Identifier
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
[[1]] => [1] => [1] => [.,.]
[[1,2]] => [1,2] => [1,2] => [.,[.,.]]
[[1],[2]] => [2,1] => [2,1] => [[.,.],.]
[[1,2,3]] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]]
[[1,3],[2]] => [2,1,3] => [2,1,3] => [[.,.],[.,.]]
[[1,2],[3]] => [3,1,2] => [3,1,2] => [[.,.],[.,.]]
[[1],[2],[3]] => [3,2,1] => [2,3,1] => [[.,[.,.]],.]
[[1,2,3,4]] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[[1,3,4],[2]] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[[1,2,4],[3]] => [3,1,2,4] => [3,1,2,4] => [[.,.],[.,[.,.]]]
[[1,2,3],[4]] => [4,1,2,3] => [4,1,2,3] => [[.,.],[.,[.,.]]]
[[1,3],[2,4]] => [2,4,1,3] => [4,2,1,3] => [[[.,.],.],[.,.]]
[[1,2],[3,4]] => [3,4,1,2] => [4,1,3,2] => [[.,.],[[.,.],.]]
[[1,4],[2],[3]] => [3,2,1,4] => [2,3,1,4] => [[.,[.,.]],[.,.]]
[[1,3],[2],[4]] => [4,2,1,3] => [2,4,1,3] => [[.,[.,.]],[.,.]]
[[1,2],[3],[4]] => [4,3,1,2] => [3,1,4,2] => [[.,.],[[.,.],.]]
[[1],[2],[3],[4]] => [4,3,2,1] => [2,3,4,1] => [[.,[.,[.,.]]],.]
[[1,2,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[[1,3,4,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[[1,2,4,5],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
[[1,2,3,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]]
[[1,2,3,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]]
[[1,3,5],[2,4]] => [2,4,1,3,5] => [4,2,1,3,5] => [[[.,.],.],[.,[.,.]]]
[[1,2,5],[3,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [[.,.],[[.,.],[.,.]]]
[[1,3,4],[2,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [[[.,.],.],[.,[.,.]]]
[[1,2,4],[3,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [[.,.],[[.,.],[.,.]]]
[[1,2,3],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [[.,.],[.,[[.,.],.]]]
[[1,4,5],[2],[3]] => [3,2,1,4,5] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]]
[[1,3,5],[2],[4]] => [4,2,1,3,5] => [2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]]
[[1,2,5],[3],[4]] => [4,3,1,2,5] => [3,1,4,2,5] => [[.,.],[[.,.],[.,.]]]
[[1,3,4],[2],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]]
[[1,2,4],[3],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [[.,.],[[.,.],[.,.]]]
[[1,2,3],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [[.,.],[.,[[.,.],.]]]
[[1,4],[2,5],[3]] => [3,2,5,1,4] => [5,3,2,1,4] => [[[[.,.],.],.],[.,.]]
[[1,3],[2,5],[4]] => [4,2,5,1,3] => [5,4,1,2,3] => [[[.,.],.],[.,[.,.]]]
[[1,2],[3,5],[4]] => [4,3,5,1,2] => [5,1,4,3,2] => [[.,.],[[[.,.],.],.]]
[[1,3],[2,4],[5]] => [5,2,4,1,3] => [4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]]
[[1,2],[3,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [[.,.],[[[.,.],.],.]]
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]]
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => [2,4,1,5,3] => [[.,[.,.]],[[.,.],.]]
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => [3,1,4,5,2] => [[.,.],[[.,[.,.]],.]]
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]]
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]]
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]]
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [[.,.],[.,[[.,.],[.,.]]]]
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [[[.,.],.],[.,[.,[.,.]]]]
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]]
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [[.,.],[.,[[.,.],[.,.]]]]
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [[.,.],[.,[.,[[.,.],.]]]]
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]]
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => [[.,.],[.,[[.,.],[.,.]]]]
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]]
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => [[.,.],[.,[[.,.],[.,.]]]]
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => [[.,.],[.,[.,[[.,.],.]]]]
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [6,2,1,4,3,5] => [[[.,.],.],[[.,.],[.,.]]]
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [[.,.],[[.,[.,.]],[.,.]]]
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [[[.,.],.],[.,[[.,.],.]]]
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [[.,.],[[.,.],[[.,.],.]]]
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [[.,.],[.,[[.,[.,.]],.]]]
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [5,3,2,1,4,6] => [[[[.,.],.],.],[.,[.,.]]]
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [5,4,1,2,3,6] => [[[.,.],.],[.,[.,[.,.]]]]
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => [[.,.],[[[.,.],.],[.,.]]]
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [4,5,1,2,3,6] => [[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => [[.,.],[[[.,.],.],[.,.]]]
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [6,3,2,1,4,5] => [[[[.,.],.],.],[.,[.,.]]]
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [6,4,1,2,3,5] => [[[.,.],.],[.,[.,[.,.]]]]
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [6,1,4,3,2,5] => [[.,.],[[[.,.],.],[.,.]]]
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [6,5,1,3,2,4] => [[[.,.],.],[[.,.],[.,.]]]
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [6,1,5,2,3,4] => [[.,.],[[.,.],[.,[.,.]]]]
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => [[.,.],[.,[[[.,.],.],.]]]
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [4,6,1,2,3,5] => [[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => [[.,.],[[[.,.],.],[.,.]]]
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [5,6,1,3,2,4] => [[.,[.,.]],[[.,.],[.,.]]]
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [5,1,6,2,3,4] => [[.,.],[[.,.],[.,[.,.]]]]
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => [[.,.],[.,[[[.,.],.],.]]]
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]]
[[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => [2,4,1,5,3,6] => [[.,[.,.]],[[.,.],[.,.]]]
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [3,1,4,5,2,6] => [[.,.],[[.,[.,.]],[.,.]]]
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]]
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]]
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [3,1,4,6,2,5] => [[.,.],[[.,[.,.]],[.,.]]]
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [2,5,1,3,6,4] => [[.,[.,.]],[.,[[.,.],.]]]
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [3,1,5,2,6,4] => [[.,.],[[.,.],[[.,.],.]]]
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [4,1,2,5,6,3] => [[.,.],[.,[[.,[.,.]],.]]]
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [5,6,3,1,2,4] => [[[.,[.,.]],.],[.,[.,.]]]
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [5,6,1,4,2,3] => [[.,[.,.]],[[.,.],[.,.]]]
>>> Load all 1007 entries. <<<
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [5,1,6,4,3,2] => [[.,.],[[[[.,.],.],.],.]]
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [4,6,1,2,5,3] => [[.,[.,.]],[.,[[.,.],.]]]
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => [[.,.],[[[.,.],[.,.]],.]]
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [6,3,4,2,1,5] => [[[[.,.],[.,.]],.],[.,.]]
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [6,3,5,1,2,4] => [[[.,.],[.,.]],[.,[.,.]]]
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [6,4,1,5,2,3] => [[[.,.],.],[[.,.],[.,.]]]
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [6,1,4,5,3,2] => [[.,.],[[[.,[.,.]],.],.]]
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [5,3,6,1,2,4] => [[[.,.],[.,.]],[.,[.,.]]]
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [5,4,1,6,2,3] => [[[.,.],.],[[.,.],[.,.]]]
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [5,1,4,6,3,2] => [[.,.],[[[.,[.,.]],.],.]]
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [4,5,1,2,6,3] => [[.,[.,.]],[.,[[.,.],.]]]
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [4,1,5,3,6,2] => [[.,.],[[[.,.],[.,.]],.]]
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]]
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]]
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]]
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [2,4,1,5,6,3] => [[.,[.,.]],[[.,[.,.]],.]]
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [3,1,4,5,6,2] => [[.,.],[[.,[.,[.,.]]],.]]
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.]
[[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,3,4,5,6,7],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => [4,2,1,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,2,5,6,7],[3,4]] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,3,4,6,7],[2,5]] => [2,5,1,3,4,6,7] => [5,2,1,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => [5,1,3,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3,6,7],[4,5]] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,3,4,5,7],[2,6]] => [2,6,1,3,4,5,7] => [6,2,1,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => [6,1,3,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => [6,1,2,4,3,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[[1,3,4,5,6],[2,7]] => [2,7,1,3,4,5,6] => [7,2,1,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => [7,1,3,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => [7,1,2,4,3,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => [7,1,2,3,5,4,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[[1,4,5,6,7],[2],[3]] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,3,5,6,7],[2],[4]] => [4,2,1,3,5,6,7] => [2,4,1,3,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => [3,1,4,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,3,4,6,7],[2],[5]] => [5,2,1,3,4,6,7] => [2,5,1,3,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => [3,1,5,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => [4,1,2,5,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,3,4,5,7],[2],[6]] => [6,2,1,3,4,5,7] => [2,6,1,3,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => [3,1,6,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => [4,1,2,6,3,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => [5,1,2,3,6,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[[1,3,4,5,6],[2],[7]] => [7,2,1,3,4,5,6] => [2,7,1,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,4,5,6],[3],[7]] => [7,3,1,2,4,5,6] => [3,1,7,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => [4,1,2,7,3,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => [5,1,2,3,7,4,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [6,1,2,3,4,7,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [6,2,1,4,3,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[[1,2,5,7],[3,4,6]] => [3,4,6,1,2,5,7] => [6,1,3,4,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => [6,2,1,3,5,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[[1,2,4,7],[3,5,6]] => [3,5,6,1,2,4,7] => [6,1,3,2,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,2,3,7],[4,5,6]] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => [7,2,1,4,3,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[[1,2,5,6],[3,4,7]] => [3,4,7,1,2,5,6] => [7,1,3,4,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,3,4,6],[2,5,7]] => [2,5,7,1,3,4,6] => [7,2,1,3,5,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[[1,2,4,6],[3,5,7]] => [3,5,7,1,2,4,6] => [7,1,3,2,5,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,2,3,6],[4,5,7]] => [4,5,7,1,2,3,6] => [7,1,2,4,5,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,3,4,5],[2,6,7]] => [2,6,7,1,3,4,5] => [7,2,1,3,4,6,5] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[[1,2,4,5],[3,6,7]] => [3,6,7,1,2,4,5] => [7,1,3,2,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[[1,2,3,5],[4,6,7]] => [4,6,7,1,2,3,5] => [7,1,2,4,3,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [5,3,2,1,4,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [5,4,1,2,3,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,2,6,7],[3,5],[4]] => [4,3,5,1,2,6,7] => [5,1,4,3,2,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => [4,5,1,2,3,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,6,7],[3,4],[5]] => [5,3,4,1,2,6,7] => [4,1,5,3,2,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => [6,3,2,1,4,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[[1,3,5,7],[2,6],[4]] => [4,2,6,1,3,5,7] => [6,4,1,2,3,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => [6,1,4,3,2,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,3,4,7],[2,6],[5]] => [5,2,6,1,3,4,7] => [6,5,1,3,2,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[[1,2,4,7],[3,6],[5]] => [5,3,6,1,2,4,7] => [6,1,5,2,3,4,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3,7],[4,6],[5]] => [5,4,6,1,2,3,7] => [6,1,2,5,4,3,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => [4,6,1,2,3,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,5,7],[3,4],[6]] => [6,3,4,1,2,5,7] => [4,1,6,3,2,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,3,4,7],[2,5],[6]] => [6,2,5,1,3,4,7] => [5,6,1,3,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => [5,1,6,2,3,4,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3,7],[4,5],[6]] => [6,4,5,1,2,3,7] => [5,1,2,6,4,3,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => [7,3,2,1,4,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[[1,3,5,6],[2,7],[4]] => [4,2,7,1,3,5,6] => [7,4,1,2,3,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => [7,1,4,3,2,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,3,4,6],[2,7],[5]] => [5,2,7,1,3,4,6] => [7,5,1,3,2,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => [7,1,5,2,3,4,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => [7,1,2,5,4,3,6] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[[1,3,4,5],[2,7],[6]] => [6,2,7,1,3,4,5] => [7,6,1,3,4,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => [7,1,6,2,4,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => [7,1,2,6,3,4,5] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => [7,1,2,3,6,5,4] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => [4,7,1,2,3,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,5,6],[3,4],[7]] => [7,3,4,1,2,5,6] => [4,1,7,3,2,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,3,4,6],[2,5],[7]] => [7,2,5,1,3,4,6] => [5,7,1,3,2,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => [5,1,7,2,3,4,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3,6],[4,5],[7]] => [7,4,5,1,2,3,6] => [5,1,2,7,4,3,6] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[[1,3,4,5],[2,6],[7]] => [7,2,6,1,3,4,5] => [6,7,1,3,4,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => [6,1,7,2,4,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => [6,1,2,7,3,4,5] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [6,1,2,3,7,5,4] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,4,6,7],[2],[3],[5]] => [5,3,2,1,4,6,7] => [2,3,5,1,4,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,3,6,7],[2],[4],[5]] => [5,4,2,1,3,6,7] => [2,4,1,5,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2,6,7],[3],[4],[5]] => [5,4,3,1,2,6,7] => [3,1,4,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,4,5,7],[2],[3],[6]] => [6,3,2,1,4,5,7] => [2,3,6,1,4,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,3,5,7],[2],[4],[6]] => [6,4,2,1,3,5,7] => [2,4,1,6,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2,5,7],[3],[4],[6]] => [6,4,3,1,2,5,7] => [3,1,4,6,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,3,4,7],[2],[5],[6]] => [6,5,2,1,3,4,7] => [2,5,1,3,6,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[[1,2,4,7],[3],[5],[6]] => [6,5,3,1,2,4,7] => [3,1,5,2,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => [4,1,2,5,6,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,4,5,6],[2],[3],[7]] => [7,3,2,1,4,5,6] => [2,3,7,1,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,3,5,6],[2],[4],[7]] => [7,4,2,1,3,5,6] => [2,4,1,7,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2,5,6],[3],[4],[7]] => [7,4,3,1,2,5,6] => [3,1,4,7,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,3,4,6],[2],[5],[7]] => [7,5,2,1,3,4,6] => [2,5,1,3,7,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[[1,2,4,6],[3],[5],[7]] => [7,5,3,1,2,4,6] => [3,1,5,2,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => [4,1,2,5,7,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,3,4,5],[2],[6],[7]] => [7,6,2,1,3,4,5] => [2,6,1,3,4,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[[1,2,4,5],[3],[6],[7]] => [7,6,3,1,2,4,5] => [3,1,6,2,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => [4,1,2,6,3,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [5,1,2,3,6,7,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [7,3,2,1,5,4,6] => [[[[.,.],.],.],[[.,.],[.,.]]]
