Identifier
Mp00024:
Dyck paths
—to 321-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ 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] => [2,1,3] => [2,1,3] => [[.,.],[.,.]]
[1,0,1,1,0,0] => [2,3,1] => [3,2,1] => [[[.,.],.],.]
[1,1,0,0,1,0] => [3,1,2] => [2,3,1] => [[.,.],[.,.]]
[1,1,0,1,0,0] => [1,3,2] => [1,3,2] => [.,[[.,.],.]]
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [2,1,4,3] => [[.,.],[[.,.],.]]
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [3,2,4,1] => [[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [4,2,3,1] => [[[.,.],[.,.]],.]
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [3,4,1,2] => [[.,[.,.]],[.,.]]
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,4,3,1] => [[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [2,3,1,4] => [[.,.],[.,[.,.]]]
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [1,4,3,2] => [.,[[[.,.],.],.]]
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [2,3,4,1] => [[.,.],[.,[.,.]]]
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,3,4,2] => [.,[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
[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] => [2,1,4,3,5] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [3,2,5,4,1] => [[[.,.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [4,2,3,5,1] => [[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => [2,4,3,1,5] => [[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => [3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [2,5,3,4,1] => [[.,.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => [3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => [2,4,3,5,1] => [[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,4,3,5,2] => [.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => [4,3,5,1,2] => [[[.,[.,.]],.],[.,.]]
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => [2,4,5,1,3] => [[.,.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [1,3,5,4,2] => [.,[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
[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] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [2,1,5,4,6,3] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [4,2,5,1,6,3] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [3,2,5,4,6,1] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [3,2,5,4,1,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => [4,2,6,1,5,3] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => [5,2,6,4,1,3] => [[[.,.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => [3,2,6,4,5,1] => [[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [3,2,5,6,1,4] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [2,1,4,6,5,3] => [[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [5,2,4,6,1,3] => [[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [3,2,4,6,5,1] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [4,2,3,5,1,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => [5,2,3,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => [4,2,3,6,5,1] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => [3,2,1,5,6,4] => [[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => [4,2,3,5,6,1] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => [5,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[.,.]]
>>> Load all 1931 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [2,4,3,1,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [3,5,1,4,6,2] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [4,5,3,1,6,2] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [2,5,3,4,6,1] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => [2,4,3,1,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [3,5,1,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [2,5,3,4,1,6] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => [3,6,1,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => [4,6,3,1,5,2] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [2,6,3,4,5,1] => [[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [2,5,3,6,1,4] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [3,4,1,6,5,2] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [5,4,3,6,1,2] => [[[[.,[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [2,4,3,6,5,1] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => [3,4,1,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => [2,4,3,5,1,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => [2,3,1,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => [1,4,3,6,5,2] => [.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => [3,4,1,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => [2,4,3,5,6,1] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => [1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => [1,5,3,4,6,2] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [2,5,6,4,1,3] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [4,3,6,1,5,2] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [5,3,6,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [2,3,6,4,5,1] => [[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => [4,3,5,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => [2,3,5,4,1,6] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => [2,4,5,1,3,6] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]]
[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] => [4,1,2,5,6,3] => [2,4,6,1,5,3] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => [1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => [1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => [1,3,6,4,5,2] => [.,[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => [4,3,5,1,6,2] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => [2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => [2,4,5,1,6,3] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => [1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => [1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => [5,3,4,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [2,3,4,6,5,1] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => [2,5,4,6,1,3] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => [1,5,4,6,2,3] => [.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => [1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => [2,3,5,6,1,4] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => [1,3,5,6,2,4] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => [1,2,4,6,5,3] => [.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]]
[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] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
[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] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7] => [3,2,4,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7] => [2,1,5,4,6,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7] => [4,2,5,1,6,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7] => [3,2,5,4,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,7,5] => [3,2,4,1,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,1,6,4,7,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5] => [4,2,6,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5] => [3,2,6,4,7,1,5] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,7,3,5] => [2,1,5,4,7,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,7,3,5] => [4,2,5,1,7,6,3] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,7,3,5] => [6,2,5,4,7,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5] => [3,2,5,4,7,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,7,5,6] => [3,2,4,1,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6] => [2,1,5,4,6,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,7,3,5,6] => [4,2,5,1,6,7,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,7,1,3,5,6] => [3,2,5,4,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,3,5,7,6] => [3,2,4,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6] => [4,2,5,1,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6] => [3,2,5,4,1,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,3,6] => [2,1,6,4,5,7,3] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,6] => [4,2,6,1,5,7,3] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6] => [5,2,6,4,1,7,3] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [3,2,6,4,5,7,1] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7] => [3,2,4,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7] => [4,2,5,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7] => [3,2,5,4,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7] => [4,2,6,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7] => [5,2,6,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7] => [3,2,6,4,5,1,7] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3] => [4,2,7,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3] => [5,2,7,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3] => [6,2,7,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3] => [3,2,7,4,5,6,1] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7] => [3,2,5,6,1,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7] => [2,1,4,6,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7] => [5,2,4,6,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,7] => [3,2,4,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,1,5,7,3,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,7,4] => [3,2,5,7,1,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,1,6,7,5,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4] => [5,2,6,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4] => [3,2,6,7,5,1,4] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4] => [2,1,4,7,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4] => [5,2,4,7,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4] => [6,2,4,7,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,5,6,7,1,3,4] => [3,2,4,7,5,6,1] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6] => [3,2,5,6,1,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6] => [2,1,4,6,5,7,3] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,5,1,7,3,4,6] => [5,2,4,6,1,7,3] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,5,7,1,3,4,6] => [3,2,4,6,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => [2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [3,2,4,5,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6] => [4,2,3,5,1,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6] => [2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6] => [3,2,1,6,5,7,4] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,1,7,4,6] => [5,2,3,6,1,7,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [4,2,3,6,5,7,1] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [2,1,4,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7] => [3,2,4,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7] => [4,2,3,5,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7] => [5,2,3,6,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7] => [4,2,3,6,5,1,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4] => [5,2,3,7,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4] => [6,2,3,7,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4] => [4,2,3,7,5,6,1] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5] => [2,1,6,5,7,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,7,4,5] => [3,2,6,5,7,1,4] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,6,7,3,4,5] => [2,1,4,5,7,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5] => [6,2,4,5,7,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5] => [3,2,4,5,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => [2,1,4,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5] => [3,2,4,6,7,1,5] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5] => [3,2,1,6,7,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5] => [4,2,3,6,7,1,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,6,7,4,5] => [2,1,3,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5] => [3,2,1,5,7,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,7,4,5] => [6,2,3,5,7,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5] => [4,2,3,5,7,6,1] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => [2,1,4,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7] => [3,2,4,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7] => [3,2,1,5,6,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7] => [4,2,3,5,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5] => [6,2,3,4,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5] => [5,2,3,4,7,6,1] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => [2,1,4,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6] => [3,2,4,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,7,4,5,6] => [3,2,1,5,6,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6] => [4,2,3,5,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6] => [3,2,1,4,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6] => [4,2,3,1,6,7,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7] => [3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7] => [2,4,3,1,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7] => [3,5,1,4,6,2,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,7] => [4,5,3,1,6,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,7] => [2,5,3,4,6,1,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [3,4,1,2,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5] => [2,4,3,1,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [3,6,1,4,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5] => [4,6,3,1,7,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5] => [2,6,3,4,7,1,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,7,2,5] => [3,5,1,4,7,6,2] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5] => [4,5,3,1,7,6,2] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,4,6,1,7,2,5] => [6,5,3,4,7,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5] => [2,5,3,4,7,6,1] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6] => [3,4,1,2,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6] => [2,4,3,1,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6] => [3,5,1,4,6,7,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,1,7,2,5,6] => [4,5,3,1,6,7,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,4,7,1,2,5,6] => [2,5,3,4,6,7,1] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6] => [3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6] => [2,4,3,1,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6] => [3,5,1,4,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6] => [4,5,3,1,2,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,7,6] => [2,5,3,4,1,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6] => [3,6,1,4,5,7,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