Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ 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 482 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] => [[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],.]
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9] => [[.,[.,[.,.]]],[.,[.,[[.,.],[[.,.],.]]]]]
[(1,3),(2,5),(4,6),(7,8),(9,10)] => [3,5,1,6,2,4,8,7,10,9] => [[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[(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] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]]
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[[.,.],.]]]]]
[(1,4),(2,6),(3,7),(5,8),(9,10)] => [4,6,7,1,8,2,3,5,10,9] => [[.,[.,[.,.]]],[[.,.],[.,[.,[[.,.],.]]]]]
[(1,3),(2,6),(4,7),(5,8),(9,10)] => [3,6,1,7,8,2,4,5,10,9] => [[.,[.,.]],[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => [[.,.],[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]]
[(1,2),(3,5),(4,7),(6,8),(9,10)] => [2,1,5,7,3,8,4,6,10,9] => [[.,.],[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]]
[(1,3),(2,5),(4,7),(6,8),(9,10)] => [3,5,1,7,2,8,4,6,10,9] => [[.,[.,.]],[[.,.],[[.,.],[.,[[.,.],.]]]]]
[(1,4),(2,5),(3,7),(6,8),(9,10)] => [4,5,7,1,2,8,3,6,10,9] => [[.,[.,[.,.]]],[.,[[.,.],[.,[[.,.],.]]]]]
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9] => [[.,[.,.]],[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => [[.,.],[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]]
[(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] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[(1,3),(2,7),(4,8),(5,9),(6,10)] => [3,7,1,8,9,10,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[(1,4),(2,7),(3,8),(5,9),(6,10)] => [4,7,8,1,9,10,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,[.,[.,.]]]]]
[(1,5),(2,7),(3,8),(4,9),(6,10)] => [5,7,8,9,1,10,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,[.,[.,.]]]]]
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[(1,5),(2,6),(3,8),(4,9),(7,10)] => [5,6,8,9,1,2,10,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],[.,[.,.]]]]]
[(1,4),(2,6),(3,8),(5,9),(7,10)] => [4,6,8,1,9,2,10,3,5,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],[.,[.,.]]]]]
[(1,3),(2,6),(4,8),(5,9),(7,10)] => [3,6,1,8,9,2,10,4,5,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[(1,2),(3,6),(4,8),(5,9),(7,10)] => [2,1,6,8,9,3,10,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]]
[(1,2),(3,5),(4,8),(6,9),(7,10)] => [2,1,5,8,3,9,10,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]]
[(1,3),(2,5),(4,8),(6,9),(7,10)] => [3,5,1,8,2,9,10,4,6,7] => [[.,[.,.]],[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[(1,4),(2,5),(3,8),(6,9),(7,10)] => [4,5,8,1,2,9,10,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],[.,[.,.]]]]]
[(1,7),(2,3),(4,8),(5,9),(6,10)] => [7,3,2,8,9,10,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]]
[(1,2),(3,4),(5,7),(6,9),(8,10)] => [2,1,4,3,7,9,5,10,6,8] => [[.,.],[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]]
[(1,3),(2,4),(5,7),(6,9),(8,10)] => [3,4,1,2,7,9,5,10,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[(1,4),(2,5),(3,7),(6,9),(8,10)] => [4,5,7,1,2,9,3,10,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[[.,.],[.,.]]]]]
[(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] => [[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[(1,2),(3,6),(4,7),(5,9),(8,10)] => [2,1,6,7,9,3,4,10,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]]
[(1,3),(2,6),(4,7),(5,9),(8,10)] => [3,6,1,7,9,2,4,10,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[(1,4),(2,6),(3,7),(5,9),(8,10)] => [4,6,7,1,9,2,3,10,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[[.,.],[.,.]]]]]
[(1,5),(2,6),(3,7),(4,9),(8,10)] => [5,6,7,9,1,2,3,10,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],[.,.]]]]]
[(1,8),(2,5),(3,4),(6,9),(7,10)] => [8,5,4,3,2,9,10,1,6,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],[.,[.,.]]]
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => [[.,.],[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]]
[(1,3),(2,5),(4,6),(7,9),(8,10)] => [3,5,1,6,2,4,9,10,7,8] => [[.,[.,.]],[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8] => [[.,[.,[.,.]]],[.,[.,[[.,[.,.]],[.,.]]]]]