[[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [7,4,1,2,5,3,6] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[[1,2,6],[3,5,7],[4]] => [4,3,5,7,1,2,6] => [7,1,4,3,5,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => [7,5,1,2,4,3,6] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[[1,2,6],[3,4,7],[5]] => [5,3,4,7,1,2,6] => [7,1,5,3,4,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => [7,3,2,1,4,6,5] => [[[[.,.],.],.],[.,[[.,.],.]]]
[[1,3,5],[2,6,7],[4]] => [4,2,6,7,1,3,5] => [7,4,1,2,3,6,5] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[[1,2,5],[3,6,7],[4]] => [4,3,6,7,1,2,5] => [7,1,4,3,2,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]]
[[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => [7,5,1,3,2,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]]
[[1,2,4],[3,6,7],[5]] => [5,3,6,7,1,2,4] => [7,1,5,2,3,6,4] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[[1,2,3],[4,6,7],[5]] => [5,4,6,7,1,2,3] => [7,1,2,5,4,6,3] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => [7,6,1,2,3,4,5] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,2,5],[3,4,7],[6]] => [6,3,4,7,1,2,5] => [7,1,6,3,2,4,5] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,3,4],[2,5,7],[6]] => [6,2,5,7,1,3,4] => [7,6,1,3,2,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]]
[[1,2,4],[3,5,7],[6]] => [6,3,5,7,1,2,4] => [7,1,6,2,3,5,4] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[[1,2,3],[4,5,7],[6]] => [6,4,5,7,1,2,3] => [7,1,2,6,4,5,3] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => [6,7,1,2,3,4,5] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,5],[3,4,6],[7]] => [7,3,4,6,1,2,5] => [6,1,7,3,2,4,5] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,3,4],[2,5,6],[7]] => [7,2,5,6,1,3,4] => [6,7,1,3,2,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[[1,2,4],[3,5,6],[7]] => [7,3,5,6,1,2,4] => [6,1,7,2,3,5,4] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => [6,1,2,7,4,5,3] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [5,6,3,1,2,4,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [5,6,1,4,2,3,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => [5,1,6,4,3,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
[[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => [4,6,1,2,5,3,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[[1,2,7],[3,4],[5,6]] => [5,6,3,4,1,2,7] => [4,1,6,3,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [5,7,3,1,2,4,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [5,7,1,4,2,3,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => [5,1,7,4,3,2,6] => [[.,.],[[[[.,.],.],.],[.,.]]]
[[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => [4,7,1,2,5,3,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[[1,2,6],[3,4],[5,7]] => [5,7,3,4,1,2,6] => [4,1,7,3,5,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => [6,7,3,1,4,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => [6,7,1,4,3,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => [6,1,7,4,2,3,5] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => [6,7,1,3,5,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[[1,2,4],[3,6],[5,7]] => [5,7,3,6,1,2,4] => [6,1,7,2,5,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,2,3],[4,6],[5,7]] => [5,7,4,6,1,2,3] => [6,1,2,7,5,4,3] => [[.,.],[.,[[[[.,.],.],.],.]]]
[[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => [4,7,1,2,3,6,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[[1,2,5],[3,4],[6,7]] => [6,7,3,4,1,2,5] => [4,1,7,3,2,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]]
[[1,3,4],[2,5],[6,7]] => [6,7,2,5,1,3,4] => [5,7,1,3,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[[1,2,4],[3,5],[6,7]] => [6,7,3,5,1,2,4] => [5,1,7,2,3,6,4] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => [5,1,2,7,4,6,3] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [6,3,4,2,1,5,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [6,3,5,1,2,4,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [6,4,1,5,2,3,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => [6,1,4,5,3,2,7] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [5,3,6,1,2,4,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [5,4,1,6,2,3,7] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[[1,2,7],[3,5],[4],[6]] => [6,4,3,5,1,2,7] => [5,1,4,6,3,2,7] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => [4,5,1,2,6,3,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[[1,2,7],[3,4],[5],[6]] => [6,5,3,4,1,2,7] => [4,1,5,3,6,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [7,3,4,2,1,5,6] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [7,3,5,1,2,4,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => [7,4,1,5,2,3,6] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => [7,1,4,5,3,2,6] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [7,3,6,1,4,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => [7,4,1,6,3,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]]
[[1,2,5],[3,7],[4],[6]] => [6,4,3,7,1,2,5] => [7,1,4,6,2,3,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [7,5,1,3,6,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[[1,2,4],[3,7],[5],[6]] => [6,5,3,7,1,2,4] => [7,1,5,2,6,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,2,3],[4,7],[5],[6]] => [6,5,4,7,1,2,3] => [7,1,2,5,6,4,3] => [[.,.],[.,[[[.,[.,.]],.],.]]]
[[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [5,3,7,1,2,4,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [5,4,1,7,2,3,6] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[[1,2,6],[3,5],[4],[7]] => [7,4,3,5,1,2,6] => [5,1,4,7,3,2,6] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => [4,5,1,2,7,3,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[[1,2,6],[3,4],[5],[7]] => [7,5,3,4,1,2,6] => [4,1,5,3,7,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => [6,3,7,1,4,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[[1,3,5],[2,6],[4],[7]] => [7,4,2,6,1,3,5] => [6,4,1,7,3,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]]
[[1,2,5],[3,6],[4],[7]] => [7,4,3,6,1,2,5] => [6,1,4,7,2,3,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => [6,5,1,3,7,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[[1,2,4],[3,6],[5],[7]] => [7,5,3,6,1,2,4] => [6,1,5,2,7,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,2,3],[4,6],[5],[7]] => [7,5,4,6,1,2,3] => [6,1,2,5,7,4,3] => [[.,.],[.,[[[.,[.,.]],.],.]]]
[[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => [4,6,1,2,3,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[[1,2,5],[3,4],[6],[7]] => [7,6,3,4,1,2,5] => [4,1,6,3,2,7,5] => [[.,.],[[[.,.],.],[[.,.],.]]]
[[1,3,4],[2,5],[6],[7]] => [7,6,2,5,1,3,4] => [5,6,1,3,2,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[[1,2,4],[3,5],[6],[7]] => [7,6,3,5,1,2,4] => [5,1,6,2,3,7,4] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => [5,1,2,6,4,7,3] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,5,7],[2],[3],[4],[6]] => [6,4,3,2,1,5,7] => [2,3,4,6,1,5,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,4,7],[2],[3],[5],[6]] => [6,5,3,2,1,4,7] => [2,3,5,1,6,4,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[[1,3,7],[2],[4],[5],[6]] => [6,5,4,2,1,3,7] => [2,4,1,5,6,3,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[[1,2,7],[3],[4],[5],[6]] => [6,5,4,3,1,2,7] => [3,1,4,5,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[[1,5,6],[2],[3],[4],[7]] => [7,4,3,2,1,5,6] => [2,3,4,7,1,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,4,6],[2],[3],[5],[7]] => [7,5,3,2,1,4,6] => [2,3,5,1,7,4,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[[1,3,6],[2],[4],[5],[7]] => [7,5,4,2,1,3,6] => [2,4,1,5,7,3,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[[1,2,6],[3],[4],[5],[7]] => [7,5,4,3,1,2,6] => [3,1,4,5,7,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[[1,4,5],[2],[3],[6],[7]] => [7,6,3,2,1,4,5] => [2,3,6,1,4,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[[1,3,5],[2],[4],[6],[7]] => [7,6,4,2,1,3,5] => [2,4,1,6,3,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[[1,2,5],[3],[4],[6],[7]] => [7,6,4,3,1,2,5] => [3,1,4,6,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[[1,3,4],[2],[5],[6],[7]] => [7,6,5,2,1,3,4] => [2,5,1,3,6,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[[1,2,4],[3],[5],[6],[7]] => [7,6,5,3,1,2,4] => [3,1,5,2,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => [4,1,2,5,6,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [6,7,4,3,1,2,5] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [6,7,5,1,3,2,4] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [6,7,1,5,4,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => [6,1,7,5,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]]
[[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [5,7,6,1,2,3,4] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [5,7,1,6,2,4,3] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[[1,2],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2] => [5,1,7,6,3,4,2] => [[.,.],[[[[.,.],.],[.,.]],.]]
[[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => [4,7,1,2,6,5,3] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[[1,2],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2] => [4,1,7,3,6,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]]
[[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => [5,6,7,1,2,3,4] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => [5,6,1,7,2,4,3] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[[1,2],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2] => [5,1,6,7,3,4,2] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[[1,3],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3] => [4,6,1,2,7,5,3] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => [4,1,6,3,7,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]]
[[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [7,3,4,5,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [7,3,4,6,1,2,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [7,3,5,1,6,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [7,4,1,5,6,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => [7,1,4,5,6,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]]
[[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [6,3,4,7,1,2,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [6,3,5,1,7,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => [6,4,1,5,7,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[[1,2],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2] => [6,1,4,5,7,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]]
[[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => [5,3,6,1,2,7,4] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[[1,3],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3] => [5,4,1,6,2,7,3] => [[[.,.],.],[[.,.],[[.,.],.]]]