6] => [4,6,3,1,5,7,2] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6] => [5,6,3,4,1,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [2,6,3,4,5,7,1] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7] => [2,4,3,1,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7] => [3,5,1,4,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7] => [4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7] => [2,5,3,4,1,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7] => [3,6,1,4,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7] => [4,6,3,1,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7] => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7] => [2,6,3,4,5,1,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2] => [3,7,1,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2] => [4,7,3,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2] => [5,7,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [2,7,3,4,5,6,1] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7] => [3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,7] => [2,5,3,6,1,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7] => [3,4,1,6,5,2,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7] => [5,4,3,6,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7] => [2,4,3,6,5,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [3,5,1,7,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4] => [2,5,3,7,1,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [3,6,1,7,5,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4] => [5,6,3,7,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4] => [2,6,3,7,5,1,4] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4] => [3,4,1,7,5,6,2] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4] => [5,4,3,7,1,6,2] => [[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4] => [6,4,3,7,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4] => [2,4,3,7,5,6,1] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => [3,5,1,6,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6] => [2,5,3,6,1,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6] => [3,4,1,6,5,7,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6] => [5,4,3,6,1,7,2] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6] => [2,4,3,6,5,7,1] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6] => [3,4,1,5,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [2,4,3,5,1,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6] => [2,3,1,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => [1,4,3,5,2,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6] => [2,3,1,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => [1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => [1,5,3,6,2,7,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [1,4,3,6,5,7,2] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [3,4,1,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7] => [2,4,3,5,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,7] => [2,3,1,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => [1,4,3,5,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7] => [2,3,1,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => [1,5,3,6,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => [1,4,3,6,5,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4] => [2,3,1,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => [1,5,3,7,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => [1,6,3,7,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => [1,4,3,7,5,6,2] => [.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => [3,6,1,5,7,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,7,4,5] => [2,6,3,5,7,1,4] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5] => [3,4,1,5,7,6,2] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,6,1,7,2,4,5] => [6,4,3,5,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5] => [2,4,3,5,7,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => [3,4,1,6,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5] => [2,4,3,6,7,1,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [2,3,1,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => [1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => [1,4,3,6,7,2,5] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,7,4,5] => [2,3,1,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => [1,3,2,5,7,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => [1,6,3,5,7,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => [1,4,3,5,7,6,2] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7] => [3,4,1,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7] => [2,4,3,5,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,7] => [2,3,1,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => [1,4,3,5,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,7] => [2,3,1,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => [1,5,3,4,6,2,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5] => [2,3,1,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => [1,6,3,4,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => [1,5,3,4,7,6,2] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => [3,4,1,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6] => [2,4,3,5,6,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6] => [2,3,1,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => [1,4,3,5,6,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6] => [2,3,1,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => [1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [1,5,3,4,6,7,2] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [2,3,1,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => [1,6,3,4,5,7,2] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,7] => [2,5,6,4,1,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7] => [4,3,6,1,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7] => [5,3,6,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7] => [2,3,6,4,5,1,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [4,5,7,1,2,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3] => [2,5,7,4,1,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [4,6,7,1,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3] => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3] => [2,6,7,4,5,1,3] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3] => [4,3,7,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3] => [5,3,7,4,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3] => [6,3,7,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [2,3,7,4,5,6,1] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => [4,5,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6] => [2,5,6,4,1,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6] => [4,3,6,1,5,7,2] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6] => [5,3,6,4,1,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,5,7,1,2,3,6] => [2,3,6,4,5,7,1] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6] => [4,3,5,1,2,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [2,3,5,4,1,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6] => [2,4,5,1,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => [1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => [1,3,5,4,2,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [2,4,6,1,5,7,3] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => [1,4,6,2,5,7,3] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => [1,5,6,4,2,7,3] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [1,3,6,4,5,7,2] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [4,3,5,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7] => [2,3,5,4,1,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7] => [2,4,5,1,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => [1,3,5,4,2,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7] => [2,4,6,1,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => [1,4,6,2,5,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => [1,5,6,4,2,3,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => [1,3,6,4,5,2,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3] => [2,4,7,1,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => [1,4,7,2,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => [1,5,7,4,2,6,3] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => [1,6,7,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => [1,3,7,4,5,6,2] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => [4,6,5,1,7,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5] => [2,6,5,4,7,1,3] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5] => [4,3,5,1,7,6,2] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5] => [6,3,5,4,7,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5] => [2,3,5,4,7,6,1] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => [4,3,6,1,7,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5] => [2,3,6,4,7,1,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [2,4,6,1,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => [1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => [1,3,6,4,7,2,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5] => [2,4,5,1,7,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => [1,4,5,2,7,6,3] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => [1,6,5,4,7,2,3] => [.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => [1,3,5,4,7,6,2] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => [4,3,5,1,6,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7] => [2,3,5,4,6,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7] => [2,4,5,1,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => [1,4,5,2,6,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => [1,3,5,4,6,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7] => [2,3,4,1,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => [1,2,5,4,6,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5] => [2,3,4,1,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => [1,3,4,2,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => [1,2,6,4,7,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => [1,2,5,4,7,6,3] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => [4,3,5,1,6,7,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6] => [2,3,5,4,6,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => [2,4,5,1,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => [1,4,5,2,6,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => [1,3,5,4,6,7,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6] => [2,3,4,1,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,3,4,2,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [1,2,5,4,6,7,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => [1,2,6,4,5,7,3] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4] => [5,6,4,7,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4] => [2,6,4,7,5,1,3] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,1,6,7,2,3,4] => [5,3,4,7,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4] => [6,3,4,7,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [2,3,4,7,5,6,1] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4] => [5,3,6,7,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,7,4] => [2,3,6,7,5,1,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [2,5,6,7,1,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4] => [1,3,6,7,5,2,4] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4] => [2,5,4,7,1,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4] => [1,5,4,7,2,6,3] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => [1,6,4,7,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => [1,3,4,7,5,6,2] => [.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => [5,3,4,6,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7] => [2,3,4,6,5,1,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7] => [2,5,4,6,1,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7] => [1,5,4,6,2,3,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7] => [1,3,4,6,5,2,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7] => [2,3,5,6,1,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7] => [1,3,5,6,2,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => [1,2,4,6,5,3,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4] => [2,3,5,7,1,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4] => [1,3,5,7,2,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => [1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => [1,2,6,7,5,3,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => [1,2,4,7,5,6,3] => [.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6] => [5,3,4,6,1,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6] => [2,3,4,6,5,7,1] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6] => [2,5,4,6,1,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => [1,5,4,6,2,7,3] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => [1,3,4,6,5,7,2] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6] => [2,3,5,6,1,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,3,5,6,2,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => [1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [1,2,4,6,5,7,3] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => [1,3,4,5,2,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => [1,2,4,5,3,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => [1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5] => [6,3,4,5,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [2,3,4,5,7,6,1] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5] => [2,6,4,5,7,1,3] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => [1,6,4,5,7,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => [1,3,4,5,7,6,2] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5] => [2,3,6,5,7,1,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,3,6,5,7,2,4] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => [1,2,6,5,7,3,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => [1,2,4,5,7,6,3] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [2,3,4,6,7,1,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [1,3,4,6,7,2,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => [1,2,4,6,7,3,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => [1,2,3,5,7,6,4] => [.