,6] => [1,2,3,6,5,8,7,4] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6,8] => [1,2,3,6,5,7,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,7,8,6] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,5,8,4,6,7] => [1,2,3,6,5,7,8,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [1,2,5,8,3,6,7,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,2,5,3,6,7,4,8] => [1,2,5,7,3,6,4,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,5,3,6,4,8,7] => [1,2,5,6,3,4,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,2,5,3,6,8,4,7] => [1,2,5,7,3,6,8,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => [1,2,5,6,3,4,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [1,2,6,8,5,3,7,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,8] => [1,2,6,7,5,3,4,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [1,2,7,8,5,6,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,6,7,8,3,4] => [1,2,4,8,5,6,7,3] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,5,6,3,8,4,7] => [1,2,6,7,5,3,8,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,2,5,6,8,3,4,7] => [1,2,4,7,5,6,8,3] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,2,4,6,5,3,7,8] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,7,8,6] => [1,2,4,5,3,8,7,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6,8] => [1,2,4,5,3,7,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,2,5,3,7,4,8,6] => [1,2,5,7,3,8,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,2,5,3,7,8,4,6] => [1,2,5,6,3,8,7,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6,8] => [1,2,5,6,3,7,4,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,2,5,7,3,8,4,6] => [1,2,7,6,5,8,3,4] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,2,5,7,8,3,4,6] => [1,2,4,6,5,8,7,3] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [1,2,4,6,5,7,3,8] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4,8,6,7] => [1,2,4,5,3,7,8,6] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [1,2,5,6,3,7,8,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,5,3,4,6,7,8] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,5,2,3,6,7,8,4] => [1,3,5,8,2,6,7,4] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,5,2,3,6,7,4,8] => [1,3,5,7,2,6,4,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,5,2,3,6,4,8,7] => [1,3,5,6,2,4,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,2,3,6,4,7,8] => [1,3,5,6,2,4,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => [1,5,6,8,2,3,7,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [1,5,6,7,2,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,5,2,6,7,3,8,4] => [1,5,7,8,2,6,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,7,8,3,4] => [1,5,4,8,2,6,7,3] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,2,6,7,3,4,8] => [1,5,4,7,2,6,3,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => [1,5,6,7,2,3,8,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,2,6,8,3,4,7] => [1,5,4,7,2,6,8,3] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => [1,5,4,6,2,3,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,5,6,2,3,7,8,4] => [1,3,6,8,5,2,7,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,5,6,2,3,7,4,8] => [1,3,6,7,5,2,4,8] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,5,6,2,7,3,8,4] => [1,6,7,8,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,5,6,2,7,8,3,4] => [1,6,4,8,5,2,7,3] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,5,6,2,7,3,4,8] => [1,6,4,7,5,2,3,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,5,6,7,2,3,8,4] => [1,3,7,8,5,6,2,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,6,7,2,8,3,4] => [1,7,4,8,5,6,2,3] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => [1,3,4,8,5,6,7,2] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => [1,3,6,7,5,2,8,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => [1,3,4,5,2,8,7,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [1,3,4,5,2,7,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,7,4,8,6] => [1,3,5,7,2,8,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6,8] => [1,3,5,6,2,7,4,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,5,2,7,3,4,8,6] => [1,5,4,7,2,8,3,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,5,7,6,2,8,3,4] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => [1,5,4,6,2,7,3,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,5,7,2,3,4,8,6] => [1,3,4,7,5,8,2,6] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,2,3,8,4,6] => [1,3,7,6,5,8,2,4] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [1,7,4,6,5,8,2,3] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6,8] => [1,3,4,6,5,7,2,8] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,3,4,5,2,7,8,6] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [1,5,4,6,2,7,8,3] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [1,3,4,6,5,7,8,2] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => [1,3,4,5,2,6,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [2,3,5,8,1,6,7,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,6,4,7,8] => [2,3,5,6,1,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,2,6,3,7,8,4] => [2,5,6,8,1,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,7,3,8,4] => [2,5,7,8,1,6,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,3,4,8,7] => [2,5,4,6,1,3,8,7] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,1,2,6,3,8,4,7] => [2,5,6,7,1,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,2,6,3,4,7,8] => [2,5,4,6,1,3,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [5,3,6,8,1,2,7,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,1,6,2,3,7,4,8] => [5,3,6,7,1,2,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [5,1,6,2,7,8,3,4] => [5,6,4,8,1,2,7,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,1,6,2,7,3,4,8] => [5,6,4,7,1,2,3,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,6,7,2,3,8,4] => [5,3,7,8,1,6,2,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [5,1,6,7,2,8,3,4] => [5,7,4,8,1,6,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,2,3,4] => [5,3,4,8,1,6,7,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => [5,3,6,7,1,2,8,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,1,6,2,8,3,4,7] => [5,6,4,7,1,2,8,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => [2,3,6,8,5,1,7,4] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => [2,6,7,8,5,1,3,4] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => [2,6,4,8,5,1,7,3] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => [6,3,7,8,5,1,2,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [5,6,1,7,2,8,3,4] => [6,7,4,8,5,1,2,3] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,6,1,7,8,2,3,4] => [6,3,4,8,5,1,7,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => [2,3,7,8,5,6,1,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [5,6,7,1,2,8,3,4] => [2,7,4,8,5,6,1,3] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [7,3,4,8,5,6,1,2] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [2,3,4,8,5,6,7,1] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => [2,3,4,7,5,6,1,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => [2,3,6,7,5,1,8,4] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [2,3,4,7,5,6,8,1] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,1,2,3,4,7,8] => [2,3,4,6,5,1,7,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [2,3,4,5,1,8,7,6] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6,8] => [2,3,4,5,1,7,6,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6,8] => [2,3,5,6,1,7,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => [2,5,4,7,1,8,3,6] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6,8] => [2,5,4,6,1,7,3,8] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => [5,7,4,6,1,8,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,7,1,2,3,4,8,6] => [2,3,4,7,5,8,1,6] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [5,7,1,2,3,8,4,6] => [2,3,7,6,5,8,1,4] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => [2,7,4,6,5,8,1,3] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [2,3,4,6,5,8,7,1] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6,8] => [2,3,4,6,5,7,1,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [2,3,4,5,1,6,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => [2,3,4,5,1,7,8,6] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,8,4,6,7] => [2,3,5,6,1,7,8,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => [2,5,4,6,1,7,8,3] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [2,3,4,6,5,7,8,1] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [2,3,4,5,1,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,6,8,5,7] => [1,2,3,4,7,6,8,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [1,2,3,6,8,4,7,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => [1,2,3,6,7,4,5,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => [1,2,3,7,8,6,4,5] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,2,3,6,7,8,4,5] => [1,2,3,5,8,6,7,4] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,6,7,4,5,8] => [1,2,3,5,7,6,4,8] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,6,4,5,8,7] => [1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => [1,2,3,6,7,4,8,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,6,8,4,5,7] => [1,2,3,5,7,6,8,4] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [1,2,4,6,8,3,7,5] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,2,6,3,7,4,8,5] => [1,2,6,7,8,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,2,6,3,7,8,4,5] => [1,2,6,5,8,3,7,4] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,2,6,7,3,4,8,5] => [1,2,4,7,8,6,3,5] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,7,8,3,4,5] => [1,2,4,5,8,6,7,3] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,8,7] => [1,2,4,5,6,3,8,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [1,2,6,5,7,3,8,4] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