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8] => [[.,[.,.]],[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[(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] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[(1,7),(2,10),(3,5),(4,9),(6,8)] => [7,10,5,9,3,8,1,6,4,2] => [[[[.,[.,.]],[.,.]],[.,.]],[[[.,.],.],.]]
[(1,9),(2,7),(3,5),(4,10),(6,8)] => [9,7,5,10,3,8,2,6,1,4] => [[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]]
[(1,5),(2,6),(3,7),(4,10),(8,9)] => [5,6,7,10,1,2,3,9,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[[[.,.],.],.]]]]
[(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] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[(1,4),(2,5),(3,10),(6,9),(7,8)] => [4,5,10,1,2,9,8,7,6,3] => [[.,[.,[.,.]]],[.,[[[[[.,.],.],.],.],.]]]
[(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),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]]]
[(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)] => [2,1,4,3,6,5,9,11,7,12,8,10] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]]]
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => [[.,.],[[.,.],[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]]]
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => [[.,.],[[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]]
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => [[.,.],[[.,.],[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]]]
[(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)] => [2,1,4,3,7,9,5,10,6,8,12,11] => [[.,.],[[.,.],[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]]]
[(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)] => [2,1,4,3,7,9,5,11,6,12,8,10] => [[.,.],[[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]]
[(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)] => [2,1,4,3,7,10,5,11,12,6,8,9] => [[.,.],[[.,.],[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]]]
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => [[.,.],[[.,.],[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]]]
[(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)] => [2,1,4,3,8,9,11,5,6,12,7,10] => [[.,.],[[.,.],[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]]]
[(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)] => [2,1,4,3,8,10,11,5,12,6,7,9] => [[.,.],[[.,.],[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]]]
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => [[.,.],[[.,.],[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => [[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => [[.,.],[[.,[.,.]],[.,[[.,.],[[.,[.,.]],[.,.]]]]]]
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => [[.,.],[[.,[.,.]],[.,[[.,[.,.]],[.,[[.,.],.]]]]]]
[(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)] => [2,1,5,6,3,4,9,11,7,12,8,10] => [[.,.],[[.,[.,.]],[.,[[.,[.,.]],[[.,.],[.,.]]]]]]
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => [[.,.],[[.,[.,.]],[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)] => [2,1,5,7,3,8,4,6,10,9,12,11] => [[.,.],[[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]]
[(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)] => [2,1,5,7,3,8,4,6,11,12,9,10] => [[.,.],[[.,[.,.]],[[.,.],[.,[[.,[.,.]],[.,.]]]]]]
[(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)] => [2,1,5,7,3,9,4,10,6,8,12,11] => [[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,[[.,.],.]]]]]]
[(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => [2,1,5,7,3,9,4,11,6,12,8,10] => [[.,.],[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)] => [2,1,5,7,3,10,4,11,12,6,8,9] => [[.,.],[[.,[.,.]],[[.,.],[[.,[.,.]],[.,[.,.]]]]]]
[(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)] => [2,1,5,8,3,9,10,4,6,7,12,11] => [[.,.],[[.,[.,.]],[[.,[.,.]],[.,[.,[[.,.],.]]]]]]
[(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)] => [2,1,5,8,3,9,11,4,6,12,7,10] => [[.,.],[[.,[.,.]],[[.,[.,.]],[.,[[.,.],[.,.]]]]]]
[(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)] => [2,1,5,8,3,10,11,4,12,6,7,9] => [[.,.],[[.,[.,.]],[[.,[.,.]],[[.,.],[.,[.,.]]]]]]
[(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)] => [2,1,5,9,3,10,11,12,4,6,7,8] => [[.,.],[[.,[.,.]],[[.,[.,[.,.]]],[.,[.,[.,.]]]]]]
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => [[.,.],[[.,[.,[.,.]]],[.,[.,[[.,.],[[.,.],.]]]]]]
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => [[.,.],[[.,[.,[.,.]]],[.,[.,[[.,[.,.]],[.,.]]]]]]
[(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)] => [2,1,6,7,9,3,4,10,5,8,12,11] => [[.,.],[[.,[.,[.,.]]],[.,[[.,.],[.,[[.,.],.]]]]]]
[(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)] => [2,1,6,7,9,3,4,11,5,12,8,10] => [[.,.],[[.,[.,[.,.]]],[.,[[.,.],[[.,.],[.,.]]]]]]