[[1,2],[3,5],[4],[6],[7]] => [7,6,4,3,5,1,2] => [5,1,4,6,3,7,2] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[[1,3],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3] => [4,5,1,2,6,7,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => [4,1,5,3,6,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => [2,3,4,5,7,1,6] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => [2,3,4,6,1,7,5] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[[1,4],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4] => [2,3,5,1,6,7,4] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[[1,3],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3] => [2,4,1,5,6,7,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => [3,1,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,3,4,5,6,7,8],[2]] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,3,5,6,7,8],[4]] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,3,4,6,7,8],[5]] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,3,4,5,7,8],[6]] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,3,5,6,7,8],[2,4]] => [2,4,1,3,5,6,7,8] => [4,2,1,3,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,5,6,7,8],[3,4]] => [3,4,1,2,5,6,7,8] => [4,1,3,2,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,3,4,6,7,8],[2,5]] => [2,5,1,3,4,6,7,8] => [5,2,1,3,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,6,7,8],[4,5]] => [4,5,1,2,3,6,7,8] => [5,1,2,4,3,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,2,3,5,7,8],[4,6]] => [4,6,1,2,3,5,7,8] => [6,1,2,4,3,5,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,2,3,4,7,8],[5,6]] => [5,6,1,2,3,4,7,8] => [6,1,2,3,5,4,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[1,3,4,5,6,8],[2,7]] => [2,7,1,3,4,5,6,8] => [7,2,1,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => [7,1,3,2,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,2,3,5,6,8],[4,7]] => [4,7,1,2,3,5,6,8] => [7,1,2,4,3,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => [7,1,2,3,5,4,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[1,2,3,4,5,8],[6,7]] => [6,7,1,2,3,4,5,8] => [7,1,2,3,4,6,5,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[[1,3,4,5,6,7],[2,8]] => [2,8,1,3,4,5,6,7] => [8,2,1,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,4,5,6,7],[3,8]] => [3,8,1,2,4,5,6,7] => [8,1,3,2,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,2,3,5,6,7],[4,8]] => [4,8,1,2,3,5,6,7] => [8,1,2,4,3,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,2,3,4,6,7],[5,8]] => [5,8,1,2,3,4,6,7] => [8,1,2,3,5,4,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[1,2,3,4,5,7],[6,8]] => [6,8,1,2,3,4,5,7] => [8,1,2,3,4,6,5,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [8,1,2,3,4,5,7,6] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[[1,4,5,6,7,8],[2],[3]] => [3,2,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,3,5,6,7,8],[2],[4]] => [4,2,1,3,5,6,7,8] => [2,4,1,3,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,5,6,7,8],[3],[4]] => [4,3,1,2,5,6,7,8] => [3,1,4,2,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,3,4,6,7,8],[2],[5]] => [5,2,1,3,4,6,7,8] => [2,5,1,3,4,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,6,7,8],[4],[5]] => [5,4,1,2,3,6,7,8] => [4,1,2,5,3,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,3,4,5,7,8],[2],[6]] => [6,2,1,3,4,5,7,8] => [2,6,1,3,4,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,4,7,8],[5],[6]] => [6,5,1,2,3,4,7,8] => [5,1,2,3,6,4,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[1,3,4,5,6,8],[2],[7]] => [7,2,1,3,4,5,6,8] => [2,7,1,3,4,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,4,5,6,8],[3],[7]] => [7,3,1,2,4,5,6,8] => [3,1,7,2,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,2,3,5,6,8],[4],[7]] => [7,4,1,2,3,5,6,8] => [4,1,2,7,3,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,2,3,4,5,8],[6],[7]] => [7,6,1,2,3,4,5,8] => [6,1,2,3,4,7,5,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[[1,3,4,5,6,7],[2],[8]] => [8,2,1,3,4,5,6,7] => [2,8,1,3,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => [3,1,8,2,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,2,3,5,6,7],[4],[8]] => [8,4,1,2,3,5,6,7] => [4,1,2,8,3,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,2,3,4,6,7],[5],[8]] => [8,5,1,2,3,4,6,7] => [5,1,2,3,8,4,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[1,2,3,4,5,7],[6],[8]] => [8,6,1,2,3,4,5,7] => [6,1,2,3,4,8,5,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,8,6] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[[1,3,5,7,8],[2,4,6]] => [2,4,6,1,3,5,7,8] => [6,2,1,4,3,5,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,5,7,8],[3,4,6]] => [3,4,6,1,2,5,7,8] => [6,1,3,4,2,5,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[[1,3,5,6,8],[2,4,7]] => [2,4,7,1,3,5,6,8] => [7,2,1,4,3,5,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,4,6,8],[3,5,7]] => [3,5,7,1,2,4,6,8] => [7,1,3,2,5,4,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2,3,4,8],[5,6,7]] => [5,6,7,1,2,3,4,8] => [7,1,2,3,5,6,4,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[[1,2,4,6,7],[3,5,8]] => [3,5,8,1,2,4,6,7] => [8,1,3,2,5,4,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2,3,6,7],[4,5,8]] => [4,5,8,1,2,3,6,7] => [8,1,2,4,5,3,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[[1,3,4,5,7],[2,6,8]] => [2,6,8,1,3,4,5,7] => [8,2,1,3,4,6,5,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[[1,2,4,5,7],[3,6,8]] => [3,6,8,1,2,4,5,7] => [8,1,3,2,4,6,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[1,2,3,5,7],[4,6,8]] => [4,6,8,1,2,3,5,7] => [8,1,2,4,3,6,5,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[1,2,3,4,7],[5,6,8]] => [5,6,8,1,2,3,4,7] => [8,1,2,3,5,6,4,7] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[[1,3,4,5,6],[2,7,8]] => [2,7,8,1,3,4,5,6] => [8,2,1,3,4,5,7,6] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[[1,2,4,5,6],[3,7,8]] => [3,7,8,1,2,4,5,6] => [8,1,3,2,4,5,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[[1,2,3,5,6],[4,7,8]] => [4,7,8,1,2,3,5,6] => [8,1,2,4,3,5,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[[1,2,3,4,6],[5,7,8]] => [5,7,8,1,2,3,4,6] => [8,1,2,3,5,4,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => [8,1,2,3,4,6,7,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[[1,4,6,7,8],[2,5],[3]] => [3,2,5,1,4,6,7,8] => [5,3,2,1,4,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[[1,3,6,7,8],[2,5],[4]] => [4,2,5,1,3,6,7,8] => [5,4,1,2,3,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,6,7,8],[3,5],[4]] => [4,3,5,1,2,6,7,8] => [5,1,4,3,2,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[[1,3,6,7,8],[2,4],[5]] => [5,2,4,1,3,6,7,8] => [4,5,1,2,3,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,3,5,7,8],[2,6],[4]] => [4,2,6,1,3,5,7,8] => [6,4,1,2,3,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,4,7,8],[3,6],[5]] => [5,3,6,1,2,4,7,8] => [6,1,5,2,3,4,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,3,5,7,8],[2,4],[6]] => [6,2,4,1,3,5,7,8] => [4,6,1,2,3,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,5,7,8],[3,4],[6]] => [6,3,4,1,2,5,7,8] => [4,1,6,3,2,5,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[[1,2,4,7,8],[3,5],[6]] => [6,3,5,1,2,4,7,8] => [5,1,6,2,3,4,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,4,5,6,8],[2,7],[3]] => [3,2,7,1,4,5,6,8] => [7,3,2,1,4,5,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[[1,3,5,6,8],[2,7],[4]] => [4,2,7,1,3,5,6,8] => [7,4,1,2,3,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[[1,3,4,6,8],[2,7],[5]] => [5,2,7,1,3,4,6,8] => [7,5,1,3,2,4,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,3,4,5,8],[2,7],[6]] => [6,2,7,1,3,4,5,8] => [7,6,1,3,4,2,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => [7,1,2,6,3,4,5,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => [7,1,2,3,6,5,4,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[[1,3,4,6,8],[2,5],[7]] => [7,2,5,1,3,4,6,8] => [5,7,1,3,2,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3,5,8],[4,6],[7]] => [7,4,6,1,2,3,5,8] => [6,1,2,7,3,4,5,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => [6,1,2,3,7,5,4,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[[1,4,5,6,7],[2,8],[3]] => [3,2,8,1,4,5,6,7] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[[1,3,5,6,7],[2,8],[4]] => [4,2,8,1,3,5,6,7] => [8,4,1,2,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,5,6,7],[3,8],[4]] => [4,3,8,1,2,5,6,7] => [8,1,4,3,2,5,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[[1,3,4,6,7],[2,8],[5]] => [5,2,8,1,3,4,6,7] => [8,5,1,3,2,4,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,4,6,7],[3,8],[5]] => [5,3,8,1,2,4,6,7] => [8,1,5,2,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,2,3,6,7],[4,8],[5]] => [5,4,8,1,2,3,6,7] => [8,1,2,5,4,3,6,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[[1,3,4,5,7],[2,8],[6]] => [6,2,8,1,3,4,5,7] => [8,6,1,3,4,2,5,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[[1,2,4,5,7],[3,8],[6]] => [6,3,8,1,2,4,5,7] => [8,1,6,2,4,3,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => [8,1,2,6,3,4,5,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => [8,1,2,3,6,5,4,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[[1,3,4,5,6],[2,8],[7]] => [7,2,8,1,3,4,5,6] => [8,7,1,3,4,5,2,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[[1,2,4,5,6],[3,8],[7]] => [7,3,8,1,2,4,5,6] => [8,1,7,2,4,5,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[1,2,3,5,6],[4,8],[7]] => [7,4,8,1,2,3,5,6] => [8,1,2,7,3,5,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[1,2,3,4,6],[5,8],[7]] => [7,5,8,1,2,3,4,6] => [8,1,2,3,7,4,5,6] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[1,2,3,4,5],[6,8],[7]] => [7,6,8,1,2,3,4,5] => [8,1,2,3,4,7,6,5] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[[1,3,5,6,7],[2,4],[8]] => [8,2,4,1,3,5,6,7] => [4,8,1,2,3,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,5,6,7],[3,4],[8]] => [8,3,4,1,2,5,6,7] => [4,1,8,3,2,5,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[[1,2,4,6,7],[3,5],[8]] => [8,3,5,1,2,4,6,7] => [5,1,8,2,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,3,4,5,7],[2,6],[8]] => [8,2,6,1,3,4,5,7] => [6,8,1,3,4,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[[1,2,4,5,7],[3,6],[8]] => [8,3,6,1,2,4,5,7] => [6,1,8,2,4,3,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2,3,5,7],[4,6],[8]] => [8,4,6,1,2,3,5,7] => [6,1,2,8,3,4,5,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,2,3,4,7],[5,6],[8]] => [8,5,6,1,2,3,4,7] => [6,1,2,3,8,5,4,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[[1,3,4,5,6],[2,7],[8]] => [8,2,7,1,3,4,5,6] => [7,8,1,3,4,5,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => [7,1,8,2,4,5,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[1,2,3,5,6],[4,7],[8]] => [8,4,7,1,2,3,5,6] => [7,1,2,8,3,5,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[1,2,3,4,6],[5,7],[8]] => [8,5,7,1,2,3,4,6] => [7,1,2,3,8,4,5,6] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => [7,1,2,3,4,8,6,5] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[[1,5,6,7,8],[2],[3],[4]] => [4,3,2,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[1,4,6,7,8],[2],[3],[5]] => [5,3,2,1,4,6,7,8] => [2,3,5,1,4,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[1,3,6,7,8],[2],[4],[5]] => [5,4,2,1,3,6,7,8] => [2,4,1,5,3,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[1,2,6,7,8],[3],[4],[5]] => [5,4,3,1,2,6,7,8] => [3,1,4,5,2,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[[1,4,5,7,8],[2],[3],[6]] => [6,3,2,1,4,5,7,8] => [2,3,6,1,4,5,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[1,3,5,7,8],[2],[4],[6]] => [6,4,2,1,3,5,7,8] => [2,4,1,6,3,5,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[1,3,4,7,8],[2],[5],[6]] => [6,5,2,1,3,4,7,8] => [2,5,1,3,6,4,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[1,2,3,7,8],[4],[5],[6]] => [6,5,4,1,2,3,7,8] => [4,1,2,5,6,3,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[[1,4,5,6,8],[2],[3],[7]] => [7,3,2,1,4,5,6,8] => [2,3,7,1,4,5,6,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => [3,1,5,2,7,4,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2,3,6,8],[4],[5],[7]] => [7,5,4,1,2,3,6,8] => [4,1,2,5,7,3,6,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[[1,2,4,5,8],[3],[6],[7]] => [7,6,3,1,2,4,5,8] => [3,1,6,2,4,7,5,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[1,2,3,5,8],[4],[6],[7]] => [7,6,4,1,2,3,5,8] => [4,1,2,6,3,7,5,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[1,2,3,4,8],[5],[6],[7]] => [7,6,5,1,2,3,