Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Images
[(1,2)] => [2,1] => [[.,.],.] => [.,[.,.]]
[(1,2),(3,4)] => [2,1,4,3] => [[.,.],[[.,.],.]] => [[.,[.,.]],[.,.]]
[(1,3),(2,4)] => [3,4,1,2] => [[.,[.,.]],[.,.]] => [[.,.],[[.,.],.]]
[(1,4),(2,3)] => [4,3,2,1] => [[[[.,.],.],.],.] => [.,[.,[.,[.,.]]]]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,.]]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,.],.]]
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,.]]]]
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,.]]]]
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,.]]]]
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[.,.]]]]
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[.,.]]]]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],.]]
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],.]]
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[.,.]]
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,.]]
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],.]]
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],.]]
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],.]]]]
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [[[[.,.],.],[[[.,.],.],.]],[.,.]]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]]
>>> Load all 318 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]]
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [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] => [[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],[.,.]],.],[[.,.],.]]
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => [[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,[.,.]],[.,[.,.]]]]
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [8,3,2,5,4,7,6,1,10,9] => [[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [10,3,2,5,4,7,6,9,8,1] => [[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]]
[(1,3),(2,5),(4,6),(7,8),(9,10)] => [3,5,1,6,2,4,8,7,10,9] => [[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],.],[.,.]],[[.,.],.]]
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [[.,.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]],[.,.]]
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => [[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[(1,10),(2,5),(3,4),(6,7),(8,9)] => [10,5,4,3,2,7,6,9,8,1] => [[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]]
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => [[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]],[.,.]]
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => [[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,10,5,4,7,6,9,8,3] => [[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]],[.,.]]
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [10,9,4,3,6,5,8,7,2,1] => [[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]]]
[(1,8),(2,9),(3,5),(4,6),(7,10)] => [8,9,5,6,3,4,10,1,2,7] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[[.,.],[[.,.],.]]]]
[(1,3),(2,5),(4,7),(6,8),(9,10)] => [3,5,1,7,2,8,4,6,10,9] => [[.,[.,.]],[[.,.],[[.,.],[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],[.,.]],[.,.]],[[.,.],.]]
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [[.,.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]],[.,.]]
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => [[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[(1,10),(2,3),(4,7),(5,6),(8,9)] => [10,3,2,7,6,5,4,9,8,1] => [[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]]
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[(1,9),(2,7),(3,6),(4,5),(8,10)] => [9,7,6,5,4,3,2,10,1,8] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => [[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],[.,.]]
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => [[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,.]]
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [4,3,2,1,10,7,6,9,8,5] => [[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]]
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => [[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]]
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],[.,.]]
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]
[(1,4),(2,9),(3,10),(5,7),(6,8)] => [4,9,10,1,7,8,5,6,2,3] => [[.,[.,[.,.]]],[[[.,[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],.]]],[[[.,.],.],.]]
[(1,10),(2,8),(3,9),(4,6),(5,7)] => [10,8,9,6,7,4,5,2,3,1] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[(1,7),(2,3),(4,8),(5,9),(6,10)] => [7,3,2,8,9,10,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[.,.],.],.],[.,[.,.]]]]
[(1,3),(2,5),(4,7),(6,9),(8,10)] => [3,5,1,7,2,9,4,10,6,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[(1,2),(3,5),(4,7),(6,9),(8,10)] => [2,1,5,7,3,9,4,10,6,8] => [[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],[[.,.],.]],[.,.]]
[(1,8),(2,5),(3,4),(6,9),(7,10)] => [8,5,4,3,2,9,10,1,6,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]] => [[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,.]]
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]]
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => [[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,[.,.]]]]
[(1,10),(2,3),(4,5),(6,9),(7,8)] => [10,3,2,5,4,9,8,7,6,1] => [[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,.]]]]
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]]
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => [[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,10,5,4,9,8,7,6,3] => [[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],[.,.]]
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[(1,9),(2,7),(3,5),(4,10),(6,8)] => [9,7,5,10,3,8,2,6,1,4] => [[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]]
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[(1,3),(2,10),(4,9),(5,8),(6,7)] => [3,10,1,9,8,7,6,5,4,2] => [[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[(1,9),(2,10),(3,8),(4,7),(5,6)] => [9,10,8,7,6,5,4,3,1,2] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]]
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,10,9,8,7,6,5,4,3,12,11] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [12,3,2,9,8,7,6,5,4,11,10,1] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [12,11,4,3,8,7,6,5,10,9,2,1] => [[[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [[.,.],[[.,.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]],[.,.]],[.,.]]
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [12,3,2,11,8,7,6,5,10,9,4,1] => [[[[.,.],.],[[[[[[.,.],.],.],.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [12,9,4,3,8,7,6,5,2,11,10,1] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [[.,.],[[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]],[.,.]]