[(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)] => [2,1,6,7,10,3,4,11,12,5,8,9] => [[.,.],[[.,[.,[.,.]]],[.,[[.,[.,.]],[.,[.,.]]]]]]
[(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)] => [2,1,6,8,9,3,10,4,5,7,12,11] => [[.,.],[[.,[.,[.,.]]],[[.,.],[.,[.,[[.,.],.]]]]]]
[(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)] => [2,1,6,8,9,3,11,4,5,12,7,10] => [[.,.],[[.,[.,[.,.]]],[[.,.],[.,[[.,.],[.,.]]]]]]
[(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)] => [2,1,6,8,10,3,11,4,12,5,7,9] => [[.,.],[[.,[.,[.,.]]],[[.,.],[[.,.],[.,[.,.]]]]]]
[(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)] => [2,1,6,9,10,3,11,12,4,5,7,8] => [[.,.],[[.,[.,[.,.]]],[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => [[.,.],[[.,[.,[.,[.,.]]]],[.,[.,[.,[[.,.],.]]]]]]
[(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)] => [2,1,7,8,9,11,3,4,5,12,6,10] => [[.,.],[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],[.,.]]]]]]
[(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)] => [2,1,7,8,10,11,3,4,12,5,6,9] => [[.,.],[[.,[.,[.,[.,.]]]],[.,[[.,.],[.,[.,.]]]]]]
[(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)] => [2,1,7,9,10,11,3,12,4,5,6,8] => [[.,.],[[.,[.,[.,[.,.]]]],[[.,.],[.,[.,[.,.]]]]]]
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]]
[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [3,4,1,2,6,5,8,7,10,9,12,11] => [[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [3,4,1,2,6,5,8,7,11,12,9,10] => [[.,[.,.]],[.,[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]]]
[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [3,4,1,2,6,5,9,10,7,8,12,11] => [[.,[.,.]],[.,[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]]]
[(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)] => [3,4,1,2,6,5,9,11,7,12,8,10] => [[.,[.,.]],[.,[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]]]
[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [3,4,1,2,6,5,10,11,12,7,8,9] => [[.,[.,.]],[.,[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]]]
[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [3,4,1,2,7,8,5,6,10,9,12,11] => [[.,[.,.]],[.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]]
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [3,4,1,2,7,8,5,6,11,12,9,10] => [[.,[.,.]],[.,[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]]]
[(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)] => [3,4,1,2,7,9,5,10,6,8,12,11] => [[.,[.,.]],[.,[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]]]
[(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)] => [3,4,1,2,7,9,5,11,6,12,8,10] => [[.,[.,.]],[.,[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]]
[(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)] => [3,4,1,2,7,10,5,11,12,6,8,9] => [[.,[.,.]],[.,[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]]]
[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [3,4,1,2,8,9,10,5,6,7,12,11] => [[.,[.,.]],[.,[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]]]
[(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)] => [3,4,1,2,8,9,11,5,6,12,7,10] => [[.,[.,.]],[.,[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]]]
[(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)] => [3,4,1,2,8,10,11,5,12,6,7,9] => [[.,[.,.]],[.,[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]]]
[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [3,4,1,2,9,10,11,12,5,6,7,8] => [[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)] => [3,5,1,6,2,4,8,7,10,9,12,11] => [[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)] => [3,5,1,6,2,4,8,7,11,12,9,10] => [[.,[.,.]],[[.,.],[.,[[.,.],[[.,[.,.]],[.,.]]]]]]
[(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)] => [3,5,1,6,2,4,9,10,7,8,12,11] => [[.,[.,.]],[[.,.],[.,[[.,[.,.]],[.,[[.,.],.]]]]]]
[(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)] => [3,5,1,6,2,4,9,11,7,12,8,10] => [[.,[.,.]],[[.,.],[.,[[.,[.,.]],[[.,.],[.,.]]]]]]
[(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)] => [3,5,1,6,2,4,10,11,12,7,8,9] => [[.,[.,.]],[[.,.],[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)] => [3,5,1,7,2,8,4,6,10,9,12,11] => [[.,[.,.]],[[.,.],[[.,.],[.,[[.,.],[[.,.],.]]]]]]
[(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)] => [3,5,1,7,2,8,4,6,11,12,9,10] => [[.,[.,.]],[[.,.],[[.,.],[.,[[.,[.,.]],[.,.]]]]]]
