Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
[(1,2)] => [2,1] => [2,1] => [[.,.],.]
[(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3] => [[.,.],[[.,.],.]]
[(1,3),(2,4)] => [3,4,1,2] => [4,1,3,2] => [[.,[[.,.],.]],.]
[(1,4),(2,3)] => [4,3,2,1] => [2,3,4,1] => [[.,.],[.,[.,.]]]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [4,1,3,2,6,5] => [[.,[[.,.],.]],[[.,.],.]]
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [6,3,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],.]
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [4,3,5,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]]
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [3,5,2,6,4,1] => [[[.,.],.],[[.,.],[.,.]]]
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [2,6,1,5,4,3] => [[.,.],[[[[.,.],.],.],.]]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [[.,[.,[[.,.],[.,.]]]],.]
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [5,6,3,2,1,4] => [[[[.,.],.],[.,.]],[.,.]]
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,6,3,5,4] => [[.,.],[[.,[[.,.],.]],.]]
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]]
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [6,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],.]
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [5,3,1,4,6,2] => [[[.,[.,.]],[.,.]],[.,.]]
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [3,1,4,6,5,2] => [[.,[.,.]],[.,[[.,.],.]]]
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]]
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [4,1,3,2,6,5,8,7] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [6,3,5,1,2,4,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [4,3,5,6,1,2,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [8,3,7,5,2,1,4,6] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [6,3,7,5,1,8,4,2] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [6,5,2,7,1,8,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [8,5,2,7,4,1,3,6] => [[[[.,.],[[.,.],.]],[[.,.],.]],.]
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [3,5,2,6,4,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [2,6,1,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [6,1,2,4,5,3,8,7] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [5,6,3,2,1,4,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,1,6,3,5,4,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [6,4,3,5,1,2,8,7] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [5,3,1,4,6,2,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [3,1,4,6,5,2,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [8,3,4,5,7,1,2,6] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [6,3,4,5,7,8,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [5,7,4,6,2,8,3,1] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [2,8,4,6,1,7,3,5] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [8,1,4,7,2,6,3,5] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [3,4,7,8,5,2,1,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [5,7,2,4,8,1,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [7,8,3,5,1,2,4,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [2,1,8,5,7,3,4,6] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [2,1,6,5,7,8,3,4] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [8,6,3,5,1,7,4,2] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [5,8,2,4,6,7,3,1] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [3,4,8,6,5,7,1,2] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [7,5,4,8,1,6,3,2] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [5,1,4,6,8,2,7,3] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [2,5,4,6,7,1,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [2,4,6,3,7,5,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [4,1,6,3,8,5,7,2] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [3,7,4,2,8,6,5,1] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [7,4,1,3,5,8,6,2] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [6,5,8,4,1,7,3,2] => [[[[.,[[.,.],.]],.],.],[[.,.],.]]
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [8,5,3,7,4,1,6,2] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [2,1,5,7,4,8,6,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [2,1,4,8,3,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [7,4,3,8,2,1,6,5] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [6,3,7,4,1,8,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [8,3,1,2,5,7,6,4] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [3,1,8,2,7,6,5,4] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [2,3,8,1,6,7,5,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [4,3,7,2,6,8,5,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [4,7,2,3,8,5,6,1] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [3,8,2,1,7,5,6,4] => [[[.,.],.],[[[[.,.],[.,.]],.],.]]
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [2,8,1,3,6,5,7,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [7,8,2,4,3,6,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [6,8,3,2,4,1,7,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,1,8,3,4,6,7,5] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,1,7,8,5,4,3,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [5,7,3,8,1,4,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [7,1,8,4,5,3,2,6] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [2,7,8,5,4,3,1,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [8,7,1,6,3,4,2,5] => [[[.,[[[.,.],[.,[.,.]]],.]],.],.]