,3,4,5,7,8] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [1,3,4,6,7,2,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,6,2,3,7,4,8,5] => [1,3,6,7,8,2,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,2,3,7,4,5,8] => [1,3,6,5,7,2,4,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,6,2,7,3,4,8,5] => [1,6,4,7,8,2,3,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => [1,6,7,5,8,2,3,4] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => [1,6,4,5,7,2,3,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,7,2,3,8,4,5] => [1,3,7,5,8,6,2,4] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,3,4,5,8,6,7,2] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => [1,3,4,5,7,6,2,8] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,8,7] => [1,3,4,5,6,2,8,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [1,3,4,6,7,2,8,5] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => [1,6,4,5,7,2,8,3] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [1,3,4,5,7,6,8,2] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => [1,3,4,5,6,2,7,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [2,3,4,6,8,1,7,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => [2,3,4,6,7,1,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,3,7,4,8,5] => [2,3,6,7,8,1,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,1,2,7,3,8,4,5] => [2,6,7,5,8,1,3,4] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [6,1,2,7,3,4,5,8] => [2,6,4,5,7,1,3,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,1,7,2,8,3,4,5] => [6,7,4,5,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => [6,3,4,5,8,1,7,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [6,1,7,2,3,4,5,8] => [6,3,4,5,7,1,2,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => [2,3,4,7,8,6,1,5] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,7,1,2,3,8,4,5] => [2,3,7,5,8,6,1,4] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,1,8,2,3,4,5] => [7,3,4,5,8,6,1,2] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [2,3,4,5,8,6,7,1] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => [2,3,4,5,7,6,1,8] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [2,3,4,5,6,1,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => [2,6,4,5,7,1,8,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [6,3,4,5,7,1,8,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [2,3,4,5,7,6,8,1] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [2,3,4,5,6,1,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [1,2,3,4,6,8,7,5] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => [1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [1,2,3,5,7,8,4,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [1,2,3,7,6,8,4,5] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,3,7,8,4,5,6] => [1,2,3,5,6,8,7,4] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [1,2,4,5,7,8,3,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,2,7,3,4,8,5,6] => [1,2,4,7,6,8,3,5] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [1,2,7,5,6,8,3,4] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,2,4,5,6,8,7,3] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6,8] => [1,2,4,5,6,7,3,8] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [1,3,4,5,7,8,2,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [1,3,4,7,6,8,2,5] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => [1,3,7,5,6,8,2,4] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => [1,7,4,5,6,8,2,3] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [1,3,4,5,6,8,7,2] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => [1,3,4,5,6,7,2,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [2,3,4,5,7,8,1,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [2,3,4,7,6,8,1,5] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,1,2,3,8,4,5,6] => [2,3,7,5,6,8,1,4] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => [2,7,4,5,6,8,1,3] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [7,3,4,5,6,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [2,3,4,5,6,8,7,1] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [2,3,4,5,6,7,1,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [1,3,4,5,6,7,8,2] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[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] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [2,3,4,5,6,8,9,1,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [3,2,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [2,3,4,5,6,7,9,10,1,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => [1,3,4,5,6,8,9,2,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [2,3,4,5,6,7,1,9,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => [2,1,4,5,6,7,8,9,3] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7,9] => [3,2,4,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => [3,2,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,11,9] => [2,