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [[[[.,.],.],.],[[[[.,.],.],.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [12,11,10,5,4,7,6,9,8,3,2,1] => [[[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,10,5,4,7,6,9,8,3,12,11] => [[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],.]]] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],[.,[.,.]]]],[.,.]]
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [12,3,2,5,4,7,6,9,8,11,10,1] => [[[[.,.],.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,[.,.]]]]
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,12,5,4,7,6,9,8,11,10,3] => [[.,.],[[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]],[.,.]]
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [10,3,2,5,4,7,6,9,8,1,12,11] => [[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]]
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [12,11,4,3,10,7,6,9,8,5,2,1] => [[[[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]],.],.] => [.,[.,[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,10,7,6,9,8,5,12,11] => [[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]]] => [[[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,.]]
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [12,3,2,11,10,7,6,9,8,5,4,1] => [[[[.,.],.],[[[[[[.,.],.],.],[[.,.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],[.,[.,.]]]]
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]],[.,.]]
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [4,3,2,1,10,7,6,9,8,5,12,11] => [[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]]
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [12,5,4,3,2,7,6,9,8,11,10,1] => [[[[[[.,.],.],.],.],[[.,.],[[.,.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,12,7,6,9,8,11,10,5] => [[.,.],[[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]]] => [[[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]],[.,.]],[.,.]]
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [10,5,4,3,2,7,6,9,8,1,12,11] => [[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]]
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [4,3,2,1,12,7,6,9,8,11,10,5] => [[[[.,.],.],.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]]
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [12,11,8,5,4,7,6,3,10,9,2,1] => [[[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,8,5,4,7,6,3,10,9,12,11] => [[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],[.,[.,.]]]],[.,.]]
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [12,3,2,5,4,7,6,11,10,9,8,1] => [[[[.,.],.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]],.] => [.,[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,[.,.]]]]
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,12,5,4,7,6,11,10,9,8,3] => [[.,.],[[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],.]] => [[.,[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,.]]]],[.,.]]
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [8,3,2,5,4,7,6,1,10,9,12,11] => [[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [12,9,8,5,4,7,6,3,2,11,10,1] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,8,5,4,7,6,3,12,11,10,9] => [[.,.],[[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,[.,.]]]],[.,.]]
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [8,3,2,5,4,7,6,1,12,11,10,9] => [[[[.,.],.],[[.,.],[[.,.],.]]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [12,5,4,3,2,7,6,11,10,9,8,1] => [[[[[[.,.],.],.],.],[[.,.],[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,12,7,6,11,10,9,8,5] => [[.,.],[[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],.]]] => [[[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],[.,.]],[.,.]]
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [8,5,4,3,2,7,6,1,10,9,12,11] => [[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => [[[[.,.],.],.],[[[[.,.],.],[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],[.,[.,[.,.]]]]
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [8,5,4,3,2,7,6,1,12,11,10,9] => [[[[[[.,.],.],.],.],[[.,.],.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]]]
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,[.,.]],[.,[.,[.,.]]]]]],[.,.]]
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [12,3,2,9,6,5,8,7,4,11,10,1] => [[[[.,.],.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]]
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,12,9,6,5,8,7,4,11,10,3] => [[.,.],[[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]],[.,.]]
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [10,3,2,9,6,5,8,7,4,1,12,11] => [[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]]
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [12,11,4,3,6,5,8,7,10,9,2,1] => [[[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]],.],.] => [.,[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [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] => [[[[.,.],.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]],.] => [.,[[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]],[.,[.,.]]]]
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,12,11,6,5,8,7,10,9,4,3] => [[.,.],[[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],.]] => [[.,[.,[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]]],[.,.]]
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [[[[.,.],.],.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [12,9,4,3,6,5,8,7,2,11,10,1] => [[[[[[.,.],.],.],[[.,.],[[.,.],.]]],[[.,.],.]],.] => [.,[[.,[.,.]],[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]] => [[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]],[.,.]]
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [10,9,4,3,6,5,8,7,2,1,12,11] => [[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]]]
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [[[[.,.],.],.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [[[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.],.],.] => [.,[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,10,5,4,9,8,7,6,3,12,11] => [[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,[.,.]]]],[.,.]]
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [12,3,2,5,4,9,8,7,6,11,10,1] => [[[[.,.],.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]],[.,[.,.]]]]
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,12,5,4,9,8,7,6,11,10,3] => [[.,.],[[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]],[.,.]]
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [10,3,2,5,4,9,8,7,6,1,12,11] => [[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,.]]]]
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [[[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [[.,.],[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]]
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [12,3,2,11,10,9,8,7,6,5,4,1] => [[[[.,.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,[.,.]]]]