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [3,2,4,1,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,8,7] => [2,1,5,4,6,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7] => [4,2,5,1,6,3,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7] => [3,2,5,4,6,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7] => [3,2,4,1,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,8,5,7] => [2,1,6,4,7,3,8,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7] => [4,2,6,1,7,3,8,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [3,2,6,4,7,1,8,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,8,3,5,7] => [2,1,5,4,7,6,8,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7] => [4,2,5,1,7,6,8,3] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [6,2,5,4,7,1,8,3] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [3,2,5,4,7,6,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7,8] => [3,2,4,1,6,5,7,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7,8] => [4,2,5,1,6,3,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,3,6,7,5,8] => [3,2,4,1,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8] => [4,2,6,1,7,3,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5,8] => [3,2,6,4,7,1,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [3,2,5,4,7,6,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,7,8,5] => [3,2,4,1,8,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,6,3,7,8,5] => [2,1,6,4,8,3,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => [4,2,6,1,8,3,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,6,1,3,7,8,5] => [3,2,6,4,8,1,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,3,8,5] => [2,1,7,4,8,6,3,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => [4,2,7,1,8,6,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,6,1,7,3,8,5] => [6,2,7,4,8,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,8,5] => [3,2,7,4,8,6,1,5] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,6,7,8,3,5] => [2,1,5,4,8,6,7,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,6,7,8,3,5] => [4,2,5,1,8,6,7,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,6,7,1,8,3,5] => [7,2,5,4,8,6,1,3] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,6,7,8,1,3,5] => [3,2,5,4,8,6,7,1] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,8,6] => [2,1,4,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,3,7,5,8,6] => [3,2,4,1,7,8,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,7,3,5,8,6] => [4,2,5,1,7,8,3,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,4,7,1,3,5,8,6] => [3,2,5,4,7,8,1,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,7,8,5,6] => [2,1,4,3,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,7,8,5,6] => [3,2,4,1,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,7,3,8,5,6] => [2,1,7,4,6,8,3,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,4,1,7,3,8,5,6] => [4,2,7,1,6,8,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,7,1,3,8,5,6] => [3,2,7,4,6,8,1,5] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,7,8,3,5,6] => [2,1,5,4,6,8,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,8,3,5,6] => [4,2,5,1,6,8,7,3] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [3,2,5,4,6,8,7,1] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,3,7,5,6,8] => [3,2,4,1,6,7,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6,8] => [2,1,5,4,6,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,1,3,5,7,6,8] => [3,2,4,1,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,8] => [4,2,5,1,3,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6,8] => [3,2,5,4,1,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6,8] => [5,2,6,4,1,7,3,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,7,8,6] => [3,2,4,1,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,7,8,6] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,7,8,6] => [3,2,5,4,1,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,5,7,3,8,6] => [2,1,7,4,5,8,3,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,1,7,3,8,6] => [5,2,7,4,1,8,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,8,6] => [3,2,7,4,5,8,1,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,4,5,7,8,3,6] => [2,1,6,4,5,8,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,7,8,3,6] => [5,2,6,4,1,8,7,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,5,7,1,8,3,6] => [7,2,6,4,5,8,1,3] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,8,5,6,7] => [2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,8,5,6,7] => [3,2,4,1,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,4,8,3,5,6,7] => [2,1,5,4,6,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,8,3,5,6,7] => [4,2,5,1,6,7,8,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,4,8,1,3,5,6,7] => [3,2,5,4,6,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,4,3,5,8,6,7] => [2,1,4,3,5,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,3,5,8,6,7] => [3,2,4,1,5,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,3,8,6,7] => [4,2,5,1,3,7,8,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,4,5,8,3,6,7] => [2,1,6,4,5,7,8,3] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,5,8,3,6,7] => [4,2,6,1,5,7,8,3] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [5,2,6,4,1,7,8,3] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,8,7] => [3,2,4,1,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,8,7] => [4,2,5,1,3,6,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,8,7] => [5,2,6,4,1,3,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,8,7] => [3,2,6,4,5,1,8,7] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,4,1,5,6,8,3,7] => [4,2,7,1,5,6,8,3] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,4,5,1,6,8,3,7] => [5,2,7,4,1,6,8,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,4,5,6,1,8,3,7] => [6,2,7,4,5,1,8,3] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8] => [3,2,4,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7,8] => [4,2,5,1,3,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7,8] => [3,2,5,4,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7,8] => [4,2,6,1,5,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7,8] => [5,2,6,4,1,3,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [3,2,6,4,5,1,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3,8] => [4,2,7,1,5,6,3,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3,8] => [5,2,7,4,1,6,3,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3,8] => [6,2,7,4,5,1,3,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3,8] => [3,2,7,4,5,6,1,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,5,6,7,8,3] => [4,2,8,1,5,6,7,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,4,5,1,6,7,8,3] => [5,2,8,4,1,6,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,4,5,6,1,7,8,3] => [6,2,8,4,5,1,7,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,4,5,6,7,1,8,3] => [7,2,8,4,5,6,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,3] => [3,2,8,4,5,6,7,1] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,8,7] => [2,1,5,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,1,4,6,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,8,7] => [5,2,4,6,1,3,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,8,4,7] => [2,1,5,7,3,6,8,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,8,4,7] => [3,2,5,7,1,6,8,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [3,2,4,7,5,6,8,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7,8] => [2,1,5,6,3,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7,8] => [3,2,5,6,1,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7,8] => [2,1,4,6,5,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,6,7,4,8] => [3,2,5,7,1,6,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4,8] => [5,2,6,7,1,3,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4,8] => [3,2,6,7,5,1,4,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [2,1,5,8,3,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,5,1,3,6,7,8,4] => [3,2,5,8,1,6,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,8,4] => [2,1,6,8,5,3,7,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => [5,2,6,8,1,3,7,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5,6,1,3,7,8,4] => [3,2,6,8,5,1,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => [5,2,7,8,1,6,3,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,7,3,8,4] => [6,2,7,8,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5,6,7,1,3,8,4] => [3,2,7,8,5,6,1,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,5,6,7,8,3,4] => [2,1,4,8,5,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5,1,6,7,8,3,4] => [5,2,4,8,1,6,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5,6,7,8,1,3,4] => [3,2,4,8,5,6,7,1] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,8,6] => [2,1,5,7,3,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [3,2,5,7,1,8,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,7,3,4,8,6] => [5,2,4,7,1,8,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,5,7,1,3,4,8,6] => [3,2,4,7,5,8,1,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,7,8,4,6] => [2,1,5,6,3,8,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,8,4,6] => [3,2,5,6,1,8,7,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,7,3,8,4,6] => [2,1,7,6,5,8,3,4] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,5,7,1,3,8,4,6] => [3,2,7,6,5,8,1,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,7,8,3,4,6] => [2,1,4,6,5,8,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [3,2,4,6,5,8,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6,8] => [2,1,5,6,3,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6,8] => [3,2,1,6,5,7,4,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,7,8,6] => [3,2,4,5,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,4,7,8,6] => [4,2,3,5,1,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,7,4,8,6] => [2,1,3,7,5,8,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,7,8,4,6] => [2,1,3,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,7,8,4,6] => [3,2,1,6,5,8,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,7,8,1,4,6] => [4,2,3,6,5,8,7,1] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,8,4,6,7] => [2,1,5,6,3,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,5,1,3,8,4,6,7] => [3,2,5,6,1,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,5,4,8,6,7] => [2,1,3,5,4,7,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,5,8,4,6,7] => [3,2,1,6,5,7,8,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [5,2,3,6,1,7,8,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,8,7] => [2,1,4,5,3,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,8,7] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,5,6,4,8,7] => [3,2,1,6,5,4,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,8,7] => [5,2,3,6,1,4,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,5,6,8,4,7] => [3,2,1,7,5,6,8,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,1,6,8,4,7] => [5,2,3,7,1,6,8,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,6,8,1,4,7] => [4,2,3,7,5,6,8,1] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [2,1,4,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7,8] => [3,2,4,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7,8] => [3,2,1,5,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7,8] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7,8] => [3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7,8] => [5,2,3,6,1,4,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4,8] => [3,2,1,7,5,6,4,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4,8] => [5,2,3,7,1,6,4,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4,8] => [6,2,3,7,5,1,4,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4,8] => [4,2,3,7,5,6,1,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,5,1,6,7,8,4] => [5,2,3,8,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,5,6,1,7,8,4] => [6,2,3,8,5,1,7,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,5,6,7,1,8,4] => [7,2,3,8,5,6,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,6,7,8,1,4] => [4,2,3,8,5,6,7,1] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5] => [2,1,6,7,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,7,4,8,5] => [3,2,6,7,8,1,4,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,6,7,3,4,8,5] => [2,1,4,7,8,6,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,6,1,7,3,4,8,5] => [6,2,4,7,8,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [3,2,4,7,8,6,1,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,6,3,7,8,4,5] => [2,1,6,5,8,3,7,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,6,1,3,7,8,4,5] => [3,2,6,5,8,1,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,1,6,7,3,8,4,5] => [2,1,7,5,8,6,3,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,6,7,1,3,8,4,5] => [3,2,7,5,8,6,1,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,6,7,8,3,4,5] => [2,1,4,5,8,6,7,3] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [3,2,4,5,8,6,7,1] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,6,1,3,7,4,5,8] => [3,2,6,5,7,1,4,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5,8] => [3,2,1,6,7,4,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5,8] => [3,2,1,5,7,6,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [2,1,4,6,8,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,7,8,5] => [3,2,1,6,8,4,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,4,8,5] => [2,1,3,7,8,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,4,8,5] => [3,2,1,7,8,6,4,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,3,6,1,7,4,8,5] => [6,2,3,7,8,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,3,6,7,1,4,8,5] => [4,2,3,7,8,6,1,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,3,6,7,8,4,5] => [2,1,3,5,8,6,7,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,3,1,6,7,8,4,5] => [3,2,1,5,8,6,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => [6,2,3,5,8,1,7,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,8,4,5,7] => [2,1,6,5,7,3,8,4] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,8,4,5,7] => [3,2,6,5,7,1,8,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,6,1,8,3,4,5,7] => [6,2,4,5,7,1,8,3] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,6,8,1,3,4,5,7] => [3,2,4,5,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,8,5,7] => [2,1,4,6,7,3,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,8,5,7] => [2,1,3,6,7,4,8,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,8,5,7] => [3,2,1,6,7,4,8,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,8,4,5,7] => [3,2,1,5,7,6,8,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,8,7] => [2,1,4,5,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,8,7] => [2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,8,7] => [4,2,3,5,6,1,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5,8,7] => [5,2,3,4,6,1,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,3,1,4,6,8,5,7] => [3,2,1,4,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,8,5,7] => [4,2,3,1,7,6,8,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,8,5,7] => [6,2,3,4,7,1,8,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7,8] => [3,2,4,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7,8] => [3,2,1,5,6,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7,8] => [4,2,3,5