- FindStat

Identifier

Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees

Images

[(1,2)] => [2,1] => [1,2] => [.,[.,.]]

[(1,2),(3,4)] => [2,1,4,3] => [3,4,1,2] => [[.,[.,.]],[.,.]]

[(1,3),(2,4)] => [3,4,1,2] => [2,1,4,3] => [[.,.],[[.,.],.]]

[(1,4),(2,3)] => [4,3,2,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]]

[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]]

[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [5,6,2,1,4,3] => [[[.,.],[[.,.],.]],[.,.]]

[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]]

[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [4,1,6,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]]

[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]]

[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]

[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]]

[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]

[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => [[[.,.],[.,.]],[[.,.],.]]

[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [4,3,6,5,1,2] => [[[.,[.,.]],.],[[.,.],.]]

[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]]

[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [2,4,5,1,6,3] => [[.,.],[[.,.],[.,[.,.]]]]

[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]]

[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]

[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]

[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]

[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [7,8,5,6,2,1,4,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]

[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [7,8,5,6,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]

[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [7,8,4,1,6,2,3,5] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]

[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [7,8,1,4,5,2,3,6] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]

[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [6,1,8,4,5,2,3,7] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]

[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [1,6,7,4,5,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]

[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [1,6,7,3,2,5,4,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]

[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [6,1,8,3,2,5,4,7] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]

[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [7,8,1,3,2,5,4,6] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]

[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [7,8,3,1,2,6,4,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]

[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [7,8,3,2,1,6,5,4] => [[[[.,.],.],[[[.,.],.],.]],[.,.]]

[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [7,8,4,2,6,1,5,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]

[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [7,8,4,3,6,5,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]]

[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [7,8,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]

[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [7,8,2,4,5,1,6,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]

[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [7,8,2,3,1,5,6,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]

[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [7,8,2,1,3,4,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]

[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [7,8,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]

[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [6,1,8,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]

[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [1,6,7,2,3,4,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]

[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [1,5,2,7,3,4,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]

[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [5,1,2,8,3,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]

[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [5,2,1,8,3,4,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]

[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [6,2,8,1,3,4,7,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]

[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [6,2,8,3,1,5,7,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]

[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [6,2,8,4,5,1,7,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]

[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [6,3,8,4,5,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]

[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [3,6,7,4,5,8,1,2] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]

[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [2,6,7,4,5,1,8,3] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]

[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [2,6,7,3,1,5,8,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]

[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [2,6,7,1,3,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]

[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [2,5,1,7,3,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]

[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [2,1,5,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]

[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [1,2,5,6,3,4,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]

[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]

[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]

[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [2,4,1,3,7,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]

[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [2,4,3,1,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]

[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [2,5,3,7,1,6,8,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]

[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [2,5,4,7,6,1,8,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]

[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [3,5,4,7,6,8,1,2] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]

[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [5,3,4,8,6,7,1,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]

[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [5,2,4,8,6,1,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]

[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [5,2,3,8,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]

[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [4,2,3,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]

[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [4,2,1,3,8,5,7,6] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]

[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [4,1,2,3,8,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]

[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [1,4,2,3,7,5,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]

[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]

[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [4,1,3,2,8,6,5,7] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]

[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [4,3,1,2,8,7,5,6] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]]

[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]]

[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [5,3,2,8,1,7,6,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]

[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [5,4,2,8,7,1,6,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]

[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [5,4,3,8,7,6,1,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]

[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [6,4,8,3,7,5,1,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]

[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [6,4,8,2,7,1,5,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]

[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [6,3,8,2,1,7,5,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]

[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [6,3,8,1,2,7,4,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]

[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [5,3,1,8,2,7,4,6] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]]

[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [5,1,3,8,2,6,4,7] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]

[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [1,5,3,7,2,6,4,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]

[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [1,5,4,7,6,2,3,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]

[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [5,1,4,8,6,2,3,7] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]

[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [5,4,1,8,7,2,3,6] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]]

[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [6,4,8,1,7,2,3,5] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]]

[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [6,5,8,7,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]

[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [6,5,8,7,2,1,4,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]

[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [6,5,8,7,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]

[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [5,6,7,8,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]

[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [5,6,7,8,2,1,4,3] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]

[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]

[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [4,6,7,1,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]

[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [4,5,1,7,8,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]