[(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)] => [3,5,1,7,2,9,4,10,6,8,12,11] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]]]
[(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)] => [3,5,1,7,2,9,4,11,6,12,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[(1,3),(2,5),(4,7),(6,10),(8,11),(9,12)] => [3,5,1,7,2,10,4,11,12,6,8,9] => [[.,[.,.]],[[.,.],[[.,.],[[.,[.,.]],[.,[.,.]]]]]]
[(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)] => [3,5,1,8,2,9,10,4,6,7,12,11] => [[.,[.,.]],[[.,.],[[.,[.,.]],[.,[.,[[.,.],.]]]]]]
[(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)] => [3,5,1,8,2,9,11,4,6,12,7,10] => [[.,[.,.]],[[.,.],[[.,[.,.]],[.,[[.,.],[.,.]]]]]]
[(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)] => [3,5,1,8,2,10,11,4,12,6,7,9] => [[.,[.,.]],[[.,.],[[.,[.,.]],[[.,.],[.,[.,.]]]]]]
[(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)] => [3,5,1,9,2,10,11,12,4,6,7,8] => [[.,[.,.]],[[.,.],[[.,[.,[.,.]]],[.,[.,[.,.]]]]]]
[(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)] => [3,6,1,7,8,2,4,5,10,9,12,11] => [[.,[.,.]],[[.,[.,.]],[.,[.,[[.,.],[[.,.],.]]]]]]
[(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)] => [3,6,1,7,8,2,4,5,11,12,9,10] => [[.,[.,.]],[[.,[.,.]],[.,[.,[[.,[.,.]],[.,.]]]]]]
[(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)] => [3,6,1,7,9,2,4,10,5,8,12,11] => [[.,[.,.]],[[.,[.,.]],[.,[[.,.],[.,[[.,.],.]]]]]]
[(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)] => [3,6,1,7,9,2,4,11,5,12,8,10] => [[.,[.,.]],[[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]]
[(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)] => [3,6,1,7,10,2,4,11,12,5,8,9] => [[.,[.,.]],[[.,[.,.]],[.,[[.,[.,.]],[.,[.,.]]]]]]
[(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)] => [3,6,1,8,9,2,10,4,5,7,12,11] => [[.,[.,.]],[[.,[.,.]],[[.,.],[.,[.,[[.,.],.]]]]]]
[(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)] => [3,6,1,8,9,2,11,4,5,12,7,10] => [[.,[.,.]],[[.,[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]]
[(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)] => [3,6,1,8,10,2,11,4,12,5,7,9] => [[.,[.,.]],[[.,[.,.]],[[.,.],[[.,.],[.,[.,.]]]]]]
[(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)] => [3,6,1,9,10,2,11,12,4,5,7,8] => [[.,[.,.]],[[.,[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)] => [3,7,1,8,9,10,2,4,5,6,12,11] => [[.,[.,.]],[[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]]
[(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)] => [3,7,1,8,9,11,2,4,5,12,6,10] => [[.,[.,.]],[[.,[.,[.,.]]],[.,[.,[[.,.],[.,.]]]]]]
[(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)] => [3,7,1,8,10,11,2,4,12,5,6,9] => [[.,[.,.]],[[.,[.,[.,.]]],[.,[[.,.],[.,[.,.]]]]]]