,6,1,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7,8] => [4,2,3,1,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5,8] => [4,2,3,1,7,6,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5,8] => [5,2,3,4,7,6,1,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,3,4,6,1,7,8,5] => [6,2,3,4,8,1,7,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,3,4,6,7,1,8,5] => [7,2,3,4,8,6,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,7,8,1,5] => [5,2,3,4,8,6,7,1] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,7,3,8,4,5,6] => [2,1,7,5,6,8,3,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,7,8,3,4,5,6] => [2,1,4,5,6,8,7,3] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [7,2,4,5,6,8,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,7,8,1,3,4,5,6] => [3,2,4,5,6,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,7,4,8,5,6] => [3,2,1,7,6,8,4,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,1,7,8,4,5,6] => [3,2,1,5,6,8,7,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [4,2,3,5,6,8,7,1] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,7,3,4,5,8,6] => [2,1,4,5,7,8,3,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [3,2,4,5,7,8,1,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,7,4,5,8,6] => [3,2,1,5,7,8,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,3,4,7,5,8,6] => [2,1,3,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,4,1,7,5,8,6] => [4,2,3,1,7,8,5,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,8,6] => [5,2,3,4,7,8,1,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,1,4,7,8,5,6] => [3,2,1,4,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,4,1,7,8,5,6] => [4,2,3,1,6,8,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,4,7,1,8,5,6] => [7,2,3,4,6,8,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6,8] => [2,1,4,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6,8] => [3,2,4,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6,8] => [4,2,3,5,6,7,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6,8] => [6,2,3,4,5,7,1,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,7,8,6] => [4,2,3,1,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,4,5,7,1,8,6] => [7,2,3,4,5,8,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,5,7,8,1,6] => [6,2,3,4,5,8,7,1] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7] => [2,1,4,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7] => [3,2,4,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,8,4,5,6,7] => [2,1,3,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,1,8,4,5,6,7] => [3,2,1,5,6,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,8,1,4,5,6,7] => [4,2,3,5,6,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,3,4,8,5,6,7] => [2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,1,4,8,5,6,7] => [3,2,1,4,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [4,2,3,1,6,7,8,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,3,4,5,8,6,7] => [2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [3,2,1,4,5,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,3,4,1,5,8,6,7] => [4,2,3,1,5,7,8,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,3,4,5,1,8,6,7] => [5,2,3,4,1,7,8,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,3,4,5,8,1,6,7] => [6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,7] => [7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7] => [3,4,1,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [2,4,3,1,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7] => [3,5,1,4,6,2,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,8,5,7] => [3,4,1,2,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,8,5,7] => [2,4,3,1,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [3,6,1,4,7,2,8,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,8,5,7] => [4,6,3,1,7,2,8,5] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,8,2,5,7] => [3,5,1,4,7,6,8,2] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,8,2,5,7] => [4,5,3,1,7,6,8,2] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [2,5,3,4,7,6,8,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7,8] => [3,4,1,2,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7,8] => [2,4,3,1,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7,8] => [3,5,1,4,6,2,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5,8] => [3,4,1,2,7,6,5,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5,8] => [3,6,1,4,7,2,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5,8] => [4,6,3,1,7,2,5,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5,8] => [2,6,3,4,7,1,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5,8] => [4,5,3,1,7,6,2,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [3,4,1,2,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,6,2,7,8,5] => [4,6,3,1,8,2,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,6,7,2,8,5] => [4,7,3,1,8,6,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [3,4,6,1,7,2,8,5] => [6,7,3,4,8,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,6,7,8,2,5] => [4,5,3,1,8,6,7,2] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [3,4,6,1,7,8,2,5] => [6,5,3,4,8,1,7,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,6,7,8,1,2,5] => [2,5,3,4,8,6,7,1] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,8,6] => [3,4,1,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,7,5,8,6] => [2,4,3,1,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,7,2,5,8,6] => [4,5,3,1,7,8,2,6] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,7,8,5,6] => [3,4,1,2,6,8,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6] => [2,4,3,1,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,7,2,8,5,6] => [3,7,1,4,6,8,2,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,7,2,8,5,6] => [4,7,3,1,6,8,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,7,8,2,5,6] => [4,5,3,1,6,8,7,2] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [7,5,3,4,6,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [2,5,3,4,6,8,7,1] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6,8] => [3,4,1,2,6,7,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6,8] => [3,5,1,4,6,7,2,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [3,4,7,1,2,5,6,8] => [2,5,3,4,6,7,1,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6,8] => [3,4,1,2,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6,8] => [3,5,1,4,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6,8] => [5,6,3,4,1,7,2,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => [3,4,1,2,5,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,7,8,6] => [2,4,3,1,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,7,8,6] => [3,5,1,4,2,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,7,8,6] => [4,5,3,1,2,8,7,6] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,7,8,6] => [2,5,3,4,1,8,7,6] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [3,4,5,1,7,2,8,6] => [5,7,3,4,1,8,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,8,6] => [2,7,3,4,5,8,1,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,5,7,8,2,6] => [4,6,3,1,5,8,7,2] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,7,1,8,2,6] => [7,6,3,4,5,8,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,7,8,1,2,6] => [2,6,3,4,5,8,7,1] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,2,8,5,6,7] => [3,4,1,2,6,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,8,5,6,7] => [2,4,3,1,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,8,2,5,6,7] => [3,5,1,4,6,7,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,8,2,5,6,7] => [4,5,3,1,6,7,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,4,8,1,2,5,6,7] => [2,5,3,4,6,7,8,1] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,8,6,7] => [3,4,1,2,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,4,5,8,2,6,7] => [3,6,1,4,5,7,8,2] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,4,5,1,8,2,6,7] => [5,6,3,4,1,7,8,2] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [2,6,3,4,5,7,8,1] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,8,7] => [3,4,1,2,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,8,7] => [4,5,3,1,2,6,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,8,7] => [3,6,1,4,5,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,8,7] => [4,6,3,1,5,2,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [3,7,1,4,5,6,8,2] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8] => [2,4,3,1,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7,8] => [3,5,1,4,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7,8] => [2,5,3,4,1,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7,8] => [3,6,1,4,5,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7,8] => [4,6,3,1,5,2,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7,8] => [5,6,3,4,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [2,6,3,4,5,1,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2,8] => [3,7,1,4,5,6,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2,8] => [4,7,3,1,5,6,2,8] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2,8] => [5,7,3,4,1,6,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2,8] => [6,7,3,4,5,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [2,7,3,4,5,6,1,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2] => [3,8,1,4,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,5,6,7,8,2] => [4,8,3,1,5,6,7,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,4,5,1,6,7,8,2] => [5,8,3,4,1,6,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,4,5,6,1,7,8,2] => [6,8,3,4,5,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,2] => [7,8,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [2,8,3,4,5,6,7,1] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7] => [3,5,1,6,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,8,7] => [5,4,3,6,1,2,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,8,7] => [2,4,3,6,5,1,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,8,4,7] => [3,5,1,7,2,6,8,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,8,4,7] => [2,5,3,7,1,6,8,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,8,4,7] => [3,6,1,7,5,2,8,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,8,4,7] => [2,6,3,7,5,1,8,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,5,6,8,2,4,7] => [3,4,1,7,5,6,8,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,5,1,6,8,2,4,7] => [5,4,3,7,1,6,8,2] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [6,4,3,7,5,1,8,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [2,4,3,7,5,6,8,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7,8] => [3,5,1,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4,7,8] => [2,5,3,6,1,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7,8] => [5,4,3,6,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7,8] => [2,4,3,6,5,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [2,5,3,7,1,6,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4,8] => [5,6,3,7,1,2,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4,8] => [3,4,1,7,5,6,2,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4,8] => [6,4,3,7,5,1,2,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,5,1,2,6,7,8,4] => [2,5,3,8,1,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,5,6,2,7,8,4] => [3,6,1,8,5,2,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5,1,6,2,7,8,4] => [5,6,3,8,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5,6,1,2,7,8,4] => [2,6,3,8,5,1,7,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,5,6,7,2,8,4] => [3,7,1,8,5,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5,1,6,7,2,8,4] => [5,7,3,8,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5,6,1,7,2,8,4] => [6,7,3,8,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,8,4] => [2,7,3,8,5,6,1,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,5,6,7,8,2,4] => [3,4,1,8,5,6,7,2] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5,1,6,7,8,2,4] => [5,4,3,8,1,6,7,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => [6,4,3,8,5,1,7,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5,6,7,8,1,2,4] => [2,4,3,8,5,6,7,1] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6] => [3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,7,4,8,6] => [2,5,3,7,1,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,7,2,4,8,6] => [3,4,1,7,5,8,2,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,7,2,4,8,6] => [5,4,3,7,1,8,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,7,1,2,4,8,6] => [2,4,3,7,5,8,1,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,7,8,4,6] => [3,5,1,6,2,8,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,7,8,4,6] => [2,5,3,6,1,8,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,7,2,8,4,6] => [3,7,1,6,5,8,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,7,2,8,4,6] => [5,7,3,6,1,8,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,7,1,2,8,4,6] => [2,7,3,6,5,8,1,4] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,7,8,2,4,6] => [3,4,1,6,5,8,7,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,7,8,2,4,6] => [5,4,3,6,1,8,7,2] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,5,7,1,8,2,4,6] => [7,4,3,6,5,8,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [2,4,3,6,5,8,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,8] => [3,5,1,6,2,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6,8] => [2,5,3,6,1,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6,8] => [3,4,1,6,5,7,2,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6,8] => [5,4,3,6,1,7,2,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6,8] => [2,4,3,6,5,7,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,8] => [3,4,1,5,2,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [2,4,3,5,1,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,8] => [1,4,3,5,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => [2,3,1,6,5,7,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6,8] => [1,3,2,6,5,7,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6,8] => [1,5,3,6,2,7,4,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [1,4,3,6,5,7,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,8,6] => [3,4,1,5,2,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,7,8,6] => [2,4,3,5,1,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,7,4,8,6] => [2,3,1,7,5,8,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,7,4,8,6] => [1,3,2,7,5,8,4,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,8,6] => [1,4,3,7,5,8,2,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,7,8,4,6] => [2,3,1,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,7,8,4,6] => [1,3,2,6,5,8,7,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [1,5,3,6,2,8,7,4] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,6] => [1,7,3,6,5,8,2,4] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,7,8,2,4,6] => [1,4,3,6,5,8,