Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
[1,0] => [1] => [.,.]
[1,0,1,0] => [2,1] => [[.,.],.]
[1,1,0,0] => [1,2] => [.,[.,.]]
[1,0,1,0,1,0] => [3,2,1] => [[[.,.],.],.]
[1,0,1,1,0,0] => [2,3,1] => [[.,[.,.]],.]
[1,1,0,0,1,0] => [3,1,2] => [[.,.],[.,.]]
[1,1,0,1,0,0] => [2,1,3] => [[.,.],[.,.]]
[1,1,1,0,0,0] => [1,2,3] => [.,[.,[.,.]]]
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [[[[.,.],.],.],.]
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [[[.,[.,.]],.],.]
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [[[.,.],[.,.]],.]
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [[[.,.],[.,.]],.]
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[.,[.,[.,.]]],.]
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [[[.,.],.],[.,.]]
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]]
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [[[.,.],.],[.,.]]
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [[[.,.],.],[.,.]]
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [[.,[.,.]],[.,.]]
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[.,.],[.,[.,.]]]
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [[.,.],[.,[.,.]]]
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [[[[.,[.,.]],.],.],.]
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [[[[.,.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [[[[.,.],[.,.]],.],.]
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [[[.,[.,[.,.]]],.],.]
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [[[[.,.],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [[[.,[.,.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [[[[.,.],.],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [[[.,[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [[[[.,.],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [[[.,.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [[[.,.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[.,[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [[[[.,.],.],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [[[.,[.,.]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [[[[.,.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [[[.,[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [[[[[.,[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [[[[[.,.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [[[[[.,.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [[[[.,[.,[.,.]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [[[[.,[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [[[[[.,.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [[[[.,[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [[[[.,.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[[[.,.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [[[.,[.,[.,[.,.]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [[[[[.,.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [[[[.,[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [[[.,[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [[[[[.,.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [[[[.,[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [[[[[.,.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [[[[.,[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [[[.,[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [[[.,[.,.]],[.,[.,.]]],.]
>>> Load all 2098 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [[[[[.,.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [[[.,[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [[[[[.,.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [[[[.,[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [[[.,[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [[[[[.,.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [[[[.,[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [[[[[.,.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [[[[.,[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [[[.,[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [[[[[[.,[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [[[[[.,[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[[[.,[.,[.,[.,.]]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,1,3] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,1,7,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,1,5,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,2,3,4,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[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] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[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] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[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] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,1,3,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,1,4,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [9,4,1,2,3,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,1,5,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [12,2,1,3,4,5,6,7,8,9,10,11] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [11,3,1,2,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [10,4,1,2,3,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,1,5,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [9,3,4,1,2,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,1,6,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,1] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,10,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,1,6,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [9,6,1,2,3,4,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [6,2,3,4,5,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,3,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,10,1] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [10,6,1,2,3,4,5,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,1,7,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[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] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,7,8,9,1] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [10,7,1,2,3,4,5,6,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,1,8,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,1,3,4,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,6,7,8,9,10,1] => [[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,1,2] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[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] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,4,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [5,3,4,6,7,8,9,1,2] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [4,5,3,6,7,8,9,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[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] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [9,3,4,2,5,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [6,5,4,2,3,7,8,9,1] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,6,7,2,3,4,8,9,1] => [[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,3,5,6,7,8,9,10,1,2] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[] => [] => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8,6,7,5,4,3,2,1,9] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,7,8,5,4,3,2,1,9] => [[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,7,5,6,4,3,2,1,9] => [[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8,6,5,7,4,3,2,1,9] => [[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7,6,5,8,4,3,2,1,9] => [[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [6,7,5,8,4,3,2,1,9] => [[[[[[.,[.,.]],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [8,5,6,7,4,3,2,1,9] => [[[[[[.,.],[.,[.,.]]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [6,5,7,8,4,3,2,1,9] => [[[[[[.,.],[.,[.,.]]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => [[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => [[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1,9] => [[[[[[.,.],.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,8,2,1,9] => [[[[[[.,.],.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1,9] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,1,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,1,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,1,9] => [[[[[[.,.],.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,3,4,5,6,8,1,2,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,1,3,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1,4,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,2,1,5,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,2,1,6,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1,7,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,4,3,2,1,8,9] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,6,4,3,2,1,7,9] => [[[[[[.,.],[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8,7,4,5,3,2,1,6,9] => [[[[[[.,.],.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8,7,6,3,4,2,1,5,9] => [[[[[[.,.],.