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [3,8,6,7,2,4,1,5] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [5,6,7,8,3,4,2,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [5,3,8,7,4,2,6,1] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [4,3,8,7,2,1,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [8,3,6,1,4,2,7,5] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [7,3,5,8,2,4,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [2,3,4,1,8,5,7,6] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [4,1,3,2,8,5,7,6] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [4,1,3,2,6,7,8,5] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [8,3,5,6,2,7,1,4] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [7,3,6,5,1,2,8,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [5,3,6,1,8,7,2,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [4,3,5,6,7,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [3,5,6,7,8,4,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [5,6,2,8,7,4,1,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [7,8,5,6,1,4,2,3] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [2,8,6,5,4,7,1,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [8,1,6,4,5,7,2,3] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]
>>> Load all 349 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [5,8,3,6,1,7,2,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [2,1,8,6,5,7,3,4] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [2,1,7,5,3,6,8,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [6,7,3,5,2,1,8,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [8,7,5,4,2,6,1,3] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [7,1,4,2,5,6,8,3] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [2,7,4,1,6,5,8,3] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [4,6,1,2,8,7,3,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [3,4,6,1,7,8,2,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [3,4,2,5,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [2,4,1,5,8,7,6,3] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [4,1,2,5,8,6,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [6,4,2,1,5,8,7,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [8,5,2,4,6,1,7,3] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [7,5,3,2,6,8,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [2,1,5,3,6,8,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [8,4,3,5,6,7,1,2] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [7,3,5,4,6,1,8,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [6,3,4,1,5,7,8,2] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [4,3,1,5,7,6,8,2] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [3,1,4,5,6,8,7,2] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [3,4,1,2,6,5,8,7,10,9] => [4,1,3,2,6,5,8,7,10,9] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9] => [[.,.],[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => [4,3,5,6,1,2,8,7,10,9] => [[[.,[.,.]],.],[.,[.,[[.,.],[[.,.],.]]]]]
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [8,3,2,5,4,7,6,1,10,9] => [6,3,7,5,1,8,4,2,10,9] => [[[.,[.,.]],[[.,.],.]],[.,[.,[[.,.],.]]]]
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [10,3,2,5,4,7,6,9,8,1] => [8,3,9,5,1,7,4,10,6,2] => [[[.,[.,.]],[[.,.],[[.,.],.]]],[.,[.,.]]]
[(1,6),(2,4),(3,5),(7,8),(9,10)] => [6,4,5,2,3,1,8,7,10,9] => [3,5,2,6,4,1,8,7,10,9] => [[[.,.],.],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9] => [6,1,2,4,5,3,8,7,10,9] => [[.,[.,[[.,.],[.,.]]]],[[.,.],[[.,.],.]]]
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [2,1,6,3,5,4,8,7,10,9] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [2,1,4,5,6,3,8,7,10,9] => [[.,.],[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]]
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [2,3,4,5,6,1,8,7,10,9] => [[.,.],[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => [6,3,4,5,7,8,1,2,10,9] => [[[.,[.,.]],[.,[.,.]]],[.,[.,[[.,.],.]]]]
[(1,10),(2,5),(3,4),(6,7),(8,9)] => [10,5,4,3,2,7,6,9,8,1] => [8,3,4,5,9,7,1,10,6,2] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],[.,[.,.]]]
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => [2,1,6,5,7,8,3,4,10,9] => [[.,.],[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]]
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [2,5,4,6,7,1,8,3,10,9] => [[.,.],[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]]
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => [8,5,4,6,7,1,9,10,3,2] => [[[[.,[[.,.],.]],.],[.,[.,.]]],[.,[.,.]]]
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,10,5,4,7,6,9,8,3] => [2,1,8,5,9,7,3,10,6,4] => [[.,.],[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]]
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [10,9,4,3,6,5,8,7,2,1] => [2,7,4,8,6,1,9,5,10,3] => [[.,.],[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]]
[(1,2),(3,8),(4,6),(5,7),(9,10)] => [2,1,8,6,7,4,5,3,10,9] => [2,1,5,7,4,8,6,3,10,9] => [[.,.],[[[.,.],.],[[.,.],[.,[[.,.],.]]]]]
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9] => [8,1,2,3,5,6,7,4,10,9] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[[.,.],.]]
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => [2,1,8,3,4,6,7,5,10,9] => [[.,.],[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]]
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9] => [4,1,3,2,8,5,7,6,10,9] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => [2,1,4,3,8,5,7,6,10,9] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,6,7,8,5,10,9] => [[.,.],[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]]
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [2,3,4,1,6,7,8,5,10,9] => [[.,.],[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => [4,3,5,6,7,8,1,2,10,9] => [[[.,[.,.]],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[(1,10),(2,3),(4,7),(5,6),(8,9)] => [10,3,2,7,6,5,4,9,8,1] => [8,3,9,5,6,7,1,10,4,2] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],[.,[.,.]]]