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [3,5,1,6,2,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,8,2,4,6,7] => [3,4,1,6,5,7,8,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,5,1,8,2,4,6,7] => [5,4,3,6,1,7,8,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,5,8,1,2,4,6,7] => [2,4,3,6,5,7,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,5,1,2,4,8,6,7] => [2,4,3,5,1,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,5,8,4,6,7] => [1,3,2,6,5,7,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [1,5,3,6,2,7,8,4] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [1,4,3,6,5,7,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,8,7] => [2,4,3,5,1,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,8,7] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,5,6,8,4,7] => [1,3,2,7,5,6,8,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7,8] => [3,4,1,5,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7,8] => [2,4,3,5,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,5,4,6,7,8] => [2,3,1,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7,8] => [1,4,3,5,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7,8] => [2,3,1,6,5,4,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7,8] => [1,5,3,6,2,4,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [1,4,3,6,5,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4,8] => [2,3,1,7,5,6,4,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4,8] => [1,5,3,7,2,6,4,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,8] => [1,6,3,7,5,2,4,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,5,6,7,8,4] => [2,3,1,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,5,2,6,7,8,4] => [1,5,3,8,2,6,7,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,5,6,2,7,8,4] => [1,6,3,8,5,2,7,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,5,6,7,2,8,4] => [1,7,3,8,5,6,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5,6,7,8,2,4] => [1,4,3,8,5,6,7,2] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5] => [3,6,1,7,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,6,1,2,7,4,8,5] => [2,6,3,7,8,1,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,6,1,7,2,4,8,5] => [6,4,3,7,8,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,6,7,1,2,4,8,5] => [2,4,3,7,8,6,1,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,6,1,2,7,8,4,5] => [2,6,3,5,8,1,7,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,6,1,7,2,8,4,5] => [6,7,3,5,8,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,6,7,1,2,8,4,5] => [2,7,3,5,8,6,1,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,6,1,7,8,2,4,5] => [6,4,3,5,8,1,7,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [2,4,3,5,8,6,7,1] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5,8] => [3,4,1,5,7,6,2,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5,8] => [3,4,1,6,7,2,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [2,4,3,6,7,1,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5,8] => [1,3,2,6,7,4,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5,8] => [1,3,2,5,7,6,4,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5,8] => [1,4,3,5,7,6,2,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,7,8,5] => [2,4,3,6,8,1,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,7,8,5] => [2,3,1,6,8,4,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,7,8,5] => [1,3,2,6,8,4,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,6,7,4,8,5] => [2,3,1,7,8,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,6,2,7,4,8,5] => [1,6,3,7,8,2,4,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,6,7,2,4,8,5] => [1,4,3,7,8,6,2,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,8,4,5] => [1,7,3,5,8,6,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,6,7,8,2,4,5] => [1,4,3,5,8,6,7,2] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,6,8,2,4,5,7] => [3,4,1,5,7,6,8,2] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,6,1,8,2,4,5,7] => [6,4,3,5,7,1,8,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,6,8,1,2,4,5,7] => [2,4,3,5,7,6,8,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,8,5,7] => [3,4,1,6,7,2,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,8,5,7] => [1,3,2,6,7,4,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,8,5,7] => [1,4,3,6,7,2,8,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,8,4,5,7] => [2,3,1,5,7,6,8,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,8,4,5,7] => [1,6,3,5,7,2,8,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,8,7] => [3,4,1,5,6,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,8,7] => [2,4,3,5,6,1,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,8,7] => [2,3,1,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,8,7] => [1,5,3,4,6,2,8,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,8,5,7] => [2,3,1,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,8,5,7] => [1,3,2,4,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => [3,4,1,5,6,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,5,7,8] => [2,3,1,5,6,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7,8] => [1,3,2,5,6,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7,8] => [1,4,3,5,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5,8] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,6,7,5] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,6,7,8,5] => [1,4,3,2,8,6,7,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,3,4,6,2,7,8,5] => [1,6,3,4,8,2,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,4,6,7,2,8,5] => [1,7,3,4,8,6,2,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4,6,7,8,2,5] => [1,5,3,4,8,6,7,2] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,7,2,8,4,5,6] => [3,7,1,5,6,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,7,8,2,4,5,6] => [3,4,1,5,6,8,7,2] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,7,8,1,2,4,5,6] => [2,4,3,5,6,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,7,2,4,8,5,6] => [3,4,1,7,6,8,2,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,7,4,8,5,6] => [2,3,1,7,6,8,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,3,2,7,6,8,4,5] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,3,7,2,4,8,5,6] => [1,4,3,7,6,8,2,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,3,2,7,8,4,5,6] => [1,3,2,5,6,8,7,4] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [1,7,3,5,6,8,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,7,2,4,5,8,6] => [3,4,1,5,7,8,2,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,7,1,2,4,5,8,6] => [2,4,3,5,7,8,1,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,2,7,4,5,8,6] => [2,3,1,5,7,8,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,3,2,7,4,5,8,6] => [1,3,2,5,7,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,3,7,2,4,5,8,6] => [1,4,3,5,7,8,2,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [3,1,2,4,7,5,8,6] => [2,3,1,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,3,2,4,7,5,8,6] => [1,3,2,4,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,3,4,2,7,5,8,6] => [1,4,3,2,7,8,5,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,8,6] => [1,5,3,4,7,8,2,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,3,2,4,7,8,5,6] => [1,3,2,4,6,8,7,5] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,3,4,2,7,8,5,6] => [1,4,3,2,6,8,7,5] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6,8] => [3,4,1,5,6,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6,8] => [2,4,3,5,6,7,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6,8] => [2,3,1,5,6,7,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6,8] => [1,3,2,5,6,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6,8] => [1,4,3,5,6,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [2,3,1,4,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6,8] => [1,3,2,4,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6,8] => [1,4,3,2,6,7,5,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [1,5,3,4,6,7,2,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6,8] => [2,3,1,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,7,8,6] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,7,8,6] => [1,5,3,4,2,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,4,5,7,2,8,6] => [1,7,3,4,5,8,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,3,4,5,7,8,2,6] => [1,6,3,4,5,8,7,2] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [3,4,1,5,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,8,1,2,4,5,6,7] => [2,4,3,5,6,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,8,4,5,6,7] => [2,3,1,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,3,2,8,4,5,6,7] => [1,3,2,5,6,7,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,3,8,2,4,5,6,7] => [1,4,3,5,6,7,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,4,8,5,6,7] => [2,3,1,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,3,2,4,8,5,6,7] => [1,3,2,4,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [1,4,3,2,6,7,8,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [1,5,3,4,6,7,8,2] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,2,4,5,8,6,7] => [2,3,1,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,3,4,2,5,8,6,7] => [1,4,3,2,5,7,8,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,3,4,5,2,8,6,7] => [1,5,3,4,2,7,8,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,3,4,5,6,8,2,7] => [1,7,3,4,5,6,8,2] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7] => [4,5,6,1,2,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [2,5,6,4,1,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,8,7] => [4,3,6,1,5,2,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,8,7] => [5,3,6,4,1,2,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,8,7] => [2,3,6,4,5,1,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,8,3,7] => [4,5,7,1,2,6,8,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,8,3,7] => [2,5,7,4,1,6,8,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,8,3,7] => [5,6,7,4,1,2,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,8,3,7] => [2,6,7,4,5,1,8,3] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,5,6,8,2,3,7] => [4,3,7,1,5,6,8,2] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [4,5,1,6,8,2,3,7] => [5,3,7,4,1,6,8,2] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [6,3,7,4,5,1,8,2] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [2,3,7,4,5,6,8,1] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7,8] => [4,5,6,1,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7,8] => [4,3,6,1,5,2,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7,8] => [5,3,6,4,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7,8] => [2,3,6,4,5,1,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3,8] => [4,5,7,1,2,6,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [2,5,7,4,1,6,3,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3,8] => [4,6,7,1,5,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3,8] => [5,6,7,4,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3,8] => [2,6,7,4,5,1,3,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3,8] => [5,3,7,4,1,6,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [4,5,8,1,2,6,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [4,5,1,6,2,7,8,3] => [5,6,8,4,1,2,7,3] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [4,5,6,1,2,7,8,3] => [2,6,8,4,5,1,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [4,1,5,6,7,2,8,3] => [4,7,8,1,5,6,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5,1,6,7,2,8,3] => [5,7,8,4,1,6,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5,6,1,7,2,8,3] => [6,7,8,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,1,5,6,7,8,2,3] => [4,3,8,1,5,6,7,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,5,1,6,7,8,2,3] => [5,3,8,4,1,6,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [4,5,6,1,7,8,2,3] => [6,3,8,4,5,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,3] => [7,3,8,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [2,3,8,4,5,6,7,1] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6] => [4,5,7,1,2,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,7,3,8,6] => [2,5,7,4,1,8,3,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,5,7,2,3,8,6] => [4,3,7,1,5,8,2,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,7,8,3,6] => [4,5,6,1,2,8,7,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,1,5,7,2,8,3,6] => [4,7,6,1,5,8,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,5,1,7,2,8,3,6] => [5,7,6,4,1,8,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,5,7,1,2,8,3,6] => [2,7,6,4,5,8,1,3] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [4,1,5,7,8,2,3,6] => [4,3,6,1,5,8,7,2] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,5,1,7,8,2,3,6] => [5,3,6,4,1,8,7,2] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [4,5,7,1,8,2,3,6] => [7,3,6,4,5,8,1,2] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [2,3,6,4,5,8,7,1] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6,8] => [4,5,6,1,2,7,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6,8] => [2,5,6,4,1,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6,8] => [4,3,6,1,5,7,2,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6,8] => [5,3,6,4,1,7,2,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6,8] => [4,3,5,1,2,7,6,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6,8] => [2,3,5,4,1,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6,8] => [2,4,5,1,3,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,8] => [1,4,5,2,3,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6,8] => [1,3,5,4,2,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6,8] => [2,4,6,1,5,7,3,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => [1,3,6,4,5,7,2,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [4,3,5,1,2,8,7,6] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3,7,8,6] => [2,3,5,4,1,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,7,8,6] => [2,4,5,1,3,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [1,4,7,2,5,8,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,7,3,8,6] => [1,5,7,4,2,8,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,8,6] => [1,3,7,4,5,8,2,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,7,8,3,6] => [2,4,6,1,5,8,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,7,8,3,6] => [1,5,6,4,2,8,7,3] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,7,8,2,3,6] => [1,3,6,4,5,8,7,2] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,8,3,6,7] => [4,5,6,1,2,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,8,3,6,7] => [2,5,6,4,1,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,8,2,3,6,7] => [4,3,6,1,5,7,8,2] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [4,5,8,1,2,3,6,7] => [2,3,6,4,5,7,8,1] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,8,6,7] => [2,4,5,1,3,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