4,8] => [5,1,2,3,6,7,4,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[[1,4,5,6,7],[2],[3],[8]] => [8,3,2,1,4,5,6,7] => [2,3,8,1,4,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[1,3,5,6,7],[2],[4],[8]] => [8,4,2,1,3,5,6,7] => [2,4,1,8,3,5,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[1,2,5,6,7],[3],[4],[8]] => [8,4,3,1,2,5,6,7] => [3,1,4,8,2,5,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[[1,3,4,6,7],[2],[5],[8]] => [8,5,2,1,3,4,6,7] => [2,5,1,3,8,4,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[1,2,4,6,7],[3],[5],[8]] => [8,5,3,1,2,4,6,7] => [3,1,5,2,8,4,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2,3,6,7],[4],[5],[8]] => [8,5,4,1,2,3,6,7] => [4,1,2,5,8,3,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[[1,2,3,5,7],[4],[6],[8]] => [8,6,4,1,2,3,5,7] => [4,1,2,6,3,8,5,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[1,2,3,4,7],[5],[6],[8]] => [8,6,5,1,2,3,4,7] => [5,1,2,3,6,8,4,7] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[[1,3,4,5,6],[2],[7],[8]] => [8,7,2,1,3,4,5,6] => [2,7,1,3,4,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[[1,2,3,5,6],[4],[7],[8]] => [8,7,4,1,2,3,5,6] => [4,1,2,7,3,5,8,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[[1,2,3,4,6],[5],[7],[8]] => [8,7,5,1,2,3,4,6] => [5,1,2,3,7,4,8,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => [6,1,2,3,4,7,8,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[[1,3,5,7],[2,4,6,8]] => [2,4,6,8,1,3,5,7] => [8,2,1,4,3,6,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[[1,2,5,7],[3,4,6,8]] => [3,4,6,8,1,2,5,7] => [8,1,3,4,2,6,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[[1,2,4,7],[3,5,6,8]] => [3,5,6,8,1,2,4,7] => [8,1,3,2,5,6,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[1,2,3,7],[4,5,6,8]] => [4,5,6,8,1,2,3,7] => [8,1,2,4,5,6,3,7] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[[1,3,5,6],[2,4,7,8]] => [2,4,7,8,1,3,5,6] => [8,2,1,4,3,5,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[[1,2,4,6],[3,5,7,8]] => [3,5,7,8,1,2,4,6] => [8,1,3,2,5,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,3,6],[4,5,7,8]] => [4,5,7,8,1,2,3,6] => [8,1,2,4,5,3,7,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[[1,2,4,5],[3,6,7,8]] => [3,6,7,8,1,2,4,5] => [8,1,3,2,4,6,7,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[[1,4,6,8],[2,5,7],[3]] => [3,2,5,7,1,4,6,8] => [7,3,2,1,5,4,6,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[[1,4,5,8],[2,6,7],[3]] => [3,2,6,7,1,4,5,8] => [7,3,2,1,4,6,5,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[[1,3,4,8],[2,6,7],[5]] => [5,2,6,7,1,3,4,8] => [7,5,1,3,2,6,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[[1,2,4,8],[3,6,7],[5]] => [5,3,6,7,1,2,4,8] => [7,1,5,2,3,6,4,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[1,2,3,8],[4,6,7],[5]] => [5,4,6,7,1,2,3,8] => [7,1,2,5,4,6,3,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[[1,3,5,8],[2,4,7],[6]] => [6,2,4,7,1,3,5,8] => [7,6,1,2,3,4,5,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,8],[4,5,7],[6]] => [6,4,5,7,1,2,3,8] => [7,1,2,6,4,5,3,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[[1,3,5,8],[2,4,6],[7]] => [7,2,4,6,1,3,5,8] => [6,7,1,2,3,4,5,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,5,8],[3,4,6],[7]] => [7,3,4,6,1,2,5,8] => [6,1,7,3,2,4,5,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[[1,3,4,8],[2,5,6],[7]] => [7,2,5,6,1,3,4,8] => [6,7,1,3,2,5,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[1,4,6,7],[2,5,8],[3]] => [3,2,5,8,1,4,6,7] => [8,3,2,1,5,4,6,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[[1,3,6,7],[2,5,8],[4]] => [4,2,5,8,1,3,6,7] => [8,4,1,2,5,3,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[[1,2,6,7],[3,5,8],[4]] => [4,3,5,8,1,2,6,7] => [8,1,4,3,5,2,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[[1,3,6,7],[2,4,8],[5]] => [5,2,4,8,1,3,6,7] => [8,5,1,2,4,3,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[[1,2,6,7],[3,4,8],[5]] => [5,3,4,8,1,2,6,7] => [8,1,5,3,4,2,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[[1,4,5,7],[2,6,8],[3]] => [3,2,6,8,1,4,5,7] => [8,3,2,1,4,6,5,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[[1,2,5,7],[3,6,8],[4]] => [4,3,6,8,1,2,5,7] => [8,1,4,3,2,6,5,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[1,2,3,7],[4,6,8],[5]] => [5,4,6,8,1,2,3,7] => [8,1,2,5,4,6,3,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[[1,3,5,7],[2,4,8],[6]] => [6,2,4,8,1,3,5,7] => [8,6,1,2,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,4,7],[3,5,8],[6]] => [6,3,5,8,1,2,4,7] => [8,1,6,2,3,5,4,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[1,2,3,7],[4,5,8],[6]] => [6,4,5,8,1,2,3,7] => [8,1,2,6,4,5,3,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[[1,4,5,6],[2,7,8],[3]] => [3,2,7,8,1,4,5,6] => [8,3,2,1,4,5,7,6] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[[1,2,5,6],[3,7,8],[4]] => [4,3,7,8,1,2,5,6] => [8,1,4,3,2,5,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[[1,3,4,6],[2,7,8],[5]] => [5,2,7,8,1,3,4,6] => [8,5,1,3,2,4,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[[1,2,4,5],[3,7,8],[6]] => [6,3,7,8,1,2,4,5] => [8,1,6,2,4,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,3,4],[5,7,8],[6]] => [6,5,7,8,1,2,3,4] => [8,1,2,3,6,5,7,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[1,2,5,6],[3,4,8],[7]] => [7,3,4,8,1,2,5,6] => [8,1,7,3,2,5,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[1,3,4,6],[2,5,8],[7]] => [7,2,5,8,1,3,4,6] => [8,7,1,3,2,4,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,4,6],[3,5,8],[7]] => [7,3,5,8,1,2,4,6] => [8,1,7,2,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,3,4,5],[2,6,8],[7]] => [7,2,6,8,1,3,4,5] => [8,7,1,3,4,2,6,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[[1,2,4,5],[3,6,8],[7]] => [7,3,6,8,1,2,4,5] => [8,1,7,2,4,3,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,3,5],[4,6,8],[7]] => [7,4,6,8,1,2,3,5] => [8,1,2,7,3,4,6,5] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[[1,2,3,4],[5,6,8],[7]] => [7,5,6,8,1,2,3,4] => [8,1,2,3,7,5,6,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[1,3,5,7],[2,4,6],[8]] => [8,2,4,6,1,3,5,7] => [6,8,1,2,3,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,3,4,7],[2,5,6],[8]] => [8,2,5,6,1,3,4,7] => [6,8,1,3,2,5,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[1,2,4,7],[3,5,6],[8]] => [8,3,5,6,1,2,4,7] => [6,1,8,2,3,5,4,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[1,3,5,6],[2,4,7],[8]] => [8,2,4,7,1,3,5,6] => [7,8,1,2,3,5,4,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[[1,2,5,6],[3,4,7],[8]] => [8,3,4,7,1,2,5,6] => [7,1,8,3,2,5,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[1,3,4,6],[2,5,7],[8]] => [8,2,5,7,1,3,4,6] => [7,8,1,3,2,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[1,2,4,6],[3,5,7],[8]] => [8,3,5,7,1,2,4,6] => [7,1,8,2,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,3,4,5],[2,6,7],[8]] => [8,2,6,7,1,3,4,5] => [7,8,1,3,4,2,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[[1,2,4,5],[3,6,7],[8]] => [8,3,6,7,1,2,4,5] => [7,1,8,2,4,3,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => [7,1,2,3,8,5,6,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[1,3,7,8],[2,5],[4,6]] => [4,6,2,5,1,3,7,8] => [5,6,1,4,2,3,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[1,2,7,8],[3,5],[4,6]] => [4,6,3,5,1,2,7,8] => [5,1,6,4,3,2,7,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[[1,3,7,8],[2,4],[5,6]] => [5,6,2,4,1,3,7,8] => [4,6,1,2,5,3,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[1,2,7,8],[3,4],[5,6]] => [5,6,3,4,1,2,7,8] => [4,1,6,3,5,2,7,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[[1,4,6,8],[2,5],[3,7]] => [3,7,2,5,1,4,6,8] => [5,7,3,1,2,4,6,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[[1,3,6,8],[2,5],[4,7]] => [4,7,2,5,1,3,6,8] => [5,7,1,4,2,3,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[1,3,6,8],[2,4],[5,7]] => [5,7,2,4,1,3,6,8] => [4,7,1,2,5,3,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[1,4,5,8],[2,6],[3,7]] => [3,7,2,6,1,4,5,8] => [6,7,3,1,4,2,5,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[[1,3,5,8],[2,6],[4,7]] => [4,7,2,6,1,3,5,8] => [6,7,1,4,3,2,5,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[[1,2,5,8],[3,6],[4,7]] => [4,7,3,6,1,2,5,8] => [6,1,7,4,2,3,5,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[[1,2,4,8],[3,6],[5,7]] => [5,7,3,6,1,2,4,8] => [6,1,7,2,5,3,4,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2,5,8],[3,4],[6,7]] => [6,7,3,4,1,2,5,8] => [4,1,7,3,2,6,5,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[1,3,4,8],[2,5],[6,7]] => [6,7,2,5,1,3,4,8] => [5,7,1,3,2,6,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[1,4,6,7],[2,5],[3,8]] => [3,8,2,5,1,4,6,7] => [5,8,3,1,2,4,6,7] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[[1,3,6,7],[2,5],[4,8]] => [4,8,2,5,1,3,6,7] => [5,8,1,4,2,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[1,3,6,7],[2,4],[5,8]] => [5,8,2,4,1,3,6,7] => [4,8,1,2,5,3,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[1,2,6,7],[3,4],[5,8]] => [5,8,3,4,1,2,6,7] => [4,1,8,3,5,2,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[[1,4,5,7],[2,6],[3,8]] => [3,8,2,6,1,4,5,7] => [6,8,3,1,4,2,5,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[[1,2,4,7],[3,6],[5,8]] => [5,8,3,6,1,2,4,7] => [6,1,8,2,5,3,4,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,3,5,7],[2,4],[6,8]] => [6,8,2,4,1,3,5,7] => [4,8,1,2,3,6,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[[1,3,4,7],[2,5],[6,8]] => [6,8,2,5,1,3,4,7] => [5,8,1,3,2,6,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[1,3,5,6],[2,7],[4,8]] => [4,8,2,7,1,3,5,6] => [7,8,1,4,3,5,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[[1,2,5,6],[3,7],[4,8]] => [4,8,3,7,1,2,5,6] => [7,1,8,4,2,5,3,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[1,2,4,6],[3,7],[5,8]] => [5,8,3,7,1,2,4,6] => [7,1,8,2,5,4,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[[1,2,3,6],[4,7],[5,8]] => [5,8,4,7,1,2,3,6] => [7,1,2,8,5,3,4,6] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[[1,2,4,5],[3,7],[6,8]] => [6,8,3,7,1,2,4,5] => [7,1,8,2,4,6,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[1,2,3,5],[4,7],[6,8]] => [6,8,4,7,1,2,3,5] => [7,1,2,8,3,6,4,5] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[1,2,3,4],[5,7],[6,8]] => [6,8,5,7,1,2,3,4] => [7,1,2,3,8,6,5,4] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[[1,3,5,6],[2,4],[7,8]] => [7,8,2,4,1,3,5,6] => [4,8,1,2,3,5,7,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[[1,3,4,6],[2,5],[7,8]] => [7,8,2,5,1,3,4,6] => [5,8,1,3,2,4,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[[1,2,4,6],[3,5],[7,8]] => [7,8,3,5,1,2,4,6] => [5,1,8,2,3,4,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[[1,2,3,6],[4,5],[7,8]] => [7,8,4,5,1,2,3,6] => [5,1,2,8,4,3,7,6] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[[1,3,4,5],[2,6],[7,8]] => [7,8,2,6,1,3,4,5] => [6,8,1,3,4,2,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[[1,2,4,5],[3,6],[7,8]] => [7,8,3,6,1,2,4,5] => [6,1,8,2,4,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,3,5],[4,6],[7,8]] => [7,8,4,6,1,2,3,5] => [6,1,2,8,3,4,7,5] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => [6,1,2,3,8,5,7,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[1,5,7,8],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8] => [6,3,4,2,1,5,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[[1,4,7,8],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8] => [6,3,5,1,2,4,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[[1,3,7,8],[2,6],[4],[5]] => [5,4,2,6,1,3,7,8] => [6,4,1,5,2,3,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,7,8],[3,6],[4],[5]] => [5,4,3,6,1,2,7,8] => [6,1,4,5,3,2,7,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[[1,4,7,8],[2,5],[3],[6]] => [6,3,2,5,1,4,7,8] => [5,3,6,1,2,4,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[[1,4,6,8],[2,7],[3],[5]] => [5,3,2,7,1,4,6,8] => [7,3,5,1,2,4,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[[1,3,6,8],[2,7],[4],[5]] => [5,4,2,7,1,3,6,8] => [7,4,1,5,2,3,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,6,8],[3,7],[4],[5]] => [5,4,3,7,1,2,6,8] => [7,1,4,5,3,2,6,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[[1,3,4,8],[2,7],[5],[6]] => [6,5,2,7,1,3,4,8] => [7,5,1,3,6,2,4,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[[1,2,4,8],[3,7],[5],[6]] => [6,5,3,7,1,2,4,8] => [7,1,5,2,6,3,4,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,4,6,8],[2,5],[3