3,4,5,6,7,8,10,11,1,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => [2,3,4,5,6,7,8,1,10,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => [2,1,4,5,6,7,8,9,10,3] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,11,1,3,4,5,6,7,8,9,10] => [3,2,4,5,6,7,8,9,10,11,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,11,10] => [2,3,4,5,6,7,8,9,1,11,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7,9] => [2,1,4,5,6,7,8,3,9] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,9,10,1,3,4,5,6,7,8] => [3,2,4,5,6,7,8,10,9,1] => [[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7] => [1,2,3,4,5,8,9,6,7] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,9,8] => [2,3,1,4,5,6,7,9,8] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,9,7,8] => [2,1,3,4,5,6,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,3,4,8,5,9,6] => [2,3,4,7,8,9,1,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,9,2,4,5,6,7,8] => [1,4,3,5,6,7,8,9,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,6,9,7,10,8] => [1,2,3,4,5,6,9,10,7,8] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,8,9,6] => [2,3,4,5,7,9,1,8,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,7,10,8,9] => [2,1,3,4,5,6,7,9,10,8] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7,9] => [2,3,4,5,6,1,8,7,9] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,9,1,4,5,6,7,8] => [4,2,3,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1,2,3,4,5,9,6,10,7] => [2,3,4,5,8,9,10,1,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,8,9,7] => [2,3,4,5,6,1,9,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,1,9,4,5,6,7,8] => [3,2,1,5,6,7,8,9,4] => [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[] => [] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,1,2] => [2,9,3,4,5,6,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,1,2,9] => [2,8,3,4,5,6,7,1,9] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,1,2,4,5,6,9,7,8] => [2,3,1,4,5,6,8,9,7] => [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => [2,3,1,5,6,7,8,9,4] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,9,2,4,5,6,7,8] => [3,4,1,5,6,7,8,9,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,9,1,2,4,5,6,7,8] => [2,4,3,5,6,7,8,9,1] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,9,2,3] => [1,3,9,4,5,6,7,8,2] => [.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,1,2,3] => [2,3,9,4,5,6,7,8,1] => [[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [2,3,6,4,5,1,7,8,9] => [[.,[.,[[.,.],[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8,9] => [2,3,5,4,1,6,7,8,9] => [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => [2,3,4,1,6,7,8,9,5] => [[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8,9] => [1,3,4,5,2,6,7,8,9] => [.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [2,3,4,9,5,6,7,8,1] => [[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [2,3,4,8,5,6,7,1,9] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,.]]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,6,1,2,3,4,7,8,9] => [2,3,4,6,5,1,7,8,9] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5,1,2,3,4,9,6,7,8] => [2,3,4,5,1,7,8,9,6] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [5,9,1,2,3,4,6,7,8] => [2,3,4,6,5,7,8,9,1] => [[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,6,3,4,5,7,8,9] => [1,2,4,5,6,3,7,8,9] => [.,[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [2,3,4,5,9,6,7,8,1] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [6,7,9,1,2,3,4,5,8] => [2,3,4,5,8,6,7,9,1] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7,9] => [2,3,4,5,7,6,8,1,9] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,9,7,8] => [2,3,4,5,6,1,8,9,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [6,9,1,2,3,4,5,7,8] => [2,3,4,5,7,6,8,9,1] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [2,3,4,5,6,1,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,7,9,2,3,4,5,6,8] => [1,3,4,5,6,8,7,9,2] => [.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8,9] => [1,3,4,5,6,7,2,8,9] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6,9] => [7,3,4,5,6,8,1,2,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => [2,3,4,5,6,9,7,8,1] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6,9] => [2,3,4,5,6,8,7,1,9] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,9,6,8] => [2,3,4,5,7,8,1,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [7,9,1,2,3,4,5,6,8] => [2,3,4,5,6,8,7,9,1] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9] => [2,3,4,5,6,7,1,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,8,9,6,7] => [1,2,3,4,5,7,9,8,6] => [.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,5,8,6,7,9] => [1,2,3,4,5,7,8,6,9] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [1,2,3,4,8,9,5,6,7] => [1,2,3,4,6,7,9,8,5] => [.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7,9] => [1,2,3,5,6,7,8,4,9] => [.