,4,5,2,3,7,8,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [1,3,5,4,2,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,8,2,3,6,7] => [1,3,6,4,5,7,8,2] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,8,7] => [2,3,5,4,1,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,8,7] => [2,4,6,1,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,8,7] => [1,3,6,4,5,2,8,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [2,4,7,1,5,6,8,3] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,5,6,8,3,7] => [1,4,7,2,5,6,8,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,5,2,6,8,3,7] => [1,5,7,4,2,6,8,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,5,6,2,8,3,7] => [1,6,7,4,5,2,8,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,5,6,8,2,3,7] => [1,3,7,4,5,6,8,2] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => [4,3,5,1,2,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7,8] => [2,3,5,4,1,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7,8] => [2,4,5,1,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7,8] => [1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7,8] => [2,4,6,1,5,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7,8] => [1,4,6,2,5,3,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,5,6,4,2,3,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3,8] => [1,4,7,2,5,6,3,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3,8] => [1,5,7,4,2,6,3,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3,8] => [1,6,7,4,5,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3,8] => [1,3,7,4,5,6,2,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,8,3] => [2,4,8,1,5,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,3] => [1,4,8,2,5,6,7,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,5,2,6,7,8,3] => [1,5,8,4,2,6,7,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,5,6,2,7,8,3] => [1,6,8,4,5,2,7,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,5,6,7,2,8,3] => [1,7,8,4,5,6,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,5,6,7,8,2,3] => [1,3,8,4,5,6,7,2] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5] => [4,6,7,1,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,6,1,2,7,3,8,5] => [2,6,7,4,8,1,3,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,6,1,7,2,3,8,5] => [6,3,7,4,8,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,6,1,2,7,8,3,5] => [2,6,5,4,8,1,7,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,6,1,7,2,8,3,5] => [6,7,5,4,8,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,6,7,1,2,8,3,5] => [2,7,5,4,8,6,1,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,6,7,8,2,3,5] => [4,3,5,1,8,6,7,2] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,6,1,7,8,2,3,5] => [6,3,5,4,8,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [7,3,5,4,8,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [2,3,5,4,8,6,7,1] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5,8] => [4,6,5,1,7,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5,8] => [2,6,5,4,7,1,3,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5,8] => [6,3,5,4,7,1,2,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5,8] => [4,3,6,1,7,2,5,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [2,3,6,4,7,1,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5,8] => [1,4,6,2,7,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5,8] => [1,3,6,4,7,2,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5,8] => [2,4,5,1,7,6,3,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5,8] => [1,6,5,4,7,2,3,8] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [1,3,5,4,7,6,2,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [4,3,6,1,8,2,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,8,5] => [2,4,6,1,8,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,3,7,8,5] => [1,4,6,2,8,3,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,6,2,3,7,8,5] => [1,3,6,4,8,2,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,6,7,3,8,5] => [1,4,7,2,8,6,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,2,7,3,8,5] => [1,6,7,4,8,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,8,5] => [1,3,7,4,8,6,2,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,6,7,8,3,5] => [1,4,5,2,8,6,7,3] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,6,2,7,8,3,5] => [1,6,5,4,8,2,7,3] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,6,7,2,8,3,5] => [1,7,5,4,8,6,2,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,8,3,5,7] => [2,6,5,4,7,1,8,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,8,2,3,5,7] => [4,3,5,1,7,6,8,2] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,8,2,3,5,7] => [6,3,5,4,7,1,8,2] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,8,1,2,3,5,7] => [2,3,5,4,7,6,8,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,8,5,7] => [4,3,6,1,7,2,8,5] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [2,4,6,1,7,3,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,4,6,2,7,3,8,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [1,3,6,4,7,2,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [1,3,5,4,7,6,8,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,8,7] => [4,3,5,1,6,2,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,8,7] => [2,4,5,1,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,8,7] => [1,4,5,2,6,3,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7] => [2,3,4,1,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7] => [1,3,4,2,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,8,5,7] => [2,3,4,1,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,8,5,7] => [1,3,4,2,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,8,5,7] => [1,2,4,3,7,6,8,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,8,5,7] => [1,2,6,4,7,3,8,5] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,8,3,5,7] => [1,2,5,4,7,6,8,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [4,3,5,1,6,2,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7,8] => [2,3,5,4,6,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7,8] => [2,4,5,1,6,3,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7,8] => [1,4,5,2,6,3,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7,8] => [2,3,4,1,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5,8] => [2,3,4,1,7,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5,8] => [1,2,6,4,7,3,5,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,6,7,8,5] => [2,3,4,1,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,6,7,8,5] => [1,3,4,2,8,6,7,5] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,6,7,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,6,3,7,8,5] => [1,2,6,4,8,3,7,5] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,6,7,3,8,5] => [1,2,7,4,8,6,3,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,6,7,8,3,5] => [1,2,5,4,8,6,7,3] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,7,2,8,3,5,6] => [4,7,5,1,6,8,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,7,8,2,3,5,6] => [4,3,5,1,6,8,7,2] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,7,1,8,2,3,5,6] => [7,3,5,4,6,8,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,7,2,3,8,5,6] => [4,3,7,1,6,8,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,7,3,8,5,6] => [2,4,7,1,6,8,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,2,7,3,8,5,6] => [1,4,7,2,6,8,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,7,2,3,8,5,6] => [1,3,7,4,6,8,2,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,7,8,3,5,6] => [2,4,5,1,6,8,7,3] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,7,8,3,5,6] => [1,4,5,2,6,8,7,3] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,7,2,3,5,8,6] => [4,3,5,1,7,8,2,6] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,2,7,3,5,8,6] => [2,4,5,1,7,8,3,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,2,7,3,5,8,6] => [1,4,5,2,7,8,3,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,7,2,3,5,8,6] => [1,3,5,4,7,8,2,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,2,3,7,5,8,6] => [2,3,4,1,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,2,3,7,5,8,6] => [1,3,4,2,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,4,3,7,5,8,6] => [1,2,4,3,7,8,5,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,8,6] => [1,2,5,4,7,8,3,6] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,3,7,8,5,6] => [2,3,4,1,6,8,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,3,7,8,5,6] => [1,3,4,2,6,8,7,5] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [1,2,4,3,6,8,7,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,4,7,8,3,5,6] => [1,2,5,4,6,8,7,3] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6,8] => [2,3,5,4,6,7,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6,8] => [1,4,5,2,6,7,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => [2,3,4,1,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6,8] => [1,3,4,2,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6,8] => [1,2,4,3,6,7,5,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [1,2,5,4,6,7,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6,8] => [2,3,4,1,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6,8] => [1,3,4,2,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,8,6] => [2,3,4,1,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,7,8,6] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,4,5,7,3,8,6] => [1,2,7,4,5,8,3,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,8,2,3,5,6,7] => [4,3,5,1,6,7,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,8,1,2,3,5,6,7] => [2,3,5,4,6,7,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,8,3,5,6,7] => [2,4,5,1,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,4,2,8,3,5,6,7] => [1,4,5,2,6,7,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,3,8,5,6,7] => [2,3,4,1,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,4,2,3,8,5,6,7] => [1,3,4,2,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [1,2,4,3,6,7,8,5] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [1,2,5,4,6,7,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,2,3,5,8,6,7] => [2,3,4,1,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,3,4,2,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,4,3,5,8,6,7] => [1,2,4,3,5,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,4,5,3,8,6,7] => [1,2,5,4,3,7,8,6] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,4,5,8,3,6,7] => [1,2,6,4,5,7,8,3] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [2,3,4,1,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,8,7] => [1,3,4,2,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,8,7] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,4,5,6,8,3,7] => [1,2,7,4,5,6,8,3] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8] => [1,3,4,2,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7,8] => [1,2,6,4,5,3,7,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [5,6,1,2,7,3,8,4] => [2,6,7,8,5,1,3,4] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,6,7,2,3,8,4] => [5,3,7,8,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [5,6,1,7,2,3,8,4] => [6,3,7,8,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,1,2,3,8,4] => [2,3,7,8,5,6,1,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [5,1,6,2,7,8,3,4] => [5,6,4,8,1,2,7,3] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,6,1,2,7,8,3,4] => [2,6,4,8,5,1,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [5,1,6,7,2,8,3,4] => [5,7,4,8,1,6,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [5,6,1,7,2,8,3,4] => [6,7,4,8,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,6,7,1,2,8,3,4] => [2,7,4,8,5,6,1,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,1,6,7,8,2,3,4] => [5,3,4,8,1,6,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [5,6,1,7,8,2,3,4] => [6,3,4,8,5,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [7,3,4,8,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [2,3,4,8,5,6,7,1] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4,8] => [5,6,4,7,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4,8] => [2,3,4,7,5,6,1,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4,8] => [5,3,6,7,1,2,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4,8] => [1,5,6,7,2,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4,8] => [1,3,6,7,5,2,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4,8] => [1,5,4,7,2,6,3,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4,8] => [1,6,4,7,5,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [5,3,6,8,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [5,6,1,2,3,7,8,4] => [2,3,6,8,5,1,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [5,1,2,6,3,7,8,4] => [2,5,6,8,1,3,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [1,5,6,8,2,3,7,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,5,6,2,3,7,8,4] => [1,3,6,8,5,2,7,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,8,4] => [2,5,7,8,1,6,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,5,2,6,7,3,8,4] => [1,5,7,8,2,6,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,5,6,2,7,3,8,4] => [1,6,7,8,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,8,4] => [1,3,7,8,5,6,2,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,5,2,6,7,8,3,4] => [1,5,4,8,2,6,7,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [1,6,4,8,5,2,7,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,5,6,7,2,8,3,4] => [1,7,4,8,5,6,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,5,6,7,8,2,3,4] => [1,3,4,8,5,6,7,2] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,6,2,8,3,4,7] => [5,6,4,7,1,2,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,6,8,1,2,3,4,7] => [2,3,4,7,5,6,8,1] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,8,4,7] => [5,3,6,7,1,2,8,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,8,4,7] => [2,3,6,7,5,1,8,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,8,4,7] => [2,5,6,7,1,3,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,8,4,7] => [1,5,6,7,2,3,8,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [1,3,6,7,5,2,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,8,3,4,7] => [1,5,4,7,2,6,8,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,8,7] => [2,5,4,6,1,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,8,7] => [2,3,5,6,1,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,8,7] => [1,3,5,6,2,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,8,7] => [1,2,5,6,3,4,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,8,4,7] => [1,2,5,7,3,6,8,4] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,8,4,7] => [1,2,6,7,5,3,8,4] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,2,5,6,8,3,4,7] => [1,2,4,7,5,6,8,3] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7,8] => [2,3,4,6,5,1,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7,8] => [2,5,4,6,1,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7,8] => [1,5,4,6,