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [2,1,4,5,6,7,8,3,10,9] => [[.,.],[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [2,3,4,5,6,7,8,1,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[(1,9),(2,7),(3,6),(4,5),(8,10)] => [9,7,6,5,4,3,2,10,1,8] => [10,3,4,5,6,7,9,1,2,8] => [[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [8,3,4,5,6,7,9,10,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => [2,1,8,5,6,7,9,10,3,4] => [[.,.],[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]]
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [2,7,4,5,6,8,9,1,10,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]]
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => [2,1,4,3,8,7,9,10,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]]
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [4,3,2,1,10,7,6,9,8,5] => [2,3,4,1,8,7,9,10,5,6] => [[.,.],[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]]
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => [4,3,7,8,6,10,9,2,5,1] => [[[[.,.],.],.],[[[.,.],.],[.,[[.,.],.]]]]
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [2,1,4,7,6,8,9,3,10,5] => [[.,.],[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]]
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [2,3,6,5,7,8,1,9,10,4] => [[.,.],[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[(1,10),(2,8),(3,9),(4,6),(5,7)] => [10,8,9,6,7,4,5,2,3,1] => [3,5,2,7,4,9,6,10,8,1] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[(1,2),(3,4),(5,10),(6,8),(7,9)] => [2,1,4,3,10,8,9,6,7,5] => [2,1,4,3,7,9,6,10,8,5] => [[.,.],[[.,.],[[[.,.],.],[[.,.],[.,.]]]]]
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => [2,1,10,3,4,5,7,8,9,6] => [[.,.],[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]]
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [10,1,2,3,4,6,7,8,9,5] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7] => [4,1,3,2,10,5,6,8,9,7] => [[.,[[.,.],.]],[[.,[.,[[.,.],[.,.]]]],.]]
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => [2,1,4,3,10,5,6,8,9,7] => [[.,.],[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]]
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => [2,1,6,3,5,4,10,7,9,8] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8] => [6,1,2,4,5,3,10,7,9,8] => [[.,[.,[[.,.],[.,.]]]],[[.,[[.,.],.]],.]]
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8] => [4,1,3,2,6,5,10,7,9,8] => [[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,10,7,9,8] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,8,9,10,7] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [2,3,4,1,6,5,8,9,10,7] => [[.,.],[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]]
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => [4,3,5,6,1,2,8,9,10,7] => [[[.,[.,.]],.],[.,[.,[[.,.],[.,[.,.]]]]]]
[(1,10),(2,3),(4,5),(6,9),(7,8)] => [10,3,2,5,4,9,8,7,6,1] => [6,3,7,5,1,8,9,10,4,2] => [[[.,[.,.]],[[.,.],.]],[.,[.,[.,[.,.]]]]]
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [2,1,4,5,6,3,8,9,10,7] => [[.,.],[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]]
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [2,3,4,5,6,1,8,9,10,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => [6,3,4,5,7,8,9,10,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,10,5,4,9,8,7,6,3] => [2,1,6,5,7,8,9,10,3,4] => [[.,.],[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]]
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [2,5,4,6,7,8,9,1,10,3] => [[.,.],[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,5] => [[.,.],[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,5] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [4,3,5,6,7,8,9,10,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,3] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,4,5,6,7,8,9,10,3,12,11] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [12,3,2,9,8,7,6,5,4,11,10,1] => [10,3,11,5,6,7,8,9,1,12,4,2] => [[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => [2,1,10,5,6,7,8,9,11,12,3,4] => [[.,.],[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => [4,3,5,6,7,8,9,10,1,2,12,11] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [12,11,4,3,8,7,6,5,10,9,2,1] => [2,9,4,10,6,7,8,1,11,5,12,3] => [[.,.],[[[.,.],[[.,.],[.,[.,.]]]],[.,[.,[.,.]]]]]
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,1,4,3,6,7,8,5,10,9,12,11] => [[.,.],[[.,.],[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]]]
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [12,3,2,11,8,7,6,5,10,9,4,1] => [4,3,9,10,6,7,8,12,11,2,5,1] => [[[[.,.],.],.],[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]]
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [2,1,4,9,6,7,8,10,11,3,12,5] => [[.,.],[[.,.],[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]]]
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [2,3,4,1,6,7,8,5,10,9,12,11] => [[.,.],[.,[.,[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]]]]
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [12,9,4,3,8,7,6,5,2,11,10,1] => [10,5,4,6,7,8,9,1,11,12,3,2] => [[[[.,[[.,.],.]],.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,6,7,8,5,10,11,12,9] => [[.,.],[[.,.],[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]]]
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [2,5,4,6,7,8,9,1,10,3,12,11] => [[.,.],[[[.,.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [2,3,4,1,6,7,8,5,10,11,12,9] => [[.,.],[.,[.,[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [12,11,10,5,4,7,6,9,8,3,2,1] => [2,3,8,5,9,7,1,10,6,11,12,4] => [[.,.],[.,[[[.,.],[[.,.],.]],[.,[.,[.,[.,.]]]]]]]