],[7]] => [7,3,2,5,1,4,6,8] => [5,3,7,1,2,4,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[[1,3,6,8],[2,4],[5],[7]] => [7,5,2,4,1,3,6,8] => [4,5,1,2,7,3,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[1,2,4,8],[3,6],[5],[7]] => [7,5,3,6,1,2,4,8] => [6,1,5,2,7,3,4,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2,5,8],[3,4],[6],[7]] => [7,6,3,4,1,2,5,8] => [4,1,6,3,2,7,5,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[1,2,4,8],[3,5],[6],[7]] => [7,6,3,5,1,2,4,8] => [5,1,6,2,3,7,4,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[1,5,6,7],[2,8],[3],[4]] => [4,3,2,8,1,5,6,7] => [8,3,4,2,1,5,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[[1,4,6,7],[2,8],[3],[5]] => [5,3,2,8,1,4,6,7] => [8,3,5,1,2,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[[1,3,6,7],[2,8],[4],[5]] => [5,4,2,8,1,3,6,7] => [8,4,1,5,2,3,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,6,7],[3,8],[4],[5]] => [5,4,3,8,1,2,6,7] => [8,1,4,5,3,2,6,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[[1,3,5,7],[2,8],[4],[6]] => [6,4,2,8,1,3,5,7] => [8,4,1,6,3,2,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[[1,2,5,7],[3,8],[4],[6]] => [6,4,3,8,1,2,5,7] => [8,1,4,6,2,3,5,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[[1,3,4,7],[2,8],[5],[6]] => [6,5,2,8,1,3,4,7] => [8,5,1,3,6,2,4,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[[1,2,4,7],[3,8],[5],[6]] => [6,5,3,8,1,2,4,7] => [8,1,5,2,6,3,4,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2,3,7],[4,8],[5],[6]] => [6,5,4,8,1,2,3,7] => [8,1,2,5,6,4,3,7] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[[1,3,5,6],[2,8],[4],[7]] => [7,4,2,8,1,3,5,6] => [8,4,1,7,3,5,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[[1,2,5,6],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6] => [8,1,4,7,2,5,3,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[[1,3,4,6],[2,8],[5],[7]] => [7,5,2,8,1,3,4,6] => [8,5,1,3,7,4,2,6] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => [8,1,5,2,7,4,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[[1,2,3,6],[4,8],[5],[7]] => [7,5,4,8,1,2,3,6] => [8,1,2,5,7,3,4,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[[1,2,3,5],[4,8],[6],[7]] => [7,6,4,8,1,2,3,5] => [8,1,2,6,3,7,4,5] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[1,2,3,4],[5,8],[6],[7]] => [7,6,5,8,1,2,3,4] => [8,1,2,3,6,7,5,4] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[[1,3,6,7],[2,5],[4],[8]] => [8,4,2,5,1,3,6,7] => [5,4,1,8,2,3,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,6,7],[3,5],[4],[8]] => [8,4,3,5,1,2,6,7] => [5,1,4,8,3,2,6,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[[1,3,6,7],[2,4],[5],[8]] => [8,5,2,4,1,3,6,7] => [4,5,1,2,8,3,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[1,2,6,7],[3,4],[5],[8]] => [8,5,3,4,1,2,6,7] => [4,1,5,3,8,2,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[[1,4,5,7],[2,6],[3],[8]] => [8,3,2,6,1,4,5,7] => [6,3,8,1,4,2,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[[1,3,5,7],[2,6],[4],[8]] => [8,4,2,6,1,3,5,7] => [6,4,1,8,3,2,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[[1,2,4,7],[3,6],[5],[8]] => [8,5,3,6,1,2,4,7] => [6,1,5,2,8,3,4,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,3,5,7],[2,4],[6],[8]] => [8,6,2,4,1,3,5,7] => [4,6,1,2,3,8,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[[1,2,4,7],[3,5],[6],[8]] => [8,6,3,5,1,2,4,7] => [5,1,6,2,3,8,4,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[1,2,3,7],[4,5],[6],[8]] => [8,6,4,5,1,2,3,7] => [5,1,2,6,4,8,3,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[[1,4,5,6],[2,7],[3],[8]] => [8,3,2,7,1,4,5,6] => [7,3,8,1,4,5,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[[1,3,5,6],[2,7],[4],[8]] => [8,4,2,7,1,3,5,6] => [7,4,1,8,3,5,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[[1,3,4,6],[2,7],[5],[8]] => [8,5,2,7,1,3,4,6] => [7,5,1,3,8,4,2,6] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[[1,2,3,6],[4,7],[5],[8]] => [8,5,4,7,1,2,3,6] => [7,1,2,5,8,3,4,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[[1,3,4,5],[2,7],[6],[8]] => [8,6,2,7,1,3,4,5] => [7,6,1,3,4,8,2,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[[1,2,4,5],[3,7],[6],[8]] => [8,6,3,7,1,2,4,5] => [7,1,6,2,4,8,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[1,2,3,5],[4,7],[6],[8]] => [8,6,4,7,1,2,3,5] => [7,1,2,6,3,8,4,5] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[1,2,3,4],[5,7],[6],[8]] => [8,6,5,7,1,2,3,4] => [7,1,2,3,6,8,5,4] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[[1,3,5,6],[2,4],[7],[8]] => [8,7,2,4,1,3,5,6] => [4,7,1,2,3,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[[1,2,5,6],[3,4],[7],[8]] => [8,7,3,4,1,2,5,6] => [4,1,7,3,2,5,8,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[[1,3,4,6],[2,5],[7],[8]] => [8,7,2,5,1,3,4,6] => [5,7,1,3,2,4,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[[1,2,4,6],[3,5],[7],[8]] => [8,7,3,5,1,2,4,6] => [5,1,7,2,3,4,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[[1,2,4,5],[3,6],[7],[8]] => [8,7,3,6,1,2,4,5] => [6,1,7,2,4,3,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,3,5],[4,6],[7],[8]] => [8,7,4,6,1,2,3,5] => [6,1,2,7,3,4,8,5] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => [6,1,2,3,7,5,8,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[1,6,7,8],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8] => [2,3,4,5,1,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[[1,5,7,8],[2],[3],[4],[6]] => [6,4,3,2,1,5,7,8] => [2,3,4,6,1,5,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[[1,3,7,8],[2],[4],[5],[6]] => [6,5,4,2,1,3,7,8] => [2,4,1,5,6,3,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[[1,5,6,8],[2],[3],[4],[7]] => [7,4,3,2,1,5,6,8] => [2,3,4,7,1,5,6,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[[1,3,5,8],[2],[4],[6],[7]] => [7,6,4,2,1,3,5,8] => [2,4,1,6,3,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[1,2,3,8],[4],[5],[6],[7]] => [7,6,5,4,1,2,3,8] => [4,1,2,5,6,7,3,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[[1,5,6,7],[2],[3],[4],[8]] => [8,4,3,2,1,5,6,7] => [2,3,4,8,1,5,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[[1,4,6,7],[2],[3],[5],[8]] => [8,5,3,2,1,4,6,7] => [2,3,5,1,8,4,6,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[[1,3,6,7],[2],[4],[5],[8]] => [8,5,4,2,1,3,6,7] => [2,4,1,5,8,3,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[[1,2,6,7],[3],[4],[5],[8]] => [8,5,4,3,1,2,6,7] => [3,1,4,5,8,2,6,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[[1,4,5,7],[2],[3],[6],[8]] => [8,6,3,2,1,4,5,7] => [2,3,6,1,4,8,5,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[[1,3,5,7],[2],[4],[6],[8]] => [8,6,4,2,1,3,5,7] => [2,4,1,6,3,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[1,2,5,7],[3],[4],[6],[8]] => [8,6,4,3,1,2,5,7] => [3,1,4,6,2,8,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[[1,3,4,7],[2],[5],[6],[8]] => [8,6,5,2,1,3,4,7] => [2,5,1,3,6,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[[1,2,4,7],[3],[5],[6],[8]] => [8,6,5,3,1,2,4,7] => [3,1,5,2,6,8,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[1,2,3,7],[4],[5],[6],[8]] => [8,6,5,4,1,2,3,7] => [4,1,2,5,6,8,3,7] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[[1,4,5,6],[2],[3],[7],[8]] => [8,7,3,2,1,4,5,6] => [2,3,7,1,4,5,8,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[[1,3,5,6],[2],[4],[7],[8]] => [8,7,4,2,1,3,5,6] => [2,4,1,7,3,5,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[[1,2,5,6],[3],[4],[7],[8]] => [8,7,4,3,1,2,5,6] => [3,1,4,7,2,5,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[[1,3,4,6],[2],[5],[7],[8]] => [8,7,5,2,1,3,4,6] => [2,5,1,3,7,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[[1,2,4,6],[3],[5],[7],[8]] => [8,7,5,3,1,2,4,6] => [3,1,5,2,7,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,3,6],[4],[5],[7],[8]] => [8,7,5,4,1,2,3,6] => [4,1,2,5,7,3,8,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[[1,3,4,5],[2],[6],[7],[8]] => [8,7,6,2,1,3,4,5] => [2,6,1,3,4,7,8,5] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[[1,2,4,5],[3],[6],[7],[8]] => [8,7,6,3,1,2,4,5] => [3,1,6,2,4,7,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[[1,2,3,5],[4],[6],[7],[8]] => [8,7,6,4,1,2,3,5] => [4,1,2,6,3,7,8,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[[1,4,7],[2,5,8],[3,6]] => [3,6,2,5,8,1,4,7] => [8,6,3,1,2,5,4,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[[1,3,7],[2,5,8],[4,6]] => [4,6,2,5,8,1,3,7] => [8,6,1,4,2,5,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[[1,2,7],[3,5,8],[4,6]] => [4,6,3,5,8,1,2,7] => [8,1,6,4,3,5,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[[1,3,7],[2,4,8],[5,6]] => [5,6,2,4,8,1,3,7] => [8,6,1,2,5,4,3,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[[1,3,6],[2,5,8],[4,7]] => [4,7,2,5,8,1,3,6] => [8,7,1,4,2,3,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,3,6],[2,4,8],[5,7]] => [5,7,2,4,8,1,3,6] => [8,7,1,2,5,3,4,6] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[[1,2,6],[3,4,8],[5,7]] => [5,7,3,4,8,1,2,6] => [8,1,7,3,5,2,4,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[[1,4,5],[2,6,8],[3,7]] => [3,7,2,6,8,1,4,5] => [8,7,3,1,4,2,6,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[[1,3,5],[2,6,8],[4,7]] => [4,7,2,6,8,1,3,5] => [8,7,1,4,3,2,6,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[[1,2,5],[3,6,8],[4,7]] => [4,7,3,6,8,1,2,5] => [8,1,7,4,2,3,6,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[[1,3,4],[2,6,8],[5,7]] => [5,7,2,6,8,1,3,4] => [8,7,1,3,5,2,6,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[[1,2,4],[3,6,8],[5,7]] => [5,7,3,6,8,1,2,4] => [8,1,7,2,5,3,6,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,3,5],[2,4,8],[6,7]] => [6,7,2,4,8,1,3,5] => [8,7,1,2,3,6,4,5] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[[1,2,4],[3,5,8],[6,7]] => [6,7,3,5,8,1,2,4] => [8,1,7,2,3,6,5,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[[1,2,3],[4,5,8],[6,7]] => [6,7,4,5,8,1,2,3] => [8,1,2,7,4,6,5,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[[1,4,6],[2,5,7],[3,8]] => [3,8,2,5,7,1,4,6] => [7,8,3,1,2,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[[1,3,6],[2,5,7],[4,8]] => [4,8,2,5,7,1,3,6] => [7,8,1,4,2,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[1,3,6],[2,4,7],[5,8]] => [5,8,2,4,7,1,3,6] => [7,8,1,2,5,3,4,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[1,4,5],[2,6,7],[3,8]] => [3,8,2,6,7,1,4,5] => [7,8,3,1,4,2,6,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[[1,2,5],[3,6,7],[4,8]] => [4,8,3,6,7,1,2,5] => [7,1,8,4,2,3,6,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[[1,3,4],[2,6,7],[5,8]] => [5,8,2,6,7,1,3,4] => [7,8,1,3,5,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[[1,2,4],[3,6,7],[5,8]] => [5,8,3,6,7,1,2,4] => [7,1,8,2,5,3,6,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,3,5],[2,4,7],[6,8]] => [6,8,2,4,7,1,3,5] => [7,8,1,2,3,6,4,5] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[[1,3,4],[2,5,7],[6,8]] => [6,8,2,5,7,1,3,4] => [7,8,1,3,2,6,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[[1,2,4],[3,5,7],[6,8]] => [6,8,3,5,7,1,2,4] => [7,1,8,2,3,6,5,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[[1,2,3],[4,5,7],[6,8]] => [6,8,4,5,7,1,2,3] => [7,1,2,8,4,6,5,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[[1,3,5],[2,4,6],[7,8]] => [7,8,2,4,6,1,3,5] => [6,8,1,2,3,4,7,5] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[[1,2,5],[3,4,6],[7,8]] => [7,8,3,4,6,1,2,5] => [6,1,8,3,2,4,7,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[[1,3,4],[2,5,6],[7,8]] => [7,8,2,5,6,1,3,4] => [6,8,1,3,2,5,7,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[[1,2,4],[3,5,6],[7,8]] => [7,8,3,5,6,1,2,4] => [6,1,8,2,3,5,7,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => [6,1,2,8,4,5,7,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[[1,5,7],[2,6,8],[3],[4]] => [4,3,2,6,8,1,5,7] => [8,3,4,2,1,6,5,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[[1,4,7],[2,6,8],[3],[5]] => [5,3,2,6,8,1,4,7] => [8,3,5,1,2,6,4,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[[1,3,7],[2,6,8],[4],[5]] => [5,4,2,6,8,1,3,7] => [8,4,1,5,2,6,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[[1,2,7],[3,6,8],[4],[5]] => [5,4,3,6,8,1,2,7] => [8,1,4,5,3,6,2,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[[1,3,7],[2,5,8],[4],[6]] => [6,4,2,5,8,1,3,7] => [8,4,1,6,2,5,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[[1,2,7],[3,5,8],[4],[6]] => [6,4,3,5,8,1,2,7] => [8,1,4,6,3,5,2,