[(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)] => [3,7,1,9,10,11,2,12,4,5,6,8] => [[.,[.,.]],[[.,[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]]]
[(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)] => [3,8,1,9,10,11,12,2,4,5,6,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [4,5,6,1,2,3,8,7,10,9,12,11] => [[.,[.,[.,.]]],[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [4,5,6,1,2,3,8,7,11,12,9,10] => [[.,[.,[.,.]]],[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]]
[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [4,5,6,1,2,3,9,10,7,8,12,11] => [[.,[.,[.,.]]],[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]]
[(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)] => [4,5,6,1,2,3,9,11,7,12,8,10] => [[.,[.,[.,.]]],[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]]
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => [[.,[.,[.,.]]],[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)] => [4,5,7,1,2,8,3,6,10,9,12,11] => [[.,[.,[.,.]]],[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]]
[(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)] => [4,5,7,1,2,8,3,6,11,12,9,10] => [[.,[.,[.,.]]],[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]]
[(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)] => [4,5,7,1,2,9,3,10,6,8,12,11] => [[.,[.,[.,.]]],[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]]
[(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)] => [4,5,7,1,2,9,3,11,6,12,8,10] => [[.,[.,[.,.]]],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)] => [4,5,7,1,2,10,3,11,12,6,8,9] => [[.,[.,[.,.]]],[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]]
[(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)] => [4,5,8,1,2,9,10,3,6,7,12,11] => [[.,[.,[.,.]]],[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]]
[(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)] => [4,5,8,1,2,9,11,3,6,12,7,10] => [[.,[.,[.,.]]],[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]]
[(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)] => [4,5,8,1,2,10,11,3,12,6,7,9] => [[.,[.,[.,.]]],[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]]
[(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)] => [4,5,9,1,2,10,11,12,3,6,7,8] => [[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]]
[(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)] => [4,6,7,1,8,2,3,5,10,9,12,11] => [[.,[.,[.,.]]],[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]]
[(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)] => [4,6,7,1,8,2,3,5,11,12,9,10] => [[.,[.,[.,.]]],[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]]
[(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)] => [4,6,7,1,9,2,3,10,5,8,12,11] => [[.,[.,[.,.]]],[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]]
[(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)] => [4,6,7,1,9,2,3,11,5,12,8,10] => [[.,[.,[.,.]]],[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]]
[(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)] => [4,6,7,1,10,2,3,11,12,5,8,9] => [[.,[.,[.,.]]],[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]]
[(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)] => [4,6,8,1,9,2,10,3,5,7,12,11] => [[.,[.,[.,.]]],[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]]
[(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)] => [4,6,8,1,9,2,11,3,5,12,7,10] => [[.,[.,[.,.]]],[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]]
[(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)] => [4,6,8,1,10,2,11,3,12,5,7,9] => [[.,[.,[.,.]]],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)] => [4,6,9,1,10,2,11,12,3,5,7,8] => [[.,[.,[.,.]]],[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)] => [4,7,8,1,9,10,2,3,5,6,12,11] => [[.,[.,[.,.]]],[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]]
[(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)] => [4,7,8,1,9,11,2,3,5,12,6,10] => [[.,[.,[.,.]]],[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]]
[(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)] => [4,7,8,1,10,11,2,3,12,5,6,9] => [[.,[.,[.,.]]],[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]]
[(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)] => [4,7,9,1,10,11,2,12,3,5,6,8] => [[.,[.,[.,.]]],[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]]
[(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)] => [4,8,9,1,10,11,12,2,3,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [5,6,7,8,1,2,3,4,10,9,12,11] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [5,6,7,8,1,2,3,4,11,12,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)] => [5,6,7,9,1,2,3,10,4,8,12,11] => [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)] => [5,6,7,9,1,2,3,11,4,12,8,10] => [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)] => [5,6,7,10,1,2,3,11,12,4,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)] => [5,6,8,9,1,2,10,3,4,7,12,11] => [[.,[.,[.,[.,.]]]],[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)] => [5,6,8,9,1,2,11,3,4,12,7,10] => [[.,[.,[.,[.,.]]]],[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)] => [5,6,8,10,1,2,11,3,12,4,7,9] => [[.,[.,[.,[.,.]]]],[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)] => [5,6,9,10,1,2,11,12,3,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)] => [5,7,8,9,1,10,2,3,4,6,12,11] => [[.,[.,[.,[.,.]]]],[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)] => [5,7,8,9,1,11,2,3,4,12,6,10] => [[.,[.,[.,[.,.]]]],[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)] => [5,7,8,10,1,11,2,3,12,4,6,9] => [[.,[.,[.,[.,.]]]],[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)] => [5,7,9,10,1,11,2,12,3,4,6,8] => [[.,[.,[.,[.,.]]]],[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)] => [5,8,9,10,1,11,12,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [6,7,8,9,10,1,2,3,4,5,12,11] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,[[.,.],.]]]]]]
[(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)] => [6,7,8,9,11,1,2,3,4,12,5,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[[.,.],[.,.]]]]]]
[(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)] => [6,7,8,10,11,1,2,3,12,4,5,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[[.,.],[.,[.,.]]]]]]
[(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)] => [6,7,9,10,11,1,2,12,3,4,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],[.,[.,[.,.]]]]]]
[(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)] => [6,8,9,10,11,1,12,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,[.,[.,[.,.]]]]]]
[(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.