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,10,5,4,7,6,9,8,3,12,11] => [2,1,8,5,9,7,3,10,6,4,12,11] => [[.,.],[[[.,[.,.]],[[.,.],.]],[.,[.,[[.,.],.]]]]]
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [12,3,2,5,4,7,6,9,8,11,10,1] => [10,3,11,5,1,7,4,9,6,12,8,2] => [[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]],[.,[.,.]]]
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,12,5,4,7,6,9,8,11,10,3] => [2,1,10,5,11,7,3,9,6,12,8,4] => [[.,.],[[[.,[.,.]],[[.,.],[[.,.],.]]],[.,[.,.]]]]
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [10,3,2,5,4,7,6,9,8,1,12,11] => [8,3,9,5,1,7,4,10,6,2,12,11] => [[[.,[.,.]],[[.,.],[[.,.],.]]],[.,[.,[[.,.],.]]]]
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [12,11,4,3,10,7,6,9,8,5,2,1] => [2,5,4,8,9,7,11,10,3,6,12,1] => [[.,.],[[[.,.],.],[[[.,.],.],[.,[[.,.],[.,.]]]]]]
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,10,7,6,9,8,5,12,11] => [2,1,4,3,8,7,9,10,5,6,12,11] => [[.,.],[[.,.],[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]]]
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [12,3,2,11,10,7,6,9,8,5,4,1] => [4,3,5,8,9,7,12,10,1,11,6,2] => [[[.,[.,.]],.],[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]]
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [2,1,4,5,8,7,9,10,3,11,12,6] => [[.,.],[[.,.],[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]]
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [4,3,2,1,10,7,6,9,8,5,12,11] => [2,3,4,1,8,7,9,10,5,6,12,11] => [[.,.],[.,[.,[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]]]]
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [12,5,4,3,2,7,6,9,8,11,10,1] => [10,3,4,5,11,7,1,9,6,12,8,2] => [[[.,[.,.]],[.,[.,[[.,.],[[.,.],.]]]]],[.,[.,.]]]
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,12,7,6,9,8,11,10,5] => [2,1,4,3,10,7,11,9,5,12,8,6] => [[.,.],[[.,.],[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]]]
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [10,5,4,3,2,7,6,9,8,1,12,11] => [8,3,4,5,9,7,1,10,6,2,12,11] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],[.,[.,[[.,.],.]]]]
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [4,3,2,1,12,7,6,9,8,11,10,5] => [2,3,4,1,10,7,11,9,5,12,8,6] => [[.,.],[.,[.,[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]]]]
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [12,11,8,5,4,7,6,3,10,9,2,1] => [2,9,6,5,7,8,1,10,11,4,12,3] => [[.,.],[[[[[.,.],.],.],[.,[.,.]]],[.,[.,[.,.]]]]]
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,8,5,4,7,6,3,10,9,12,11] => [2,1,6,5,7,8,3,4,10,9,12,11] => [[.,.],[[[.,[.,.]],.],[.,[.,[[.,.],[[.,.],.]]]]]]
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [12,3,2,5,4,7,6,11,10,9,8,1] => [8,3,9,5,1,7,4,10,11,12,6,2] => [[[.,[.,.]],[[.,.],[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,12,5,4,7,6,11,10,9,8,3] => [2,1,8,5,9,7,3,10,11,12,6,4] => [[.,.],[[[.,[.,.]],[[.,.],.]],[.,[.,[.,[.,.]]]]]]
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [8,3,2,5,4,7,6,1,10,9,12,11] => [6,3,7,5,1,8,4,2,10,9,12,11] => [[[.,[.,.]],[[.,.],.]],[.,[.,[[.,.],[[.,.],.]]]]]
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [12,9,8,5,4,7,6,3,2,11,10,1] => [10,3,6,5,7,8,1,9,11,12,4,2] => [[[.,[.,.]],[[[.,.],.],[.,[.,[.,.]]]]],[.,[.,.]]]
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,8,5,4,7,6,3,12,11,10,9] => [2,1,6,5,7,8,3,4,10,11,12,9] => [[.,.],[[[.,[.,.]],.],[.,[.,[[.,.],[.,[.,.]]]]]]]
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [2,3,6,5,7,8,1,9,10,4,12,11] => [[.,.],[.,[[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]]]]
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [8,3,2,5,4,7,6,1,12,11,10,9] => [6,3,7,5,1,8,4,2,10,11,12,9] => [[[.,[.,.]],[[.,.],.]],[.,[.,[[.,.],[.,[.,.]]]]]]