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[[1,3,7],[2,4,8],[5],[6]] => [6,5,2,4,8,1,3,7] => [8,5,1,2,6,4,3,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[[1,4,6],[2,7,8],[3],[5]] => [5,3,2,7,8,1,4,6] => [8,3,5,1,2,4,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[[1,3,6],[2,7,8],[4],[5]] => [5,4,2,7,8,1,3,6] => [8,4,1,5,2,3,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[[1,2,6],[3,7,8],[4],[5]] => [5,4,3,7,8,1,2,6] => [8,1,4,5,3,2,7,6] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[[1,4,5],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5] => [8,3,6,1,4,2,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[[1,2,4],[3,7,8],[5],[6]] => [6,5,3,7,8,1,2,4] => [8,1,5,2,6,3,7,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,4,6],[2,5,8],[3],[7]] => [7,3,2,5,8,1,4,6] => [8,3,7,1,2,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[[1,3,6],[2,5,8],[4],[7]] => [7,4,2,5,8,1,3,6] => [8,4,1,7,2,3,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,6],[3,5,8],[4],[7]] => [7,4,3,5,8,1,2,6] => [8,1,4,7,3,2,5,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[[1,3,6],[2,4,8],[5],[7]] => [7,5,2,4,8,1,3,6] => [8,5,1,2,7,3,4,6] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[[1,2,6],[3,4,8],[5],[7]] => [7,5,3,4,8,1,2,6] => [8,1,5,3,7,2,4,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[[1,4,5],[2,6,8],[3],[7]] => [7,3,2,6,8,1,4,5] => [8,3,7,1,4,2,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[[1,3,5],[2,6,8],[4],[7]] => [7,4,2,6,8,1,3,5] => [8,4,1,7,3,2,6,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[[1,2,5],[3,6,8],[4],[7]] => [7,4,3,6,8,1,2,5] => [8,1,4,7,2,3,6,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[[1,3,4],[2,6,8],[5],[7]] => [7,5,2,6,8,1,3,4] => [8,5,1,3,7,2,6,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[[1,2,4],[3,6,8],[5],[7]] => [7,5,3,6,8,1,2,4] => [8,1,5,2,7,3,6,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,3],[4,6,8],[5],[7]] => [7,5,4,6,8,1,2,3] => [8,1,2,5,7,4,6,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[[1,3,5],[2,4,8],[6],[7]] => [7,6,2,4,8,1,3,5] => [8,6,1,2,3,7,4,5] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[[1,2,5],[3,4,8],[6],[7]] => [7,6,3,4,8,1,2,5] => [8,1,6,3,2,7,4,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[1,2,4],[3,5,8],[6],[7]] => [7,6,3,5,8,1,2,4] => [8,1,6,2,3,7,5,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[[1,2,3],[4,5,8],[6],[7]] => [7,6,4,5,8,1,2,3] => [8,1,2,6,4,7,5,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[[1,4,6],[2,5,7],[3],[8]] => [8,3,2,5,7,1,4,6] => [7,3,8,1,2,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[[1,3,6],[2,5,7],[4],[8]] => [8,4,2,5,7,1,3,6] => [7,4,1,8,2,3,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[1,3,6],[2,4,7],[5],[8]] => [8,5,2,4,7,1,3,6] => [7,5,1,2,8,3,4,6] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[[1,4,5],[2,6,7],[3],[8]] => [8,3,2,6,7,1,4,5] => [7,3,8,1,4,2,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[[1,3,5],[2,6,7],[4],[8]] => [8,4,2,6,7,1,3,5] => [7,4,1,8,3,2,6,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[[1,2,5],[3,6,7],[4],[8]] => [8,4,3,6,7,1,2,5] => [7,1,4,8,2,3,6,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[[1,3,4],[2,6,7],[5],[8]] => [8,5,2,6,7,1,3,4] => [7,5,1,3,8,2,6,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[[1,2,4],[3,6,7],[5],[8]] => [8,5,3,6,7,1,2,4] => [7,1,5,2,8,3,6,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,3],[4,6,7],[5],[8]] => [8,5,4,6,7,1,2,3] => [7,1,2,5,8,4,6,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[[1,3,5],[2,4,7],[6],[8]] => [8,6,2,4,7,1,3,5] => [7,6,1,2,3,8,4,5] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[[1,2,5],[3,4,7],[6],[8]] => [8,6,3,4,7,1,2,5] => [7,1,6,3,2,8,4,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[1,2,4],[3,5,7],[6],[8]] => [8,6,3,5,7,1,2,4] => [7,1,6,2,3,8,5,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[[1,3,5],[2,4,6],[7],[8]] => [8,7,2,4,6,1,3,5] => [6,7,1,2,3,4,8,5] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[[1,3,4],[2,5,6],[7],[8]] => [8,7,2,5,6,1,3,4] => [6,7,1,3,2,5,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[[1,2,4],[3,5,6],[7],[8]] => [8,7,3,5,6,1,2,4] => [6,1,7,2,3,5,8,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => [6,1,2,7,4,5,8,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [6,7,5,1,3,2,4,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [5,7,6,1,2,3,4,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => [5,7,1,6,2,4,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[1,2,8],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2,8] => [5,1,7,6,3,4,2,8] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [5,6,7,1,2,3,4,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[1,3,8],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3,8] => [5,6,1,7,2,4,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[1,2,8],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2,8] => [5,1,6,7,3,4,2,8] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[[1,2,8],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2,8] => [4,1,6,3,7,5,2,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [6,8,1,5,4,2,3,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [5,8,6,1,2,3,4,7] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[[1,3,7],[2,5],[4,8],[6]] => [6,4,8,2,5,1,3,7] => [5,8,1,6,2,4,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[1,2,7],[3,5],[4,8],[6]] => [6,4,8,3,5,1,2,7] => [5,1,8,6,3,4,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[[1,3,7],[2,4],[5,8],[6]] => [6,5,8,2,4,1,3,7] => [4,8,1,2,6,5,3,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[[1,2,7],[3,4],[5,8],[6]] => [6,5,8,3,4,1,2,7] => [4,1,8,3,6,5,2,7] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[[1,5,6],[2,7],[3,8],[4]] => [4,3,8,2,7,1,5,6] => [7,8,4,3,1,5,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[[1,2,6],[3,7],[4,8],[5]] => [5,4,8,3,7,1,2,6] => [7,1,8,5,4,2,3,6] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[[1,4,5],[2,7],[3,8],[6]] => [6,3,8,2,7,1,4,5] => [7,8,6,1,4,3,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => [7,8,1,6,3,4,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[[1,2,5],[3,7],[4,8],[6]] => [6,4,8,3,7,1,2,5] => [7,1,8,6,2,4,3,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[1,3,4],[2,7],[5,8],[6]] => [6,5,8,2,7,1,3,4] => [7,8,1,3,6,5,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[[1,2,3],[4,7],[5,8],[6]] => [6,5,8,4,7,1,2,3] => [7,1,2,8,6,5,4,3] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[[1,4,6],[2,5],[3,8],[7]] => [7,3,8,2,5,1,4,6] => [5,8,7,1,2,4,3,6] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[[1,3,6],[2,4],[5,8],[7]] => [7,5,8,2,4,1,3,6] => [4,8,1,2,7,3,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[1,3,5],[2,6],[4,8],[7]] => [7,4,8,2,6,1,3,5] => [6,8,1,7,3,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[[1,2,5],[3,6],[4,8],[7]] => [7,4,8,3,6,1,2,5] => [6,1,8,7,2,3,4,5] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[[1,3,4],[2,6],[5,8],[7]] => [7,5,8,2,6,1,3,4] => [6,8,1,3,7,2,5,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[[1,2,4],[3,6],[5,8],[7]] => [7,5,8,3,6,1,2,4] => [6,1,8,2,7,3,5,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,3],[4,6],[5,8],[7]] => [7,5,8,4,6,1,2,3] => [6,1,2,8,7,4,5,3] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[[1,2,5],[3,4],[6,8],[7]] => [7,6,8,3,4,1,2,5] => [4,1,8,3,2,7,6,5] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[[1,4,7],[2,5],[3,6],[8]] => [8,3,6,2,5,1,4,7] => [5,6,8,1,2,3,4,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[1,2,7],[3,5],[4,6],[8]] => [8,4,6,3,5,1,2,7] => [5,1,6,8,3,4,2,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[[1,2,7],[3,4],[5,6],[8]] => [8,5,6,3,4,1,2,7] => [4,1,6,3,8,5,2,7] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[[1,4,6],[2,5],[3,7],[8]] => [8,3,7,2,5,1,4,6] => [5,7,8,1,2,4,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[[1,2,6],[3,5],[4,7],[8]] => [8,4,7,3,5,1,2,6] => [5,1,7,8,3,2,4,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[[1,3,6],[2,4],[5,7],[8]] => [8,5,7,2,4,1,3,6] => [4,7,1,2,8,3,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[1,4,5],[2,6],[3,7],[8]] => [8,3,7,2,6,1,4,5] => [6,7,8,1,4,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[[1,3,5],[2,6],[4,7],[8]] => [8,4,7,2,6,1,3,5] => [6,7,1,8,3,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[[1,2,5],[3,6],[4,7],[8]] => [8,4,7,3,6,1,2,5] => [6,1,7,8,2,3,4,5] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[[1,3,5],[2,4],[6,7],[8]] => [8,6,7,2,4,1,3,5] => [4,7,1,2,3,8,6,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[[1,2,5],[3,4],[6,7],[8]] => [8,6,7,3,4,1,2,5] => [4,1,7,3,2,8,6,5] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[[1,3,4],[2,5],[6,7],[8]] => [8,6,7,2,5,1,3,4] => [5,7,1,3,2,8,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[[1,2,4],[3,5],[6,7],[8]] => [8,6,7,3,5,1,2,4] => [5,1,7,2,3,8,6,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[[1,6,8],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6,8] => [7,3,4,5,2,1,6,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[[1,4,8],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4,8] => [7,3,5,1,6,2,4,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[[1,3,8],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3,8] => [7,4,1,5,6,2,3,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[[1,4,8],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4,8] => [6,3,5,1,7,2,4,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[[1,3,8],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3,8] => [6,4,1,5,7,2,3,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[[1,4,8],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4,8] => [5,3,6,1,2,7,4,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[[1,3,8],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3,8] => [5,4,1,6,2,7,3,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[[1,3,8],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3,8] => [4,5,1,2,6,7,3,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[[1,6,7],[2,8],[3],[4],[5]] => [5,4,3,2,8,1,6,7] => [8,3,4,5,2,1,6,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[[1,4,7],[2,8],[3],[5],[6]] => [6,5,3,2,8,1,4,7] => [8,3,5,1,6,2,4,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[[1,3,7],[2,8],[4],[5],[6]] => [6,5,4,2,8,1,3,7] => [8,4,1,5,6,2,3,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[[1,2,7],[3,8],[4],[5],[6]] => [6,5,4,3,8,1,2,7] => [8,1,4,5,6,3,2,7] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[[1,4,6],[2,8],[3],[5],[7]] => [7,5,3,2,8,1,4,6] => [8,3,5,1,7,4,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[[1,3,6],[2,8],[4],[5],[7]] => [7,5,4,2,8,1,3,6] => [8,4,1,5,7,3,2,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[[1,2,6],[3,8],[4],[5],[7]] => [7,5,4,3,8,1,2,6] => [8,1,4,5,7,2,3,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[[1,4,5],[2,8],[3],[6],[7]] => [7,6,3,2,8,1,4,5] => [8,3,6,1,4,7,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[[1,2,5],[3,8],[4],[6],[7]] => [7,6,4,3,8,1,2,5] => [8,1,4,6,2,7,3,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[[1,3,4],[2,8],[5],[6],[7]] => [7,6,5,2,8,1,3,4] => [8,5,1,3,6,7,2,4] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[[1,2,4],[3,8],[5],[6],[7]] => [7,6,5,3,8,1,2,4] => [8,1,5,2,6,7,3,4] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[1,2,3],[4,8],[5],[6],[7]] => [7,6,5,4,8,1,2,3] => [8,1,2,5,6,7,4,3] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[[1,4,7],[2,6],[3],[5],[8]] => [8,5,3,2,6,1,4,7] => [6,3,5,1,8,2,4,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[[1,2,7],[3,6],[4],[5],[8]] => [8,5,4,3,6,1,2,7] => [6,1,4,5,8,3,2,7] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[[1,4,7],[2,5],[3],[6],[8]] => [8,6,3,2,5,1,4,7] => [5,3,6,1,2,8,4,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[[1,3,7],[2,5],[4],[6],[8]] => [8,6,4,2,5,1,3,7] => [5,4,1,6,2,8,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[[1,3,7],[2,4],[5],[6],[8]] => [8,6,5,2,4,1,3,7] => [4,5,1,2,6,8,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[[1,2,7],[3,4],[5],[6],[8]] => [8,6,5,3,4,1,2,7] => [4,1,5,3,6,8,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[[1,4,6],[2,7],[3],[5],[8]] => [8,5,3,2,7,1,4,6] => [7,3,5,1,8,4,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[[1,3,6],[2,7],[4],[5],[8]] => [8,5,4,2,7,1,3,6] => [7,4,1,5,8,