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,2,3,1,4,9] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,1,8,9] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,7,1,8,9] => [[[[[.,[.,.]],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,2,3,4,5,6,1,8,9] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1,2,3,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,1,2,8,9] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,6,5,3,2,1,4,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [6,7,4,3,2,1,5,8,9] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,1,7,8,9] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,2,6,1,7,8,9] => [[[[.,.],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [6,2,3,4,5,1,7,8,9] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [8,7,5,3,1,2,4,6,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [7,5,4,3,1,2,6,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,2,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2,1,3,5,7,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,5,3,2,1,6,7,8,9] => [[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8,9] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,1,6,7,8,9] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,2,3,4,1,6,7,8,9] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1,2,4,6,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1,2,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,1,2,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,1,3,6,7,8,9] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,1,4,5,6,7,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,3,1,2,4,5,6,7,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1,2,4,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [8,7,5,6,9,4,3,2,1] => [[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,9,3,2,1] => [[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => [[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,1,2,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,6,9,2,1] => [[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,2,1,3,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,3,2,1,4,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,1,5,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,9,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,4,3,2,1,6,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,9,1] => [[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9,8,6,5,4,3,2,1,7,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,1,2,3,4,5,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,10,1] => [[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,7,6,5,4,3,2,1,8,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,10,1] => [[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,2,1] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,9,6,7,5,4,3,2,1] => [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [9,6,7,8,5,4,3,2,1] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,4,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,3,2,1] => [[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,3,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,3,1] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,2,3,1] => [[[[[[[.,.],.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,2,3,1] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,4,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,5,1] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,3,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,1,2] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,1,2] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,3,1,2] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,1,2] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => [[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [9,8,3,4,5,6,7,1,2] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [8,9,3,4,5,6,7,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => [[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[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] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => [[[[.,.],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => [[[[.,.],.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[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] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [7,8,9,6,1,2,3,4,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[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] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[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] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [10,8,9,7,6,5,4,3,2,1] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [10,9,8,6,7,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,2,1] => [[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,3,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,3,1] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,4,5,6,2,3,1] => [[[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,2,3,1] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,2,3,4,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [10,9,2,3,4,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,1,2] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => [[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => [[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [10,9,3,4,5,6,7,8,1,2] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [9,10,3,4,5,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,1,2] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]]
[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] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[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] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[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] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[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] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[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] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,1,3] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,1,4] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,1,5] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,3,2,1,6] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,2,1,7] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,1,8] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,1,3] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,1,4] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,1,4] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,3,4,2,1,5] => [[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,1,5] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,3,2,1,6] => [[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,4,3,2,1,6] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [9,8,5,6,4,3,2,1,7] => [[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,4,3,2,1,7] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,6,7,5,4,3,2,1,8] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,2,1,8] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,1,9] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9,10] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,1,2,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1,8,9,10,11] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [6,7,5,4,3,2,1,8,9,10] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,1,2,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [7,6,5,4,3,1,2,8,9,10,11] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,1,2] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10,11] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9,10] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,1,2] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,1,3] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,3,1] => [[[[[[[.,.],[.,.]],.],.],.],[.,.]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,1,3] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,1,7,8] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [9,8,5,4,3,2,1,6,7] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,3,2,1,5,6] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,3,2,1,4,5] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,1,3,4] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,2,1,3,4,5,6,7,8,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [9,8,6,1,2,3,4,5,7] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,1,2,3,4,6] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,1,2,3,5] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,1,2,4] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [8,9,5,4,3,2,1,6,7] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,8,9,1,2] => [[[[[[.,.],.