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [12,5,4,3,2,7,6,11,10,9,8,1] => [8,3,4,5,9,7,1,10,11,12,6,2] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],[.,[.,[.,[.,.]]]]]
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,12,7,6,11,10,9,8,5] => [2,1,4,3,8,7,9,10,11,12,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]]]
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [8,5,4,3,2,7,6,1,10,9,12,11] => [6,3,4,5,7,8,1,2,10,9,12,11] => [[[.,[.,.]],[.,[.,.]]],[.,[.,[[.,.],[[.,.],.]]]]]
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => [2,3,4,1,8,7,9,10,11,12,5,6] => [[.,.],[.,[.,[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]]]]
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [8,5,4,3,2,7,6,1,12,11,10,9] => [6,3,4,5,7,8,1,2,10,11,12,9] => [[[.,[.,.]],[.,[.,.]]],[.,[.,[[.,.],[.,[.,.]]]]]]
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [2,3,4,7,6,8,9,1,10,11,12,5] => [[.,.],[.,[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]]]
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [2,1,4,7,6,8,9,3,10,5,12,11] => [[.,.],[[.,.],[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]]]
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [12,3,2,9,6,5,8,7,4,11,10,1] => [10,3,11,7,6,8,9,4,1,12,5,2] => [[[.,[.,.]],[[[.,[.,.]],.],[.,[.,.]]]],[.,[.,.]]]
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,12,9,6,5,8,7,4,11,10,3] => [2,1,10,7,6,8,9,3,11,12,5,4] => [[.,.],[[[[.,[[.,.],.]],.],[.,[.,.]]],[.,[.,.]]]]
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [10,3,2,9,6,5,8,7,4,1,12,11] => [4,3,7,8,6,10,9,2,5,1,12,11] => [[[[.,.],.],.],[[[.,.],.],[.,[[.,.],[[.,.],.]]]]]
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [12,11,4,3,6,5,8,7,10,9,2,1] => [2,9,4,10,6,1,8,5,11,7,12,3] => [[.,.],[[[.,.],[[.,.],[[.,.],.]]],[.,[.,[.,.]]]]]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [12,3,2,11,6,5,8,7,10,9,4,1] => [4,3,9,10,6,12,8,2,11,7,5,1] => [[[[.,.],.],.],[[[.,.],[[.,.],.]],[.,[[.,.],.]]]]
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,12,11,6,5,8,7,10,9,4,3] => [2,1,4,9,6,10,8,3,11,7,12,5] => [[.,.],[[.,.],[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]]]
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [2,3,4,1,6,5,8,7,10,9,12,11] => [[.,.],[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]]
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [12,9,4,3,6,5,8,7,2,11,10,1] => [10,7,4,8,6,1,9,5,11,12,3,2] => [[[[.,[[.,.],.]],[[.,.],.]],[.,[.,.]]],[.,[.,.]]]
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,10,11,12,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]]
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [10,9,4,3,6,5,8,7,2,1,12,11] => [2,7,4,8,6,1,9,5,10,3,12,11] => [[.,.],[[[.,.],[[.,.],.]],[.,[.,[.,[[.,.],.]]]]]]
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [2,3,4,1,6,5,8,7,10,11,12,9] => [[.,.],[.,[.,[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]]]
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [2,3,6,5,7,8,9,10,1,11,12,4] => [[.,.],[.,[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,10,5,4,9,8,7,6,3,12,11] => [2,1,6,5,7,8,9,10,3,4,12,11] => [[.,.],[[[.,[.,.]],.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [12,3,2,5,4,9,8,7,6,11,10,1] => [10,3,11,5,1,7,8,9,4,12,6,2] => [[[.,[.,.]],[[.,.],[[.,.],[.,[.,.]]]]],[.,[.,.]]]
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,12,5,4,9,8,7,6,11,10,3] => [2,1,10,5,11,7,8,9,3,12,6,4] => [[.,.],[[[.,[.,.]],[[.,.],[.,[.,.]]]],[.,[.,.]]]]
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [10,3,2,5,4,9,8,7,6,1,12,11] => [6,3,7,5,1,8,9,10,4,2,12,11] => [[[.,[.,.]],[[.,.],.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [2,5,4,6,7,8,9,10,11,1,12,3] => [[.,.],[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,1,4,3,6,7,8,9,10,5,12,11] => [[.,.],[[.,.],[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]]
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [12,3,2,11,10,9,8,7,6,5,4,1] => [4,3,5,6,7,8,9,10,11,12,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,11,12,3] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [2,3,4,1,6,7,8,9,10,5,12,11] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [12,5,4,3,2,9,8,7,6,11,10,1] => [10,3,4,5,11,7,8,9,1,12,6,2] => [[[.,[.,.]],[.,[.,[[.,.],[.,[.,.]]]]]],[.,[.,.]]]