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,8,2,9,3,4,5,6,7] => [1,8,4,5,6,7,9,2,3] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => [1,3,4,5,6,7,9,8,2] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7,9] => [1,3,4,5,6,7,8,2,9] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [8,1,2,3,9,4,5,6,7] => [2,3,8,5,6,7,9,1,4] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [2,3,4,5,6,7,9,8,1] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => [2,3,4,5,6,7,8,1,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,8,9,7] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,9,6,7,8] => [1,2,3,4,5,7,8,9,6] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [1,2,3,4,6,7,8,9,5] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [1,2,3,5,6,7,8,9,4] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => [1,2,4,5,6,7,8,9,3] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [1,3,4,5,6,7,8,9,2] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,9,1] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => [8,2,3,4,5,6,7,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,1,7] => [7,2,3,4,5,6,9,8,1] => [[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,7,8,9,1,6] => [6,2,3,4,5,9,7,8,1] => [[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,9,1,5] => [5,2,3,4,9,6,7,8,1] => [[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,1,4] => [4,2,3,9,5,6,7,8,1] => [[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,1,3] => [3,2,9,4,5,6,7,8,1] => [[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,10,1,9] => [9,2,3,4,5,6,7,8,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,6,1,9,7,8] => [6,2,3,4,5,1,8,9,7] => [[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,7,9,10,1,8] => [8,2,3,4,5,6,7,10,9,1] => [[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,5,1,8,9,6,7] => [5,2,3,4,1,7,9,8,6] => [[[.,.],[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,10,1,7] => [7,2,3,4,5,6,10,8,9,1] => [[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,1,7,8,9,5,6] => [4,2,3,1,6,9,7,8,5] => [[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,7,8,9,10,1,6] => [6,2,3,4,5,10,7,8,9,1] => [[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,9,4,5] => [3,2,1,5,9,6,7,8,4] => [[[.,.],.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,9,10,1,5] => [5,2,3,4,10,6,7,8,9,1] => [[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,9,3,4] => [2,1,4,9,5,6,7,8,3] => [[.,.],[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,10,1,4] => [4,2,3,10,5,6,7,8,9,1] => [[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,10,1,3] => [3,2,10,4,5,6,7,8,9,1] => [[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,1,2] => [2,10,3,4,5,6,7,8,9,1] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,9,11,1,10] => [10,2,3,4,5,6,7,8,9,11,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,10,1,6,7,8,9] => [6,2,3,4,5,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,5,6,1,2,3,9,10,7,8] => [2,3,6,4,5,1,8,10,9,7] => [[.,[.,[[.,.],[.,.]]]],[[.,[[.,.],.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8] => [7,2,3,4,5,6,1,9,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8] => [3,2,1,5,4,7,6,9,8] => [[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,4,5,6,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,2] => [1,9,3,4,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,8,7] => [.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,1,5,4,7,6,9,8,10] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,3,4,5,6,7,8,9,2] => [.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,9,8] => [.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3] => [.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4] => [.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5] => [.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,6,5,8,7,10,9] => [.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6] => [.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7] => [.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[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] => [3,1,4,5,6,7,8,9,2] => [3,9,1,4,5,6,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,6,1,7,8,9,2] => [6,9,3,4,5,1,7,8,2] => [[[.,[.,.]],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,1,8,9,2] => [7,9,3,4,5,6,1,8,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,1,9,2] => [8,9,3,4,5,6,7,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [3,10,1,4,5,6,7,8,9,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,8,1,9,10,2] => [8,10,3,4,5,6,7,1,9,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,1,10,2] => [9,10,3,4,5,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,7,9,2,8] => [1,8,3,4,5,6,7,9,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => [2,3,4,5,6,7,8,9,1,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,10,2] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [2,3,4,5,6,7,8,9,10,1,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [2,3,4,5,6,7,9,8,1,10] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [1,3,4,5,6,7,8,10,9,2] => [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [1,3,4,5,6,7,8,9,10,11,2] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,8,2,9] => [3,8,1,4,5,6,7,2,9] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,9,10,8] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [1,2,3,4,5,6,7,8,10,11,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,4,7,5,8,9,6] => [1,2,3,4,7,9,5,8,6] => [.