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [12,5,4,3,2,9,8,7,6,11,10,1] => [[[[[[.,.],.],.],.],[[[[.,.],.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => [[.,.],[[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]]
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => [[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [4,3,2,1,12,9,8,7,6,11,10,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [12,11,6,5,4,3,8,7,10,9,2,1] => [[[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [[.,.],[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]],[.,.]]
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [12,3,2,5,4,11,8,7,10,9,6,1] => [[[[.,.],.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,[.,.]]]]
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,12,5,4,11,8,7,10,9,6,3] => [[.,.],[[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]],[.,.]]
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [6,3,2,5,4,1,8,7,10,9,12,11] => [[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],[.,[.,.]]]]
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [12,9,6,5,4,3,8,7,2,11,10,1] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [[.,.],[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]],[.,.]]
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [6,3,2,5,4,1,8,7,12,11,10,9] => [[[[.,.],.],[[.,.],.]],[[.,.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[[.,[.,.]],[.,[.,.]]]]
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [12,5,4,3,2,11,8,7,10,9,6,1] => [[[[[[.,.],.],.],.],[[[[.,.],.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [[.,.],[[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],.]]] => [[[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],[.,.]],[.,.]]
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [[[[[[.,.],.],.],.],.],[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [[[[[[.,.],.],.],.],.],[[.,.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,10,7,6,5,4,9,8,3,12,11] => [[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]],[.,.]]
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [12,3,2,7,6,5,4,9,8,11,10,1] => [[[[.,.],.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]]
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,12,7,6,5,4,9,8,11,10,3] => [[.,.],[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]],[.,.]]
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [10,3,2,7,6,5,4,9,8,1,12,11] => [[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]]
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [12,11,4,3,6,5,10,9,8,7,2,1] => [[[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]]
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [12,3,2,11,6,5,10,9,8,7,4,1] => [[[[.,.],.],[[[[.,.],.],[[[[.,.],.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],[.,[.,.]]]]
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [[.,.],[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]],[.,.]]
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [[[[.,.],.],.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [12,7,4,3,6,5,2,9,8,11,10,1] => [[[[[[.,.],.],.],[[.,.],.]],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,12,9,8,11,10,7] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,.]],[.,.]]
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [10,7,4,3,6,5,2,9,8,1,12,11] => [[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [4,3,2,1,6,5,12,9,8,11,10,7] => [[[[.,.],.],.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [[.,.],[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [12,3,2,7,6,5,4,11,10,9,8,1] => [[[[.,.],.],[[[[.,.],.],.],[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,[.,.]]]]
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,12,7,6,5,4,11,10,9,8,3] => [[.,.],[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]],[.,.]]
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => [[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [12,9,8,7,6,5,4,3,2,11,10,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [[.,.],[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => [[[[.,.],.],[[[[.,.],.],.],.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [12,7,4,3,6,5,2,11,10,9,8,1] => [[[[[[.,.],.],.],[[.,.],.]],[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [[.,.],[[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]],[.,.]]
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [[[[.,.],.],.],[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,[.,[.,.]]]]
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [[[[[[.,.],.],.],[[.,.],.]],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]]
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [12,3,2,5,4,11,10,9,8,7,6,1] => [[[[.,.],.],[[.,.],[[[[[[.,.],.],.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,[.,.]]]]
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,12,5,4,11,10,9,8,7,6,3] => [[.,.],[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]],[.,.]]
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [6,3,2,5,4,1,10,9,8,7,12,11] => [[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,.]]]],[[.,[.,.]],[.,[.,.]]]]
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [12,7,6,5,4,3,2,9,8,11,10,1] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,6,5,4,3,12,9,8,11,10,7] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]]
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [10,7,6,5,4,3,2,9,8,1,12,11] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [6,3,2,5,4,1,12,9,8,11,10,7] => [[[[.,.],.],[[.,.],.]],[[[[.,.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,.]]]],[[.,[.,.]],[.,[.,.]]]]
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => [[[[[[.,.],.],.],.],[[[[[[.,.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [[.,.],[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],[.,.]]
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,[.,[.,.]]]]
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [6,5,4,3,2,1,12,9,8,11,10,7] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [12,7,6,5,4,3,2,11,10,9,8,1] => [[[[[[[[.,.],.],.],.],.],.],[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [[.,.],[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]],[.,.]]
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => [[[[.,.],.],[[.,.],.]],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],[.,[.,.]]]]
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,[.,.]]]]]]
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]]] => [[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,.]],[.,.]]
[(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => [2,1,5,7,3,9,4,11,6,12,8,10] => [[.,.],[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]],[.,.]]
[(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)] => [3,5,1,7,2,9,4,11,6,12,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
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.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.