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => [2,1,4,3,10,7,8,9,11,12,5,6] => [[.,.],[[.,.],[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]]]
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => [6,3,4,5,7,8,9,10,1,2,12,11] => [[[.,[.,.]],[.,[.,.]]],[.,[.,[.,[.,[[.,.],.]]]]]]
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [4,3,2,1,12,9,8,7,6,11,10,5] => [2,3,4,1,10,7,8,9,11,12,5,6] => [[.,.],[.,[.,[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]]]]
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [12,11,6,5,4,3,8,7,10,9,2,1] => [2,9,4,5,6,10,8,1,11,7,12,3] => [[.,.],[[[.,.],[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]]
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,4,5,6,3,8,7,10,9,12,11] => [[.,.],[[.,.],[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [12,3,2,5,4,11,8,7,10,9,6,1] => [6,3,9,5,2,10,8,12,11,4,7,1] => [[[[.,.],.],[[.,.],.]],[[[.,.],.],[.,[[.,.],.]]]]
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,12,5,4,11,8,7,10,9,6,3] => [2,1,6,5,9,10,8,12,11,4,7,3] => [[.,.],[[[[.,.],.],.],[[[.,.],.],[.,[[.,.],.]]]]]
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [6,3,2,5,4,1,8,7,10,9,12,11] => [4,3,5,6,1,2,8,7,10,9,12,11] => [[[.,[.,.]],.],[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [12,9,6,5,4,3,8,7,2,11,10,1] => [10,7,4,5,6,8,9,1,11,12,3,2] => [[[[.,[[.,.],.]],[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,4,5,6,3,8,7,10,11,12,9] => [[.,.],[[.,.],[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]]]
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [2,7,4,5,6,8,9,1,10,3,12,11] => [[.,.],[[[.,.],[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]]
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [6,3,2,5,4,1,8,7,12,11,10,9] => [4,3,5,6,1,2,8,7,10,11,12,9] => [[[.,[.,.]],.],[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]]
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [12,5,4,3,2,11,8,7,10,9,6,1] => [6,3,4,5,9,10,8,12,11,2,7,1] => [[[[.,.],.],[.,[.,.]]],[[[.,.],.],[.,[[.,.],.]]]]
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [2,1,4,3,6,9,8,10,11,5,12,7] => [[.,.],[[.,.],[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]]]
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [2,3,4,5,6,1,8,7,10,9,12,11] => [[.,.],[.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]]
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [2,3,4,1,6,9,8,10,11,5,12,7] => [[.,.],[.,[.,[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]]]]
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [2,3,4,5,6,1,8,7,10,11,12,9] => [[.,.],[.,[.,[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]]]]
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [2,3,8,5,6,7,9,10,1,11,12,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]]]
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,10,7,6,5,4,9,8,3,12,11] => [2,1,8,5,6,7,9,10,3,4,12,11] => [[.,.],[[[.,[.,.]],[.,[.,.]]],[.,[.,[[.,.],.]]]]]
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [12,3,2,7,6,5,4,9,8,11,10,1] => [10,3,11,5,6,7,1,9,4,12,8,2] => [[[.,[.,.]],[[.,.],[.,[.,[[.,.],.]]]]],[.,[.,.]]]
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,12,7,6,5,4,9,8,11,10,3] => [2,1,10,5,6,7,11,9,3,12,8,4] => [[.,.],[[[.,[.,.]],[.,[.,[[.,.],.]]]],[.,[.,.]]]]
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [10,3,2,7,6,5,4,9,8,1,12,11] => [8,3,9,5,6,7,1,10,4,2,12,11] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],[.,[.,[[.,.],.]]]]
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [12,11,4,3,6,5,10,9,8,7,2,1] => [2,7,4,8,6,1,9,10,11,5,12,3] => [[.,.],[[[.,.],[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]]
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,1,4,3,6,5,8,9,10,7,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]]]
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [12,3,2,11,6,5,10,9,8,7,4,1] => [4,3,7,8,6,9,10,12,11,5,1,2] => [[[.,[.,.]],.],[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]]
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [2,1,4,7,6,8,9,10,11,3,12,5] => [[.,.],[[.,.],[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]]
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [2,3,4,1,6,5,8,9,10,7,12,11] => [[.,.],[.,[.,[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]]]]
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [12,7,4,3,6,5,2,9,8,11,10,1] => [10,5,4,6,7,1,11,9,3,12,8,2] => [[[[.,[[.,.],.]],.],[.,[.,[[.,.],.]]]],[.,[.,.]]]