3,2,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[[1,4,5],[2,7],[3],[6],[8]] => [8,6,3,2,7,1,4,5] => [7,3,6,1,4,8,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[[1,3,5],[2,7],[4],[6],[8]] => [8,6,4,2,7,1,3,5] => [7,4,1,6,3,8,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[[1,2,4],[3,7],[5],[6],[8]] => [8,6,5,3,7,1,2,4] => [7,1,5,2,6,8,3,4] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[1,2,6],[3,5],[4],[7],[8]] => [8,7,4,3,5,1,2,6] => [5,1,4,7,3,2,8,6] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[[1,3,6],[2,4],[5],[7],[8]] => [8,7,5,2,4,1,3,6] => [4,5,1,2,7,3,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[[1,2,6],[3,4],[5],[7],[8]] => [8,7,5,3,4,1,2,6] => [4,1,5,3,7,2,8,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[[1,4,5],[2,6],[3],[7],[8]] => [8,7,3,2,6,1,4,5] => [6,3,7,1,4,2,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[[1,3,5],[2,6],[4],[7],[8]] => [8,7,4,2,6,1,3,5] => [6,4,1,7,3,2,8,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[[1,2,5],[3,6],[4],[7],[8]] => [8,7,4,3,6,1,2,5] => [6,1,4,7,2,3,8,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[[1,3,4],[2,6],[5],[7],[8]] => [8,7,5,2,6,1,3,4] => [6,5,1,3,7,2,8,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[[1,2,4],[3,6],[5],[7],[8]] => [8,7,5,3,6,1,2,4] => [6,1,5,2,7,3,8,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,5],[3,4],[6],[7],[8]] => [8,7,6,3,4,1,2,5] => [4,1,6,3,2,7,8,5] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[[1,3,4],[2,5],[6],[7],[8]] => [8,7,6,2,5,1,3,4] => [5,6,1,3,2,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[[1,2,4],[3,5],[6],[7],[8]] => [8,7,6,3,5,1,2,4] => [5,1,6,2,3,7,8,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[[1,7,8],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8] => [2,3,4,5,6,1,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[1,6,8],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6,8] => [2,3,4,5,7,1,6,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[1,5,8],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5,8] => [2,3,4,6,1,7,5,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[[1,3,8],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3,8] => [2,4,1,5,6,7,3,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[[1,2,8],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8] => [3,1,4,5,6,7,2,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[[1,6,7],[2],[3],[4],[5],[8]] => [8,5,4,3,2,1,6,7] => [2,3,4,5,8,1,6,7] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[1,5,7],[2],[3],[4],[6],[8]] => [8,6,4,3,2,1,5,7] => [2,3,4,6,1,8,5,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[[1,4,7],[2],[3],[5],[6],[8]] => [8,6,5,3,2,1,4,7] => [2,3,5,1,6,8,4,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[[1,3,7],[2],[4],[5],[6],[8]] => [8,6,5,4,2,1,3,7] => [2,4,1,5,6,8,3,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[[1,2,7],[3],[4],[5],[6],[8]] => [8,6,5,4,3,1,2,7] => [3,1,4,5,6,8,2,7] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[[1,5,6],[2],[3],[4],[7],[8]] => [8,7,4,3,2,1,5,6] => [2,3,4,7,1,5,8,6] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[[1,4,6],[2],[3],[5],[7],[8]] => [8,7,5,3,2,1,4,6] => [2,3,5,1,7,4,8,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[[1,3,6],[2],[4],[5],[7],[8]] => [8,7,5,4,2,1,3,6] => [2,4,1,5,7,3,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[[1,2,6],[3],[4],[5],[7],[8]] => [8,7,5,4,3,1,2,6] => [3,1,4,5,7,2,8,6] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[[1,4,5],[2],[3],[6],[7],[8]] => [8,7,6,3,2,1,4,5] => [2,3,6,1,4,7,8,5] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[[1,3,5],[2],[4],[6],[7],[8]] => [8,7,6,4,2,1,3,5] => [2,4,1,6,3,7,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[[1,2,5],[3],[4],[6],[7],[8]] => [8,7,6,4,3,1,2,5] => [3,1,4,6,2,7,8,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[[1,3,4],[2],[5],[6],[7],[8]] => [8,7,6,5,2,1,3,4] => [2,5,1,3,6,7,8,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[[1,2,4],[3],[5],[6],[7],[8]] => [8,7,6,5,3,1,2,4] => [3,1,5,2,6,7,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => [4,1,2,5,6,7,8,3] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [6,7,8,4,1,2,3,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [6,7,8,1,5,2,3,4] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [6,7,1,8,5,2,4,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[[1,2],[3,6],[4,7],[5,8]] => [5,8,4,7,3,6,1,2] => [6,1,7,8,5,3,4,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [5,7,8,1,2,6,3,4] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[[1,2],[3,5],[4,7],[6,8]] => [6,8,4,7,3,5,1,2] => [5,1,7,8,3,6,4,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[[1,3],[2,4],[5,7],[6,8]] => [6,8,5,7,2,4,1,3] => [4,7,1,2,8,6,5,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => [5,6,8,1,2,3,7,4] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[[1,2],[3,5],[4,6],[7,8]] => [7,8,4,6,3,5,1,2] => [5,1,6,8,3,4,7,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[[1,3],[2,4],[5,6],[7,8]] => [7,8,5,6,2,4,1,3] => [4,6,1,2,8,5,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => [4,1,6,3,8,5,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[[1,5],[2,7],[3,8],[4],[6]] => [6,4,3,8,2,7,1,5] => [7,8,4,6,1,3,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[[1,4],[2,7],[3,8],[5],[6]] => [6,5,3,8,2,7,1,4] => [7,8,5,1,6,3,2,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[[1,3],[2,7],[4,8],[5],[6]] => [6,5,4,8,2,7,1,3] => [7,8,1,5,6,4,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[[1,4],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4] => [6,8,5,1,7,2,3,4] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[[1,2],[3,5],[4,8],[6],[7]] => [7,6,4,8,3,5,1,2] => [5,1,8,6,3,7,4,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[[1,3],[2,4],[5,8],[6],[7]] => [7,6,5,8,2,4,1,3] => [4,8,1,2,6,7,5,3] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[[1,2],[3,4],[5,8],[6],[7]] => [7,6,5,8,3,4,1,2] => [4,1,8,3,6,7,5,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[[1,5],[2,6],[3,7],[4],[8]] => [8,4,3,7,2,6,1,5] => [6,7,4,8,1,2,3,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[[1,4],[2,6],[3,7],[5],[8]] => [8,5,3,7,2,6,1,4] => [6,7,5,1,8,2,3,4] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[[1,3],[2,6],[4,7],[5],[8]] => [8,5,4,7,2,6,1,3] => [6,7,1,5,8,2,4,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[[1,2],[3,6],[4,7],[5],[8]] => [8,5,4,7,3,6,1,2] => [6,1,7,5,8,3,4,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[[1,4],[2,5],[3,7],[6],[8]] => [8,6,3,7,2,5,1,4] => [5,7,6,1,2,8,3,4] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[[1,3],[2,5],[4,7],[6],[8]] => [8,6,4,7,2,5,1,3] => [5,7,1,6,2,8,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[[1,2],[3,4],[5,7],[6],[8]] => [8,6,5,7,3,4,1,2] => [4,1,7,3,6,8,5,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[[1,4],[2,5],[3,6],[7],[8]] => [8,7,3,6,2,5,1,4] => [5,6,7,1,2,3,8,4] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[[1,3],[2,5],[4,6],[7],[8]] => [8,7,4,6,2,5,1,3] => [5,6,1,7,2,4,8,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[[1,2],[3,5],[4,6],[7],[8]] => [8,7,4,6,3,5,1,2] => [5,1,6,7,3,4,8,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[[1,3],[2,4],[5,6],[7],[8]] => [8,7,5,6,2,4,1,3] => [4,6,1,2,7,5,8,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => [4,1,6,3,7,5,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[[1,7],[2,8],[3],[4],[5],[6]] => [6,5,4,3,2,8,1,7] => [8,3,4,5,6,2,1,7] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[[1,6],[2,8],[3],[4],[5],[7]] => [7,5,4,3,2,8,1,6] => [8,3,4,5,7,1,2,6] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[[1,5],[2,8],[3],[4],[6],[7]] => [7,6,4,3,2,8,1,5] => [8,3,4,6,1,7,2,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[[1,4],[2,8],[3],[5],[6],[7]] => [7,6,5,3,2,8,1,4] => [8,3,5,1,6,7,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[[1,3],[2,8],[4],[5],[6],[7]] => [7,6,5,4,2,8,1,3] => [8,4,1,5,6,7,2,3] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[[1,2],[3,8],[4],[5],[6],[7]] => [7,6,5,4,3,8,1,2] => [8,1,4,5,6,7,3,2] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[[1,6],[2,7],[3],[4],[5],[8]] => [8,5,4,3,2,7,1,6] => [7,3,4,5,8,1,2,6] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[[1,4],[2,7],[3],[5],[6],[8]] => [8,6,5,3,2,7,1,4] => [7,3,5,1,6,8,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[[1,3],[2,7],[4],[5],[6],[8]] => [8,6,5,4,2,7,1,3] => [7,4,1,5,6,8,2,3] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[[1,2],[3,7],[4],[5],[6],[8]] => [8,6,5,4,3,7,1,2] => [7,1,4,5,6,8,3,2] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[[1,4],[2,6],[3],[5],[7],[8]] => [8,7,5,3,2,6,1,4] => [6,3,5,1,7,2,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[[1,3],[2,6],[4],[5],[7],[8]] => [8,7,5,4,2,6,1,3] => [6,4,1,5,7,2,8,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[[1,4],[2,5],[3],[6],[7],[8]] => [8,7,6,3,2,5,1,4] => [5,3,6,1,2,7,8,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[[1,3],[2,5],[4],[6],[7],[8]] => [8,7,6,4,2,5,1,3] => [5,4,1,6,2,7,8,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[[1,3],[2,4],[5],[6],[7],[8]] => [8,7,6,5,2,4,1,3] => [4,5,1,2,6,7,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => [4,1,5,3,6,7,8,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[[1,8],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,1,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[[1,7],[2],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,1,7] => [2,3,4,5,6,8,1,7] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[[1,6],[2],[3],[4],[5],[7],[8]] => [8,7,5,4,3,2,1,6] => [2,3,4,5,7,1,8,6] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[[1,5],[2],[3],[4],[6],[7],[8]] => [8,7,6,4,3,2,1,5] => [2,3,4,6,1,7,8,5] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[[1,4],[2],[3],[5],[6],[7],[8]] => [8,7,6,5,3,2,1,4] => [2,3,5,1,6,7,8,4] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[[1,3],[2],[4],[5],[6],[7],[8]] => [8,7,6,5,4,2,1,3] => [2,4,1,5,6,7,8,3] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => [3,1,4,5,6,7,8,2] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[[1,2,4,6,8],[3,5,7,9,10]] => [3,5,7,9,10,1,2,4,6,8] => [10,1,3,2,5,4,7,6,9,8] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => [10,1,2,3,4,6,7,8,9,5] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => [3,5,7,9,11,12,1,2,4,6,8,10] => [12,1,3,2,5,4,7,6,9,8,11,10] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[[1,2,3,4,5,6],[7,8,9,10,11,12]] => [7,8,9,10,11,12,1,2,3,4,5,6] => [12,1,2,3,4,5,7,8,9,10,11,6] => [[.,.],[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]]
[[1,2,3,4,5,6,7,8,9]] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => [9,1,2,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,9,7] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => [9,1,2,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,8,9,6] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => [6,1,2,3,4,7,8,9,5] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,9,4] => [[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => [4,1,2,5,6,7,8,9,3] => [[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => [3,1,4,5,6,7,8,9,2] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,1] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[[1,2,3,4,5,6,7,8,9,10]] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[[1,2,3,4,5,6,7,8,9],[10]] => [10,1,2,3,4,5,6,7,8,9] => [10,1,2,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,3,4,5,6,7,8],[9,10]] => [9,10,1,2,3,4,5,6,7,8] => [10,1,2,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[[1,2,3,4,5,6,7,8],[9],[10]] => [10,9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,10,8] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[[1,2,3,4,5,6,7],[8],[9],[10]] => [10,9,8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,9,10,7] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[[1,2,3,4,5,6],[7],[8],[9],[10]] => [10,9,8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,8,9,10,6] => [[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,1,2,3,4,5] => [6,1,2,3,4,7,8,9,10,5] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,9,10,4] => [[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => [4,1,2,5,6,7,8,9,10,3] => [[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => [3,1,4,5,6,7,8,9,10,2] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]],.]