[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [4,1,5,6,8,2,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]

[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [1,4,5,6,7,2,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]

[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [1,3,5,6,2,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]

[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [3,1,5,6,2,8,4,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]

[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]

[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [3,6,7,1,2,8,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]

[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [3,6,7,2,1,8,5,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]

>>> Load all 313 entries. <<<

[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [4,6,7,2,8,1,5,3] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]

[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [4,6,7,3,8,5,1,2] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]

[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [4,5,3,7,8,6,1,2] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]

[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [4,5,2,7,8,1,6,3] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]

[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [3,5,2,7,1,8,6,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]

[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [3,4,2,1,7,8,6,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]

[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [3,4,1,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]

[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [3,1,4,2,6,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]

[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [1,3,4,2,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]

[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]

[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [3,1,2,4,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]

[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]

[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [3,2,4,1,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]

[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [3,2,5,6,1,8,7,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]

[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [4,2,5,6,8,1,7,3] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]

[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [4,3,5,6,8,7,1,2] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]

[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [3,4,5,6,7,8,1,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]

[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [2,4,5,6,7,1,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]

[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [2,3,5,6,1,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]

[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [2,3,4,1,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]

[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [2,3,1,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]

[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]

[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]

[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [9,10,7,8,5,6,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]

[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [9,10,7,8,5,6,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]]

[(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => [9,10,7,8,1,4,5,2,3,6] => [[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,.]]

[(1,8),(2,3),(4,5),(6,7),(9,10)] => [8,3,2,5,4,7,6,1,10,9] => [9,10,1,6,7,4,5,2,3,8] => [[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]],[.,.]]

[(1,10),(2,3),(4,5),(6,7),(8,9)] => [10,3,2,5,4,7,6,9,8,1] => [1,8,9,6,7,4,5,2,3,10] => [.,[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]]

[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [9,10,7,8,3,4,5,6,1,2] => [[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]],[.,.]]

[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [9,10,7,8,1,2,3,4,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]]

[(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => [9,10,1,6,7,2,3,4,5,8] => [[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],[.,.]]

[(1,10),(2,5),(3,4),(6,7),(8,9)] => [10,5,4,3,2,7,6,9,8,1] => [1,8,9,6,7,2,3,4,5,10] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,.]]]]

[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => [9,10,3,6,7,4,5,8,1,2] => [[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]],[.,.]]

[(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [9,10,1,2,5,6,3,4,7,8] => [[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],[.,.]]

[(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => [1,8,9,2,5,6,3,4,7,10] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]]

[(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,10,5,4,7,6,9,8,3] => [3,8,9,6,7,4,5,10,1,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],[.,[.,.]]]]

[(1,10),(2,9),(3,4),(5,6),(7,8)] => [10,9,4,3,6,5,8,7,2,1] => [1,2,7,8,5,6,3,4,9,10] => [.,[.,[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]]]

[(1,8),(2,9),(3,5),(4,6),(7,10)] => [8,9,5,6,3,4,10,1,2,7] => [7,2,1,10,4,3,6,5,9,8] => [[[.,.],[[.,.],[[.,.],.]]],[[[.,.],.],.]]

[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [9,10,5,6,7,8,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]],[.,.]]

[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [9,10,5,6,7,8,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]]

[(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => [9,10,1,4,5,6,7,2,3,8] => [[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],[.,.]]

[(1,10),(2,3),(4,7),(5,6),(8,9)] => [10,3,2,7,6,5,4,9,8,1] => [1,8,9,4,5,6,7,2,3,10] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]]

[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [9,10,3,4,5,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]

[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [9,10,1,2,3,4,5,6,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]

[(1,9),(2,7),(3,6),(4,5),(8,10)] => [9,7,6,5,4,3,2,10,1,8] => [8,1,10,2,3,4,5,6,7,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]

[(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [1,8,9,2,3,4,5,6,7,10] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]

[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => [3,8,9,4,5,6,7,10,1,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]

[(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [1,2,7,8,3,4,5,6,9,10] => [.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]

[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => [5,8,9,6,7,10,3,4,1,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],[.,[.,.]]]]

[(1,4),(2,3),(5,10),(6,7),(8,9)] => [4,3,2,1,10,7,6,9,8,5] => [5,8,9,6,7,10,1,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,[.,.]]]]