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,12,9,8,11,10,7] => [2,1,4,3,6,5,10,9,11,12,7,8] => [[.,.],[[.,.],[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]]]
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [10,7,4,3,6,5,2,9,8,1,12,11] => [8,5,4,6,7,1,9,10,3,2,12,11] => [[[[.,[[.,.],.]],.],[.,[.,.]]],[.,[.,[[.,.],.]]]]
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [4,3,2,1,6,5,12,9,8,11,10,7] => [2,3,4,1,6,5,10,9,11,12,7,8] => [[.,.],[.,[.,[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]]]]
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [2,9,4,5,6,7,8,10,11,1,12,3] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]]
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,4,5,6,7,8,3,10,9,12,11] => [[.,.],[[.,.],[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [12,3,2,7,6,5,4,11,10,9,8,1] => [8,3,9,5,6,7,1,10,11,12,4,2] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,12,7,6,5,4,11,10,9,8,3] => [2,1,8,5,6,7,9,10,11,12,3,4] => [[.,.],[[[.,[.,.]],[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => [4,3,5,6,7,8,1,2,10,9,12,11] => [[[.,[.,.]],.],[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [12,9,8,7,6,5,4,3,2,11,10,1] => [10,3,4,5,6,7,8,9,11,12,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,4,5,6,7,8,3,10,11,12,9] => [[.,.],[[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => [4,3,5,6,7,8,1,2,10,11,12,9] => [[[.,[.,.]],.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [12,7,4,3,6,5,2,11,10,9,8,1] => [8,5,4,6,7,1,9,10,11,12,3,2] => [[[[.,[[.,.],.]],.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,1,4,3,6,5,8,9,10,11,12,7] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]]
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [2,5,4,6,7,1,8,3,10,9,12,11] => [[.,.],[[[.,.],.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [2,3,4,1,6,5,8,9,10,11,12,7] => [[.,.],[.,[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [2,5,4,6,7,1,8,3,10,11,12,9] => [[.,.],[[[.,.],.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [2,7,4,5,6,8,9,10,11,1,12,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]]
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,4,5,6,3,8,9,10,7,12,11] => [[.,.],[[.,.],[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]]
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [12,3,2,5,4,11,10,9,8,7,6,1] => [6,3,7,5,1,8,9,10,11,12,4,2] => [[[.,[.,.]],[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,12,5,4,11,10,9,8,7,6,3] => [2,1,6,5,7,8,9,10,11,12,3,4] => [[.,.],[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [6,3,2,5,4,1,10,9,8,7,12,11] => [4,3,5,6,1,2,8,9,10,7,12,11] => [[[.,[.,.]],.],[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [12,7,6,5,4,3,2,9,8,11,10,1] => [10,3,4,5,6,7,11,9,1,12,8,2] => [[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]],[.,[.,.]]]
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,6,5,4,3,12,9,8,11,10,7] => [2,1,4,5,6,3,10,9,11,12,7,8] => [[.,.],[[.,.],[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]]]
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [10,7,6,5,4,3,2,9,8,1,12,11] => [8,3,4,5,6,7,9,10,1,2,12,11] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,[.,[[.,.],.]]]]