2,3,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7,8] => [2,3,5,6,1,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7,8] => [1,3,5,6,2,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7,8] => [1,2,5,6,3,4,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,2,4,6,5,3,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4,8] => [1,3,5,7,2,6,4,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4,8] => [1,2,5,7,3,6,4,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4,8] => [1,2,6,7,5,3,4,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,6,7,8,4] => [2,3,5,8,1,6,7,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,6,7,8,4] => [1,3,5,8,2,6,7,4] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,2,5,3,6,7,8,4] => [1,2,5,8,3,6,7,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,2,5,6,3,7,8,4] => [1,2,6,8,5,3,7,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,2,5,6,7,3,8,4] => [1,2,7,8,5,6,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,5,6,7,8,3,4] => [1,2,4,8,5,6,7,3] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,7,2,8,3,4,6] => [5,7,4,6,1,8,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,7,1,2,8,3,4,6] => [2,7,4,6,5,8,1,3] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,7,8,1,2,3,4,6] => [2,3,4,6,5,8,7,1] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,7,1,2,3,8,4,6] => [2,3,7,6,5,8,1,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,5,7,6,2,8,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,5,7,2,3,8,4,6] => [1,3,7,6,5,8,2,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [1,7,4,6,5,8,2,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [2,3,4,7,5,8,1,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,7,3,4,8,6] => [2,5,4,7,1,8,3,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,7,3,4,8,6] => [1,5,4,7,2,8,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,5,7,2,3,4,8,6] => [1,3,4,7,5,8,2,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,7,4,8,6] => [2,3,5,7,1,8,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,7,4,8,6] => [1,3,5,7,2,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,7,4,8,6] => [1,2,5,7,3,8,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,7,8,4,6] => [1,2,5,6,3,8,7,4] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,7,3,8,4,6] => [1,2,7,6,5,8,3,4] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,7,8,3,4,6] => [1,2,4,6,5,8,7,3] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6,8] => [2,3,4,6,5,7,1,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6,8] => [2,5,4,6,1,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6,8] => [1,5,4,6,2,7,3,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6,8] => [1,3,4,6,5,7,2,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6,8] => [2,3,5,6,1,7,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6,8] => [1,3,5,6,2,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6,8] => [1,2,5,6,3,7,4,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [1,2,4,6,5,7,3,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6,8] => [2,3,4,5,1,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6,8] => [1,3,4,5,2,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6,8] => [1,2,4,5,3,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,8] => [1,2,3,6,5,7,4,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,8,6] => [2,3,4,5,1,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,7,8,6] => [1,3,4,5,2,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,7,8,6] => [1,2,4,5,3,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,7,4,8,6] => [1,2,3,7,5,8,4,6] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,7,8,4,6] => [1,2,3,6,5,8,7,4] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,8,1,2,3,4,6,7] => [2,3,4,6,5,7,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,8,3,4,6,7] => [2,5,4,6,1,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,5,2,8,3,4,6,7] => [1,5,4,6,2,7,8,3] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,5,8,2,3,4,6,7] => [1,3,4,6,5,7,8,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,3,8,4,6,7] => [2,3,5,6,1,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,5,2,3,8,4,6,7] => [1,3,5,6,2,7,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [1,2,5,6,3,7,8,4] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,2,3,4,8,6,7] => [2,3,4,5,1,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,3,4,5,2,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,2,5,3,4,8,6,7] => [1,2,4,5,3,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,7,8,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,5,8,4,6,7] => [1,2,3,6,5,7,8,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [2,3,4,5,1,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,5,6,8,4,7] => [1,2,3,7,5,6,8,4] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7,8] => [1,3,4,5,2,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7,8] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,5] => [6,7,4,5,8,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [6,1,7,8,2,3,4,5] => [6,3,4,5,8,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,7,1,8,2,3,4,5] => [7,3,4,5,8,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [2,3,4,5,8,6,7,1] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,7,1,2,3,8,4,5] => [2,3,7,5,8,6,1,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [6,1,2,7,3,8,4,5] => [2,6,7,5,8,1,3,4] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,5] => [1,6,7,5,8,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,6,7,2,3,8,4,5] => [1,3,7,5,8,6,2,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [6,1,2,7,8,3,4,5] => [2,6,4,5,8,1,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,3,4,5,8,6,7,2] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,7,1,2,3,4,8,5] => [2,3,4,7,8,6,1,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,6,2,7,3,4,8,5] => [1,6,4,7,8,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [6,1,2,3,7,4,8,5] => [2,3,6,7,8,1,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,6,2,3,7,4,8,5] => [1,3,6,7,8,2,4,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,3,7,4,8,5] => [1,2,6,7,8,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,8,5] => [1,2,4,7,8,6,3,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [1,2,6,5,8,3,7,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,7,3,8,4,5] => [1,2,7,5,8,6,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,7,8,3,4,5] => [1,2,4,5,8,6,7,3] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5,8] => [6,3,4,5,7,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5,8] => [2,3,4,5,7,6,1,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5,8] => [2,6,4,5,7,1,3,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5,8] => [1,6,4,5,7,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5,8] => [1,3,4,5,7,6,2,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5,8] => [1,3,6,5,7,2,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5,8] => [2,3,4,6,7,1,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5,8] => [1,3,4,6,7,2,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,8] => [1,2,3,6,7,4,5,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5,8] => [1,2,3,5,7,6,4,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,8,5] => [2,3,4,6,8,1,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,7,8,5] => [1,2,4,6,8,3,7,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,7,8,5] => [1,2,3,6,8,4,7,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,2,3,6,7,4,8,5] => [1,2,3,7,8,6,4,5] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,6,7,8,4,5] => [1,2,3,5,8,6,7,4] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,8,2,3,4,5,7] => [6,3,4,5,7,1,8,2] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,8,1,2,3,4,5,7] => [2,3,4,5,7,6,8,1] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,8,3,4,5,7] => [2,6,4,5,7,1,8,3] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,6,2,8,3,4,5,7] => [1,6,4,5,7,2,8,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,6,8,2,3,4,5,7] => [1,3,4,5,7,6,8,2] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [1,2,6,5,7,3,8,4] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [1,3,4,6,7,2,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,8,5,7] => [1,2,3,6,7,4,8,5] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,8,4,5,7] => [1,2,3,5,7,6,8,4] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [2,3,4,5,6,1,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,8,7] => [1,3,4,5,6,2,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,8,7] => [1,2,4,5,6,3,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,8,7] => [1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7] => [1,2,3,4,7,6,8,5] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7,8] => [1,3,4,5,6,2,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7,8] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6] => [7,3,4,5,6,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [2,3,4,5,6,8,7,1] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,8,3,4,5,6] => [2,7,4,5,6,8,1,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,7,2,8,3,4,5,6] => [1,7,4,5,6,8,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,8,2,3,4,5,6] => [1,3,4,5,6,8,7,2] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1,2,3,8,4,5,6] => [2,3,7,5,6,8,1,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,7,2,3,8,4,5,6] => [1,3,7,5,6,8,2,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [1,2,7,5,6,8,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,2,4,5,6,8,7,3] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1,2,3,4,8,5,6] => [2,3,4,7,6,8,1,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [1,3,4,7,6,8,2,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [1,2,4,7,6,8,3,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,6] => [1,2,3,7,6,8,4,5] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,7,8,4,5,6] => [1,2,3,5,6,8,7,4] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [2,3,4,5,7,8,1,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [1,3,4,5,7,8,2,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,2,7,3,4,5,8,6] => [1,2,4,5,7,8,3,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,2,3,7,4,5,8,6] => [1,2,3,5,7,8,4,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6] => [1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6] => [1,2,3,4,6,8,7,5] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8] => [1,3,4,5,6,7,2,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6,8] => [1,2,4,5,6,7,3,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6,8] => [1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7] => [1,3,4,5,6,7,8,2] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,8,3,4,5,6,7] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [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] => [1,2,3,4,8,5,6,7] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => [2,3,4,5,6,7,8,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => [2,3,4,5,6,7,8,9,1,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [2,3,4,5,6,8,9,1,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8,9] => [2,3,4,5,6,7,1,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,1,8] => [8,2,3,4,5,6,7,9,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [2,3,4,5,6,7,8,9,10,11,12,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9,11] => [2,3,4,5,6,7,8,9,10,1,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [2,3,4,5,6,7,9,10,1,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9,10] => [2,3,4,5,6,7,8,1,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [2,3,4,5,6,7,1,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8,9] => [2,3,4,5,6,1,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,9,8] => [7,2,3,4,5,6,1,9,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,8,9,1,7] => [7,2,3,4,5,6,9,8,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,10,1,9] => [9,2,3,4,5,6,7,8,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,11,9] => [2,3,4,5,6,7,8,10,11,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => [2,3,4,5,6,7,8,1,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [2,3,4,5,7,8,1,9,6] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,9,6] => [2,3,4,5,7,9,1,8,6] => [[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,9,7] => [8,2,3,4,5,6,9,1,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,7,8,9,1,6] => [6,2,3,4,5,9,7,8,1] => [[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,10,1,8] => [8,2,3,4,5,6,7,10,9,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,11,1,10] => [10,2,3,4,5,6,7,8,9,11,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,11,10] => [2,3,4,5,6,7,8,9,1,11,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,10,7,9] => [2,3,4,5,6,8,9,1,10,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1,2,3,9,4,5,6,7] => [2,3,8,5,6,7,9,1,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,9,7,8] => [2,3,4,5,6,1,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,9,7] => [2,3,4,5,6,1,9,8,7] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,9,7,8] => [6,2,3,4,5,1,8,9,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,1,10,8] => [9,2,3,4,5,6,7,10,1,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,6,7,8,9,1,5] => [5,2,3,4,9,6,7,8,1] => [[[.,.],[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,8,9,10,1,7] => [7,2,3,4,5,6,10,8,9,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,1,2,3,4,10,5,6,7,8] => [2,3,4,9,6,7,8,10,1,5] => [[.,.],[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7,9] => [2,3,4,5,6,1,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [2,3,4,5,6,7,9,8,1] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [2,9,3,4,5,6,7,8,1] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,6,7,8,9,1,4] => [4,2,3,9,5,6,7,8,1] => [[[.,.],[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,7,8,9,10,1,6] => [6,2,3,4,5,10,7,8,9,1] => [[[.,.],[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [5,1,2,3,4,9,6,7,8] => [2,3,4,5,1,7,8,9,6] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,9,1,2,3,4,5,6,8] => [2,3,4,5,6,8,7,9,1] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,9,2] => [8,9,3,4,5,6,7,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,1,3] => [3,2,9,4,5,6,7,8,1] => [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,6,7,8,9,10,1,5] => [5,2,3,4,10,6,7,8,9,1] => [[[.,.],[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,10,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6,9] => [2,3,4,5,6,8,7,1,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [6,9,1,2,3,4,5,7,8] => [2,3,4,5,7,6,8,9,1] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,9,2] => [7,9,3,4,5,6,1,8,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => [2,8,3,4,5,6,7,1,9] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,9,3] => [8,2,9,4,5,6,7,1,3] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [2,10,3,4,5,6,7,8,9,1] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,5,6,7,8,9,10,1,4] => [4,2,3,10,5,6,7,8,9,1] => [[[.,.],[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,1,10,2,3,4,5,6,7,8] => [9,3,4,5,6,7,8,10,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6,9] => [7,3,4,5,6,8,1,2,9] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [4,1,2,3,9,5,6,7,8] => [2,3,4,1,6,7,8,9,5] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,9,7,8] => [2,1,3,4,5,6,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [5,9,1,2,3,4,6,7,8] => [2,3,4,6,5,7,8,9,1] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,10,2] => [9,10,3,4,5,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,10,1,3] => [3,2,10,4,5,6,7,8,9,1] => [[[.,.],.