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,3,6,4,7,8,9,5] => [1,2,3,6,9,4,7,8,5] => [.,[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,9,4] => [1,2,5,9,3,6,7,8,4] => [.,[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,9,3] => [1,4,9,2,5,6,7,8,3] => [.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [2,3,4,5,6,7,8,1,9,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => [3,2,4,5,6,10,7,8,9,1] => [[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,1,6,2,7,8,9] => [5,6,3,4,1,2,7,8,9] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,1,4,8,9,2,5,6,7] => [3,5,1,4,6,7,9,8,2] => [[.,[.,.]],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [2,3,4,10,5,6,7,8,9,1] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,7,6,8,9] => [2,3,4,5,1,7,6,8,9] => [[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [1,2,3,6,5,7,8,9,4] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,5,7,9,6,8] => [1,2,3,4,5,8,7,9,6] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [1,2,3,4,5,6,8,9,10,7] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,4,6,9,5,7,8] => [1,2,3,4,7,6,8,9,5] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [1,2,3,4,5,7,8,9,10,6] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [1,2,3,4,6,7,8,9,10,5] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [1,2,5,4,6,7,8,9,3] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [1,2,3,5,6,7,8,9,10,4] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [1,2,4,5,6,7,8,9,10,3] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,4,7,5,8,6,9] => [1,2,3,4,7,8,5,6,9] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [2,3,1,5,4,7,6,9,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,9,8] => [3,4,1,5,2,7,6,9,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7,9] => [3,5,1,6,2,4,8,7,9] => [[.,[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,9] => [3,4,1,2,6,5,8,7,9] => [[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8,10] => [2,3,1,5,4,7,6,9,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,9,6,10,8] => [3,5,1,7,2,9,4,10,6,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,8,6,10,9] => [3,5,1,7,2,8,4,6,10,9] => [[.,[.,.]],[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7,10,9] => [3,5,1,6,2,4,8,7,10,9] => [[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [3,4,1,2,6,5,8,7,10,9] => [[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [2,4,3,1,5,6,7,8,9,10] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [2,3,10,4,5,6,7,8,9,1] => [[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8,10] => [1,3,4,5,6,7,8,9,2,10] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,8,4,5,6,7,9,10] => [1,2,3,5,6,7,8,4,9,10] => [.,[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [3,2,5,4,7,6,9,8,10,1] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [6,7,8,9,10,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,4,6,8,10,12,1,3,5,7,9,11] => [3,2,5,4,7,6,9,8,11,10,12,1] => [[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => [7,8,9,10,11,12,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,[.,.]]]]]]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [2,3,1,4,5,6,7,8,9,10,11] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,10,7,9] => [2,3,4,5,6,8,9,1,10,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,10,2,4,5,6,7,8,9] => [3,4,1,5,6,7,8,9,10,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,11,2] => [3,11,1,4,5,6,7,8,9,10,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [2,3,4,5,10,6,7,8,9,1] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => [9,3,4,5,6,7,8,10,1,2] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [3,7,8,9,10,1,2,4,5,6] => [2,4,3,5,6,10,7,8,9,1] => [[.,[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,10,1,4,5,6,7,8,9] => [4,2,3,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,2,3,4,7,8,9,5] => [2,3,4,6,9,1,7,8,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,4,5,8,6,7,9,10] => [1,2,3,4,5,7,8,6,9,10] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [5,10,1,2,3,4,6,7,8,9] => [2,3,4,6,5,7,8,9,10,1] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,10,9,1] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,11,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,8,1,9,7] => [8,2,3,4,5,6,9,1,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,7,9,1,10,8] => [9,2,3,4,5,6,7,10,1,