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [6,3,2,5,4,1,12,9,8,11,10,7] => [4,3,5,6,1,2,10,9,11,12,7,8] => [[[.,[.,.]],.],[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]]
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => [6,3,4,5,7,8,9,10,11,12,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,11,12,5] => [[.,.],[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [2,3,4,5,6,1,8,9,10,7,12,11] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]]]
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,11,12,5] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [6,5,4,3,2,1,12,9,8,11,10,7] => [2,3,4,5,6,1,10,9,11,12,7,8] => [[.,.],[.,[.,[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]]]]
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [12,7,6,5,4,3,2,11,10,9,8,1] => [8,3,4,5,6,7,9,10,11,12,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,4,5,6,3,8,9,10,11,12,7] => [[.,.],[[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [2,3,4,5,6,7,8,1,10,9,12,11] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]]
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => [4,3,5,6,1,2,8,9,10,11,12,7] => [[[.,[.,.]],.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [2,3,4,5,6,7,8,1,10,11,12,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]]
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [2,3,4,5,6,1,8,9,10,11,12,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]]
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => [2,1,4,3,6,5,8,7,12,9,11,10] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]]
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => [2,1,4,3,6,5,10,7,9,8,12,11] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => [2,1,4,3,6,5,12,7,8,10,11,9] => [[.,.],[[.,.],[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]]]
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => [2,1,4,3,8,5,7,6,10,9,12,11] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => [2,1,4,3,8,5,7,6,12,9,11,10] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => [2,1,4,3,10,5,6,8,9,7,12,11] => [[.,.],[[.,.],[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]]]
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => [2,1,4,3,12,5,6,7,9,10,11,8] => [[.,.],[[.,.],[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]]]
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => [2,1,6,3,5,4,8,7,10,9,12,11] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => [2,1,6,3,5,4,8,7,12,9,11,10] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]]
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,6,3,5,4,10,7,9,8,12,11] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => [2,1,6,3,5,4,12,7,8,10,11,9] => [[.,.],[[.,[[.,.],.]],[[.,[.,[[.,.],[.,.]]]],.]]]
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => [2,1,8,3,4,6,7,5,10,9,12,11] => [[.,.],[[.,[.,[[.,.],[.,.]]]],[[.,.],[[.,.],.]]]]
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => [2,1,8,3,4,6,7,5,12,9,11,10] => [[.,.],[[.,[.,[[.,.],[.,.]]]],[[.,[[.,.],.]],.]]]
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => [2,1,10,3,4,5,7,8,9,6,12,11] => [[.,.],[[.,[.,[.,[[.,.],[.,[.,.]]]]]],[[.,.],.]]]
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => [2,1,12,3,4,5,6,8,9,10,11,7] => [[.,.],[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]]
[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [3,4,1,2,6,5,8,7,10,9,12,11] => [4,1,3,2,6,5,8,7,10,9,12,11] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [3,4,1,2,6,5,8,7,11,12,9,10] => [4,1,3,2,6,5,8,7,12,9,11,10] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [3,4,1,2,6,5,9,10,7,8,12,11] => [4,1,3,2,6,5,10,7,9,8,12,11] => [[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]
[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [3,4,1,2,6,5,10,11,12,7,8,9] => [4,1,3,2,6,5,12,7,8,10,11,9] => [[.,[[.,.],.]],[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]]
[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [3,4,1,2,7,8,5,6,10,9,12,11] => [4,1,3,2,8,5,7,6,10,9,12,11] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [3,4,1,2,7,8,5,6,11,12,9,10] => [4,1,3,2,8,5,7,6,12,9,11,10] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [3,4,1,2,8,9,10,5,6,7,12,11] => [4,1,3,2,10,5,6,8,9,7,12,11] => [[.,[[.,.],.]],[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]]
[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [3,4,1,2,9,10,11,12,5,6,7,8] => [4,1,3,2,12,5,6,7,9,10,11,8] => [[.,[[.,.],.]],[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]]
[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [4,5,6,1,2,3,8,7,10,9,12,11] => [6,1,2,4,5,3,8,7,10,9,12,11] => [[.,[.,[[.,.],[.,.]]]],[[.,.],[[.,.],[[.,.],.]]]]
[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [4,5,6,1,2,3,8,7,11,12,9,10] => [6,1,2,4,5,3,8,7,12,9,11,10] => [[.,[.,[[.,.],[.,.]]]],[[.,.],[[.,[[.,.],.]],.]]]
[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [4,5,6,1,2,3,9,10,7,8,12,11] => [6,1,2,4,5,3,10,7,9,8,12,11] => [[.,[.,[[.,.],[.,.]]]],[[.,[[.,.],.]],[[.,.],.]]]
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => [6,1,2,4,5,3,12,7,8,10,11,9] => [[.,[.,[[.,.],[.,.]]]],[[.,[.,[[.,.],[.,.]]]],.]]
[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [5,6,7,8,1,2,3,4,10,9,12,11] => [8,1,2,3,5,6,7,4,10,9,12,11] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[[.,.],[[.,.],.]]]
[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [5,6,7,8,1,2,3,4,11,12,9,10] => [8,1,2,3,5,6,7,4,12,9,11,10] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],[[.,[[.,.],.]],.]]
[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [6,7,8,9,10,1,2,3,4,5,12,11] => [10,1,2,3,4,6,7,8,9,5,12,11] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],[[.,.],.]]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [12,1,2,3,4,5,7,8,9,10,11,6] => [[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]],.]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
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
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.