[[1,3,4,5,6,7,8,9],[2]] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,4,5,6,7,8,9],[2],[3]] => [3,2,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,5,6,7,8,9],[2],[3],[4]] => [4,3,2,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[[1,6,7,8,9],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[[1,7,8,9],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,1,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,9,1,7] => [9,3,4,5,6,8,1,2,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,1,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[[1,3,4,5,6,7,8,9,10],[2]] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,4,5,6,7,8,9,10],[2],[3]] => [3,2,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,5,6,7,8,9,10],[2],[3],[4]] => [4,3,2,1,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,6,7,8,9,10],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[[1,7,8,9,10],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9,10] => [2,3,4,5,6,7,8,1,9,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,10,1,8] => [10,3,4,5,6,7,9,1,2,8] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,1,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[[1,8],[2,9],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,9,1,8] => [9,3,4,5,6,7,2,1,8] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],[.,.]]
[[1,3,5,7,9],[2,4,6,8]] => [2,4,6,8,1,3,5,7,9] => [8,2,1,4,3,6,5,7,9] => [[[.,.],.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,10,1,9] => [10,3,4,5,6,7,8,2,1,9] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[[1,3],[2,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,2,4,1,3] => [4,5,1,2,6,7,8,9,3] => [[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]]
[[1,5],[2,6],[3,7],[4,8],[9]] => [9,4,8,3,7,2,6,1,5] => [6,7,8,9,1,2,3,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[[1,3,5],[2,4,6],[7],[8],[9]] => [9,8,7,2,4,6,1,3,5] => [6,7,1,2,3,4,8,9,5] => [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[[1,2,4,6],[3,5,7],[8],[9]] => [9,8,3,5,7,1,2,4,6] => [7,1,8,2,3,4,5,9,6] => [[.,.],[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[[1,3,5,7],[2,4,6,8],[9]] => [9,2,4,6,8,1,3,5,7] => [8,9,1,2,3,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,3,5,7],[4,6,8],[9]] => [9,4,6,8,1,2,3,5,7] => [8,1,2,9,3,4,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[[1,2,3,4,5,7],[6,8],[9]] => [9,6,8,1,2,3,4,5,7] => [8,1,2,3,4,9,5,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[[1,2,3,4,5,6,8],[7,9]] => [7,9,1,2,3,4,5,6,8] => [9,1,2,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[[1,2,6],[3,7],[4,8],[5,9],[10]] => [10,5,9,4,8,3,7,1,2,6] => [7,1,8,9,10,2,3,4,5,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[[1,4,7],[2,5,8],[3,6,9],[10]] => [10,3,6,9,2,5,8,1,4,7] => [8,9,10,1,2,3,4,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,3,5,7],[2,4,6,8],[9],[10]] => [10,9,2,4,6,8,1,3,5,7] => [8,9,1,2,3,4,5,6,10,7] => [[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[[1,2,4,6,8],[3,5,7,9],[10]] => [10,3,5,7,9,1,2,4,6,8] => [9,1,10,2,3,4,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,2,3,4,5,6,7,9],[8]] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,2,3,4,5,6,9],[7,8]] => [7,8,1,2,3,4,5,6,9] => [8,1,2,3,4,5,7,6,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[[1,2,3,4,5,6,9],[7],[8]] => [8,7,1,2,3,4,5,6,9] => [7,1,2,3,4,5,8,6,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2,9] => [3,1,4,5,6,7,8,2,9] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[[1,3],[2,9],[4],[5],[6],[7],[8]] => [8,7,6,5,4,2,9,1,3] => [9,4,1,5,6,7,8,2,3] => [[[.,.],.],[[.,[.,[.,[.,.]]]],[.,.]]]
[[1,2,3,4,5,6,7,8,10],[9]] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,3,4,5,6,7,10],[8,9]] => [8,9,1,2,3,4,5,6,7,10] => [9,1,2,3,4,5,6,8,7,10] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[[1,3],[2,10],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,2,10,1,3] => [10,4,1,5,6,7,8,9,2,3] => [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[] => [] => [] => .
[[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,3,5,6,7,8,9],[2],[4]] => [4,2,1,3,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,4,6,7,8,9],[2],[3],[5]] => [5,3,2,1,4,6,7,8,9] => [2,3,5,1,4,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[[1,5,7,8,9],[2],[3],[4],[6]] => [6,4,3,2,1,5,7,8,9] => [2,3,4,6,1,5,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[[1,6,8,9],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6,8,9] => [2,3,4,5,7,1,6,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[[1,7,9],[2],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,1,7,9] => [2,3,4,5,6,8,1,7,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,9,1,8] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[[1,2,4,5,6,7,8,9,10],[3]] => [3,1,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,3,5,6,7,8,9,10],[2],[4]] => [4,2,1,3,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [10,8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,10,1,9] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[[1,3,4,5,6,7,8],[2,9]] => [2,9,1,3,4,5,6,7,8] => [9,2,1,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,3,4,5,6,7,8],[2],[9]] => [9,2,1,3,4,5,6,7,8] => [2,9,1,3,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,3,4,5,6,7],[2],[8],[9]] => [9,8,2,1,3,4,5,6,7] => [2,8,1,3,4,5,6,9,7] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[[1,3,4,5,6],[2],[7],[8],[9]] => [9,8,7,2,1,3,4,5,6] => [2,7,1,3,4,5,8,9,6] => [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[[1,3,4],[2],[5],[6],[7],[8],[9]] => [9,8,7,6,5,2,1,3,4] => [2,5,1,3,6,7,8,9,4] => [[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]]
[[1,3],[2],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,2,1,3] => [2,4,1,5,6,7,8,9,3] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[[1,3,4,5,6,7,8,9],[2,10]] => [2,10,1,3,4,5,6,7,8,9] => [10,2,1,3,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,3,4,5,6,7,8,9],[2],[10]] => [10,2,1,3,4,5,6,7,8,9] => [2,10,1,3,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,3,4,5,6,7,8],[2,9,10]] => [2,9,10,1,3,4,5,6,7,8] => [10,2,1,3,4,5,6,7,9,8] => [[[.,.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[[1,3,4,5,6,7,8],[2],[9],[10]] => [10,9,2,1,3,4,5,6,7,8] => [2,9,1,3,4,5,6,7,10,8] => [[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[[1,3,4],[2],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,2,1,3,4] => [2,5,1,3,6,7,8,9,10,4] => [[.,[.,.]],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,2,1,3] => [2,4,1,5,6,7,8,9,10,3] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[[1,2,3,5,6,7,8,9,10],[4]] => [4,1,2,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,3,4,6,7,8,9,10],[5]] => [5,1,2,3,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,3,4,5,6,7,9,10],[8]] => [8,1,2,3,4,5,6,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,3,4,5,6,8,9,10],[7]] => [7,1,2,3,4,5,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,3,4,5,7,8,9,10],[6]] => [6,1,2,3,4,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,4,5,6,7,8,9,10,11,12],[3]] => [3,1,2,4,5,6,7,8,9,10,11,12] => [3,1,2,4,5,6,7,8,9,10,11,12] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[[1,4,5,6,7,8],[2],[3],[9]] => [9,3,2,1,4,5,6,7,8] => [2,3,9,1,4,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[[1,5,6,7,8],[2],[3],[4],[9]] => [9,4,3,2,1,5,6,7,8] => [2,3,4,9,1,5,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[[1,6,7,8],[2],[3],[4],[5],[9]] => [9,5,4,3,2,1,6,7,8] => [2,3,4,5,9,1,6,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[[1,7,8],[2],[3],[4],[5],[6],[9]] => [9,6,5,4,3,2,1,7,8] => [2,3,4,5,6,9,1,7,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[1,4,5,6,7,8,9],[2],[3],[10]] => [10,3,2,1,4,5,6,7,8,9] => [2,3,10,1,4,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,5,6,7,8,9],[2],[3],[4],[10]] => [10,4,3,2,1,5,6,7,8,9] => [2,3,4,10,1,5,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[[1,6,7,8,9],[2],[3],[4],[5],[10]] => [10,5,4,3,2,1,6,7,8,9] => [2,3,4,5,10,1,6,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[[1,7,8,9],[2],[3],[4],[5],[6],[10]] => [10,6,5,4,3,2,1,7,8,9] => [2,3,4,5,6,10,1,7,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[[1,8,9],[2],[3],[4],[5],[6],[7],[10]] => [10,7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,10,1,8,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[[1,2,5,6,7,8,9],[3],[4]] => [4,3,1,2,5,6,7,8,9] => [3,1,4,2,5,6,7,8,9] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,5,6,7,8,9,10],[3],[4]] => [4,3,1,2,5,6,7,8,9,10] => [3,1,4,2,5,6,7,8,9,10] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,2,5,6,7,8],[3],[4],[9]] => [9,4,3,1,2,5,6,7,8] => [3,1,4,9,2,5,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[[1,2,7,8],[3],[4],[5],[6],[9]] => [9,6,5,4,3,1,2,7,8] => [3,1,4,5,6,9,2,7,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,2,1,4] => [2,3,5,1,6,7,8,9,10,4] => [[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]]
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,3,2,1,5] => [2,3,4,6,1,7,8,9,10,5] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]] => [10,9,7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,9,1,10,8] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]] => [10,9,8,6,5,4,3,2,1,7] => [2,3,4,5,6,8,1,9,10,7] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]]
[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]] => [10,9,8,7,5,4,3,2,1,6] => [2,3,4,5,7,1,8,9,10,6] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]]
[[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10],[12]] => [12,10,9,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,9,10,12,1,11] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]
[[1,2,3,4,5,7],[6],[8],[9]] => [9,8,6,1,2,3,4,5,7] => [6,1,2,3,4,8,5,9,7] => [[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[[1,2,3,4,5,6,8],[7],[9]] => [9,7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,9,6,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[[1,2,3,4,5,7,9],[6,8]] => [6,8,1,2,3,4,5,7,9] => [8,1,2,3,4,6,5,7,9] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[[1,2,4,5,6,7,8],[3,9]] => [3,9,1,2,4,5,6,7,8] => [9,1,3,2,4,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,3,4,5,6],[7,9],[8]] => [8,7,9,1,2,3,4,5,6] => [9,1,2,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[[1,2,3,4,5,6,7],[8,10],[9]] => [9,8,10,1,2,3,4,5,6,7] => [10,1,2,3,4,5,6,9,8,7] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[[1,3,4,5,6,7,9],[2,8]] => [2,8,1,3,4,5,6,7,9] => [8,2,1,3,4,5,6,7,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,3,4,5,6,7,8,10],[2,9]] => [2,9,1,3,4,5,6,7,8,10] => [9,2,1,3,4,5,6,7,8,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,2,3,4,5,6,8],[7,10],[9]] => [9,7,10,1,2,3,4,5,6,8] => [10,1,2,3,4,5,9,6,7,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[[1,7,8],[2,9],[3],[4],[5],[6]] => [6,5,4,3,2,9,1,7,8] => [9,3,4,5,6,2,1,7,8] => [[[[.,.],[.,[.,[.,.]]]],.],[.,[.,.]]]
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
searching the database
Sorry, this map was not found in the database.