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,7,1,8] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,1,10] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,1,3] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,1,3,4] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,1,3,4,5] => [[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,1,3,4,5,6] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,5,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,5,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [10,9,7,6,8,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [10,8,7,6,9,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [8,9,7,6,4,3,2,1,5] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,5,1,2] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,5,1,10] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,5,2,1,10] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,5,3,2,1,10] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,7,8,9,10,1] => [[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,2,3,8,9,1] => [[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,1,2,8] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,9,6,5,4,3,2,1,7] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [7,8,9,5,4,3,2,1,6] => [[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7,8,9,6,5,4,3,2,1,10] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,3,2,1,5] => [[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7,6,8,9,5,4,3,2,1,10] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,3,2,1,4] => [[[[[.,.],[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,6,5,8,9,4,3,2,1,10] => [[[[[[[.,.],.],[.,[.,.]]],.],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,8,9,2,1,3] => [[[[[.,.],.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,8,9,3,2,1,10] => [[[[[[[.,.],.],.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,8,9,1,2] => [[[[[.,.],.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,8,9,2,1,10] => [[[[[[[.,.],.],.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,1,10] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,3,9,1,2] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,1,6,7] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [5,6,7,4,8,9,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,1,4,5,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,1,2,3,4] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,9,1,2,3,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [7,6,8,9,1,2,3,4,5] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,1,2,3] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,3,4,2,1] => [[[[[[[.,.],.],[.,.]],.],[.,.]],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [9,7,8,5,4,3,2,1,6] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [9,6,7,4,5,2,3,1,8] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [9,10,6,7,4,5,2,3,1,8] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [6,5,7,4,8,3,9,2,10,1] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [10,8,6,4,2,1,3,5,7,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => [[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,7,6,5,4,3,2,1,8,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,5,4,3,2,1,6,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9,10] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[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] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,4,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [11,9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,9,2,1] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,3,4,5,6,7,8,9,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,8,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,2,1,4] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,4,3,2,1,5,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,10,7,6,5,4,3,2,1,8] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,1,2,3,4,7] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [8,7,9,5,6,3,4,1,2] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,2,1,3,4] => [[[[[.,[.,.]],[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,3,4,1,2,5] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,3,2,1,6] => [[[[[.,[.,[.,.]]],[.,.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [8,9,4,5,6,3,2,1,7] => [[[[[.,[.,.]],[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [11,10,1,2,3,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [9,8,4,1,2,3,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,6,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,7,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,2,1,3,4,5,6] => [[[.,[.,[.,[.,.]]]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,9,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,7,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,8,3,2,1] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,7,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,8,2,1] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,3,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [8,9,10,4,5,6,1,2,3,7] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [8,9,5,6,3,4,1,2,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [10,7,8,5,6,3,4,1,2,9] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,1,2,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,8,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,2,1,8] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [9,8,5,4,6,7,3,2,1] => [[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,4,1,5,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,1,5] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [9,8,10,6,7,4,5,2,3,1] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [9,8,5,4,6,3,7,2,1] => [[[[[[[.,.],.],.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9,10] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [10,7,8,6,5,4,3,2,1,9] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,1,4,5] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,1,4] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [9,4,3,5,6,7,8,2,1] => [[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,2,3,10,1] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,3,1,2,4,6,8,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [11,12,9,10,7,8,5,6,3,4,1,2] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [10,8,9,6,5,4,3,2,1,7] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [8,9,5,6,4,3,2,1,7] => [[[[[[.,[.,.]],[.,.]],.],.],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [9,4,5,6,7,8,2,1,3] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,2,1,3,4] => [[[[.,.],[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [11,3,4,5,6,7,8,9,10,1,2] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [10,4,5,6,7,8,9,2,1,3] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [11,8,9,10,1,2,3,4,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [9,7,8,4,3,2,1,5,6] => [[[[[[.,.],[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [10,4,3,5,6,7,8,9,2,1] => [[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,2,4,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,4,5,1,6] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2,11] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5,11] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9,10] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1,10] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,2,1,3,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [12,11,10,9,8,7,6,5,4,2,1,3] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [9,8,4,3,5,6,7,2,1] => [[[[[[.,.],.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,7,8,9,10,1,2] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [8,7,9,10,5,6,2,1,3,4] => [[[[[.,.],[.,[.,.]]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [10,8,6,5,4,3,2,1,7,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [8,9,4,5,6,2,3,1,7] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [6,4,5,7,3,8,2,9,1,10] => [[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8,9,10] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [9,7,5,2,3,1,4,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,2,3,1,4,6,8,10] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [7,8,9,3,4,5,1,2,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [12,10,9,8,7,6,5,4,3,2,1,11] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length 0 to the empty tree, and sending a permutation σ of length n≥1 to a root node with two subtrees L and R by splitting σ at the index σ−1(1), normalizing both sides again to permutations and sending the permutations on the left and on the right of σ−1(1) to the trees L and R, respectively.
This tree is recursively obtained by sending the unique permutation of length 0 to the empty tree, and sending a permutation σ of length n≥1 to a root node with two subtrees L and R by splitting σ at the index σ−1(1), normalizing both sides again to permutations and sending the permutations on the left and on the right of σ−1(1) to the trees L and R, respectively.
searching the database
Sorry, this map was not found in the database.