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[] => [] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,7,9,2,4,6,8] => [1,4,3,6,5,8,7,9,2] => [.,[[[.,.],.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,3,9,2,4,5,6,7,8] => [1,4,3,5,6,7,8,9,2] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,9,2,8] => [1,8,3,4,5,6,7,9,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,3,4,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,9,8] => [1,4,5,2,3,7,6,9,8] => [.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,9,3] => [1,4,9,2,5,6,7,8,3] => [.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,5,6,7,8,9,2,3] => [1,3,9,4,5,6,7,8,2] => [.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7,9] => [1,3,4,2,6,5,8,7,9] => [.,[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [1,2,5,4,6,7,8,9,3] => [.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [1,2,3,6,5,7,8,9,4] => [.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7,8,9] => [1,3,4,5,2,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,9,5] => [1,6,7,8,9,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,6,5,8,7,9] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,9,5,7,8] => [1,2,3,4,7,6,8,9,5] => [.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7,8,9] => [1,2,4,5,6,3,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,9,6] => [1,2,3,7,8,9,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6,9] => [1,2,3,4,7,8,5,6,9] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,9,6] => [1,2,3,4,7,9,5,8,6] => [.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [1,7,9,2,3,4,5,6,8] => [1,3,4,5,6,8,7,9,2] => [.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,9,8] => [1,3,4,5,6,7,2,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,9,6,8] => [1,2,3,4,5,8,7,9,6] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8,9] => [1,3,4,5,6,7,2,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,8,2,9,3,4,5,6,7] => [1,8,4,5,6,7,9,2,3] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,8,9,2,3,4,5,6,7] => [1,3,4,5,6,7,9,8,2] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,8,9,5,6,7] => [1,2,3,4,6,7,9,8,5] => [.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,9,7] => [1,3,4,5,6,8,9,2,7] => [.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,9,7] => [1,2,3,4,5,8,9,6,7] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,8,9,6,7] => [1,2,3,4,5,7,9,8,6] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [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] => [1,2,3,8,4,5,6,7,9] => [1,2,3,5,6,7,8,4,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,7,9] => [1,2,3,4,5,7,8,6,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8] => [1,3,4,5,6,7,8,9,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,9,3,4,5,6,7,8] => [1,2,4,5,6,7,8,9,3] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [1,2,3,5,6,7,8,9,4] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [1,2,3,4,6,7,8,9,5] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => [1,2,3,4,5,7,8,9,6] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,8,9,7] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [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] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => [3,2,4,1,6,5,8,7,9] => [[[.,.],.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,9] => [4,2,5,1,6,3,8,7,9] => [[[.,.],[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,9] => [4,2,6,1,7,3,8,5,9] => [[[.,.],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7] => [4,2,6,1,8,3,9,5,7] => [[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,9,8] => [4,2,6,1,7,3,5,9,8] => [[[.,.],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,9,8] => [4,2,5,1,3,7,6,9,8] => [[[.,.],[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,9,8] => [3,2,1,5,4,7,6,9,8] => [[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9] => [3,2,4,1,6,5,8,7,10,9] => [[[.,.],.],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7,9] => [3,2,5,4,6,1,8,7,9] => [[[.,.],.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,10,9] => [4,2,5,1,6,3,8,7,10,9] => [[[.,.],[.,.]],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7,9] => [4,2,5,1,7,6,8,3,9] => [[[.,.],[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,10,9] => [4,2,6,1,7,3,8,5,10,9] => [[[.,.],[.,.]],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,8,9,5,7] => [4,2,6,1,7,3,9,8,5] => [[[.,.],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [4,2,6,1,8,3,9,5,10,7] => [[[.,.],[.,.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8,9] => [4,2,6,1,7,3,5,8,9] => [[[.,.],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7,10] => [4,2,6,1,8,3,9,5,7,10] => [[[.,.],[.,.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,8,6,9,7] => [4,2,5,1,3,8,9,6,7] => [[[.,.],[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,9,8,10] => [4,2,6,1,7,3,5,9,8,10] => [[[.,.],[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5,9,8] => [3,2,1,6,7,4,5,9,8] => [[[.,.],.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [4,2,5,1,3,7,6,9,8,10] => [[[.,.],[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,1,5,4,7,6,9,8,10] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [1,3,2,5,4,7,6,9,8,11,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7,8,9] => [4,2,5,1,3,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [3,2,5,4,7,6,9,8,10,1] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,9,5,10] => [1,6,7,8,9,2,3,4,5,10] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [2,3,1,9,4,5,6,7,8] => [3,2,1,5,6,7,8,9,4] => [[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => [1,3,4,2,6,5,8,7,10,9] => [.,[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => [2,1,4,3,6,5,7,8,9] => [[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,4,5,6,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,6,7,8,9,3,4] => [2,1,4,9,5,6,7,8,3] => [[.,.],[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,1,9,3,4,5,6,7,8] => [2,1,4,5,6,7,8,9,3] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,9,1,3,4,5,6,7,8] => [3,2,4,5,6,7,8,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,9] => [3,4,1,2,6,5,8,7,9] => [[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,4,8,9,2,5,6,7] => [3,5,1,4,6,7,9,8,2] => [[.,[.,.]],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,2] => [3,9,1,4,5,6,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7,8,9] => [4,5,6,1,2,3,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7,8,9] => [2,3,6,4,5,1,7,8,9] => [[.,.],[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [2,3,9,4,5,6,7,8,1] => [[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,9] => [5,6,7,8,1,2,3,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [2,3,4,8,5,6,7,1,9] => [[.,.],[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [2,3,4,9,5,6,7,8,1] => [[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [2,3,4,5,9,6,7,8,1] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [2,3,4,5,6,9,7,8,1] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => [2,1,4,3,6,5,8,7,9,10] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,8,10,9,7] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,10,7,8,9] => [2,1,4,3,6,5,8,9,10,7] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,1,4,3,10,5,6,7,8,9] => [2,1,4,3,6,7,8,9,10,5] => [[.,.],[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,8,7,10,9] => [2,1,4,6,5,3,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4,9,10,7,8] => [2,1,4,6,5,3,8,10,9,7] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => [3,2,4,5,6,10,7,8,9,1] => [[[.,.],.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,1,10,3,4,5,6,7,8,9] => [2,1,4,5,6,7,8,9,10,3] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,10,1,3,4,5,6,7,8,9] => [3,2,4,5,6,7,8,9,10,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [3,4,1,2,6,5,8,7,10,9] => [[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7,10,9] => [2,4,3,1,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,6,8,10,1,2,5,7,9] => [2,5,3,4,7,6,9,8,10,1] => [[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6,10,9] => [2,4,3,1,6,8,7,5,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,8,9,10,5,6,7] => [2,4,3,1,6,7,10,8,9,5] => [[.,.],[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9,10] => [3,4,1,2,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8,9,10] => [2,4,3,1,5,6,7,8,9,10] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [3,10,1,4,5,6,7,8,9,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,9,10,7,8] => [2,3,6,4,5,1,8,10,9,7] => [[.,.],[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [2,3,6,4,5,1,7,8,9,10] => [[.,.],[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [2,3,10,4,5,6,7,8,9,1] => [[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4,10,9] => [2,3,4,8,5,6,7,1,10,9] => [[.,.],[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [2,3,4,8,5,6,7,1,9,10] => [[.,.],[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [2,3,4,10,5,6,7,8,9,1] => [[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [6,7,8,9,10,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [2,3,4,5,10,6,7,8,9,1] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [2,3,4,5,6,10,7,8,9,1] => [[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [2,3,4,5,6,7,10,8,9,1] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7,9] => [3,5,1,6,2,4,8,7,9] => [[.,[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,9,8] => [3,4,1,5,2,7,6,9,8] => [[.,[.,.]],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [2,3,1,5,4,7,6,9,8] => [[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => [2,3,1,5,4,7,6,9,8,10] => [[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,9,10,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,10,8] => [1,2,3,4,5,6,9,10,7,8] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [1,2,3,4,5,6,7,8,10,11,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => [2,3,4,1,6,5,8,7,9] => [[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,3,4,5,6,7,8,9,2] => [.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,10,2,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,10,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [1,3,4,5,6,7,8,9,10,11,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8,10] => [1,3,4,5,6,7,8,9,2,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7] => [.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6] => [.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5] => [.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4] => [.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3] => [.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,8,7,9] => [2,3,1,4,6,5,8,7,9] => [[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [1,3,2,5,4,7,6,9,10,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [1,2,4,5,6,7,8,9,10,3] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [1,2,3,5,6,7,8,9,10,4] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [1,2,3,4,6,7,8,9,10,5] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [1,2,3,4,5,7,8,9,10,6] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [1,2,3,4,5,6,8,9,10,7] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,9,8] => [.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5,7,9,10,2,4,6,8] => [1,4,3,6,5,8,7,10,9,2] => [.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,10,7,8] => [1,2,3,4,5,6,8,10,9,7] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,9,10,6,7,8] => [1,2,3,4,5,7,8,10,9,6] => [.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9] => [[.,.],[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7,10,9] => [2,3,4,5,6,1,8,7,10,9] => [[.,.],[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [1,12,2,3,4,5,6,7,8,9,10,11] => [1,3,4,5,6,7,8,9,10,11,12,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,11,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,6,5,8,7,10,9] => [.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,9,3] => [7,8,9,4,5,6,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,6,7,1,8,2,9,3,10,4] => [7,8,9,10,5,6,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,8,10] => [1,2,3,4,5,6,8,9,7,10] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,1,10,3] => [9,2,10,4,5,6,7,8,1,3] => [[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9,10,11] => [2,3,1,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2,9] => [3,8,1,4,5,6,7,2,9] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [1,3,4,5,6,7,8,10,9,2] => [.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7,8,9,10] => [1,2,4,5,6,3,7,8,9,10] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,9,1,2,3,4,5,8] => [2,3,4,5,8,6,7,9,1] => [[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,3,9,1,4,5,6,7,8] => [4,2,3,5,6,7,8,9,1] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7,9] => [3,2,4,5,6,7,8,1,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7,9] => [2,1,4,5,6,7,8,3,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6,11,12,9,10] => [2,4,3,1,6,8,7,5,10,12,11,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8,9,10] => [1,3,4,2,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,10,11,2] => [3,11,1,4,5,6,7,8,9,10,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7,9,12,10,11] => [1,3,4,2,5,7,8,6,9,11,12,10] => [.,[[.,.],[.,[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [3,1,2,9,4,5,6,7,8] => [2,3,1,5,6,7,8,9,4] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7,8,9] => [3,2,1,5,4,6,7,8,9] => [[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,11,1,3,4,5,6,7,8,9,10] => [3,2,4,5,6,7,8,9,10,11,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7,12,8,9,10,11] => [1,3,2,4,6,5,7,9,10,11,12,8] => [.,[[.,.],[.,[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,9,10,2] => [8,10,3,4,5,6,7,1,9,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [1,2,3,5,4,10,6,7,8,9] => [1,2,3,5,4,7,8,9,10,6] => [.,[.,[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
searching the database
Sorry, this map was not found in the database.