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [2,3,4,5,6,10,7,8,9,1] => [[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [2,3,4,5,6,7,10,8,9,1] => [[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,10,1,11,2] => [10,11,3,4,5,6,7,8,9,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,9] => [2,3,4,1,6,5,8,7,9] => [[.,[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,1,9,3] => [8,2,9,4,5,6,7,1,3] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [2,3,4,8,5,6,7,1,9,10] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [2,3,6,4,5,1,7,8,9,10] => [[.,[.,[[.,.],[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,5,6,9,7,8,10] => [1,2,3,4,5,6,8,9,7,10] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8,9,10] => [1,3,4,2,5,6,7,8,9,10] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => [2,3,1,5,6,7,8,9,10,4] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => [2,3,4,5,1,7,8,9,10,6] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,7,8,9,10,1,2,3,4,6] => [2,3,4,6,5,10,7,8,9,1] => [[.,[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,7,8,9,10,1,2,3,5,6] => [2,3,5,4,6,10,7,8,9,1] => [[.,[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,10,1,11,9] => [10,2,3,4,5,6,7,8,11,1,9] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,7,8,10,1,2,3,4,9] => [2,3,4,9,5,6,7,8,10,1] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,9,1,10,3] => [9,2,10,4,5,6,7,8,1,3] => [[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,9,8] => [1,4,5,2,3,7,6,9,8] => [.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,9] => [1,3,4,2,6,5,8,7,9] => [.,[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,10,9] => [1,3,4,2,6,5,8,7,10,9] => [.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => [3,2,4,1,6,5,8,7,9] => [[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [2,1,7,8,9,10,3,4,5,6] => [2,1,4,5,6,10,7,8,9,3] => [[.,.],[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [3,4,1,2,8,9,10,5,6,7] => [2,4,3,1,6,7,10,8,9,5] => [[.,[[.,.],.]],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,6,7,8,1,2,3,4,10,9] => [2,3,4,8,5,6,7,1,10,9] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,7,1,8,2,9,3] => [7,8,9,4,5,6,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,9,10,7] => [2,3,4,5,6,8,10,1,9,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,6,9,10,7,8] => [1,2,3,4,5,6,8,10,9,7] => [.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [1,3,2,5,4,7,6,9,10,8] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [4,2,6,1,8,3,9,5,10,7] => [[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,5,8,10,7,9] => [2,1,4,3,6,5,9,8,10,7] => [[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,4,6,8,10,1,2,5,7,9] => [2,5,3,4,7,6,9,8,10,1] => [[.,[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,7,6,9,8,12,10,11] => [1,3,2,5,4,7,6,9,8,11,12,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [1,12,2,3,4,5,6,7,8,9,10,11] => [1,3,4,5,6,7,8,9,10,11,12,2] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [2,3,4,5,6,7,8,9,10,11,12,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [4,2,5,1,3,7,6,9,8,10] => [[[.,.],[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,7,3,8,4,9,5,10,6] => [2,1,7,8,9,10,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,4,6,5,3,8,10,9,7,12,11] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,8,3,9,4,10,5,11,6,12,7] => [2,1,8,9,10,11,12,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7,9] => [4,2,6,1,7,3,8,5,9] => [[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7,10,9] => [2,1,5,6,3,4,8,7,10,9] => [[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [3,1,4,2,9,5,10,6,11,7,12,8] => [3,4,1,2,9,10,11,12,5,6,7,8] => [[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,5,6,9,10,1,2,3,7,8] => [2,3,7,4,5,6,8,10,9,1] => [[.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,5,8,9,10,1,2,3,6,7] => [2,3,6,4,5,7,10,8,9,1] => [[.,[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7,9] => [4,2,5,1,6,3,8,7,9] => [[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8] => [4,2,5,1,3,7,6,9,8] => [[[.,.],[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,10,9] => [3,2,4,1,6,5,8,7,10,9] => [[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,8,3,9,5,10,7] => [4,6,8,1,9,2,10,3,5,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,6,8,9,10,1,3,4,5,7] => [3,2,4,5,7,6,10,8,9,1] => [[[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,10,11,12,1,3,4,5,6,7] => [3,2,4,5,6,7,12,8,9,10,11,1] => [[[.,.],[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,6,2,7,3,8,4,9,5] => [1,6,7,8,9,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,7,3,8,4,9] => [5,6,7,8,1,2,3,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,7,2,8,3,9,4,10,6] => [5,7,8,9,1,10,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,[.,[.,.]]]]]
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
searching the database
Sorry, this map was not found in the database.