- FindStat

Identifier

Mp00081: Standard tableaux —reading word permutation⟶ Permutations
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

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.