[(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => [1,4,7,8,5,6,9,2,3,10] => [.,[[.,[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]]

[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [3,4,7,8,5,6,9,10,1,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,[.,[.,.]]]]]]

[(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [1,2,3,6,7,4,5,8,9,10] => [.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]

[(1,10),(2,8),(3,9),(4,6),(5,7)] => [10,8,9,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]

[(1,9),(2,8),(3,7),(4,6),(5,10)] => [9,8,7,6,10,4,3,2,1,5] => [5,1,2,3,4,10,6,7,8,9] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]

[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]

[(1,7),(2,3),(4,8),(5,9),(6,10)] => [7,3,2,8,9,10,1,4,5,6] => [6,5,4,1,10,9,8,2,3,7] => [[[[.,[.,[.,.]]],.],.],[[[[.,.],.],.],.]]

[(1,8),(2,5),(3,4),(6,9),(7,10)] => [8,5,4,3,2,9,10,1,6,7] => [7,6,1,10,9,2,3,4,5,8] => [[[.,[.,[.,[.,[.,.]]]]],.],[[[.,.],.],.]]

[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [7,8,9,10,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]

[(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [7,8,9,10,5,6,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]

[(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => [7,8,9,10,1,4,5,2,3,6] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]]

[(1,10),(2,3),(4,5),(6,9),(7,8)] => [10,3,2,5,4,9,8,7,6,1] => [1,6,7,8,9,4,5,2,3,10] => [.,[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]]

[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [7,8,9,10,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]

[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [7,8,9,10,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]

[(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => [1,6,7,8,9,2,3,4,5,10] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]

[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,10,5,4,9,8,7,6,3] => [3,6,7,8,9,4,5,10,1,2] => [[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]

[(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [1,2,5,6,7,8,3,4,9,10] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]

[(1,7),(2,10),(3,5),(4,9),(6,8)] => [7,10,5,9,3,8,1,6,4,2] => [2,4,6,1,8,3,9,5,10,7] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]

[(1,9),(2,7),(3,5),(4,10),(6,8)] => [9,7,5,10,3,8,2,6,1,4] => [4,1,6,2,8,3,10,5,7,9] => [[.,[.,[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]

[(1,5),(2,6),(3,7),(4,10),(8,9)] => [5,6,7,10,1,2,3,9,8,4] => [4,8,9,3,2,1,10,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],[.,[.,.]]]]

[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [5,6,7,8,9,10,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]

[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [5,6,7,8,9,10,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]

[(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [1,4,5,6,7,8,9,2,3,10] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]

[(1,4),(2,5),(3,10),(6,9),(7,8)] => [4,5,10,1,2,9,8,7,6,3] => [3,6,7,8,9,2,1,10,5,4] => [[[.,.],.],[[[.,.],.],[.,[.,[.,[.,.]]]]]]

[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [3,4,5,6,7,8,9,10,1,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]

[(1,3),(2,10),(4,9),(5,8),(6,7)] => [3,10,1,9,8,7,6,5,4,2] => [2,4,5,6,7,8,9,1,10,3] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]

[(1,6),(2,10),(3,9),(4,8),(5,7)] => [6,10,9,8,7,1,5,4,3,2] => [2,3,4,5,1,7,8,9,10,6] => [[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]

[(1,9),(2,10),(3,8),(4,7),(5,6)] => [9,10,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]

[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]

[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10,11,12] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]]

[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,10,9,8,7,6,5,4,3,12,11] => [11,12,3,4,5,6,7,8,9,10,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]

[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [12,3,2,9,8,7,6,5,4,11,10,1] => [1,10,11,4,5,6,7,8,9,2,3,12] => [.,[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]

[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => [3,10,11,4,5,6,7,8,9,12,1,2] => [[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]

[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => [11,12,1,4,5,6,7,8,9,2,3,10] => [[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]

[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [12,11,4,3,8,7,6,5,10,9,2,1] => [1,2,9,10,5,6,7,8,3,4,11,12] => [.,[.,[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]

[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [11,12,9,10,5,6,7,8,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]],[.,.]],[.,.]]

[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [12,3,2,11,8,7,6,5,10,9,4,1] => [1,4,9,10,5,6,7,8,11,2,3,12] => [.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]

[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [3,4,9,10,5,6,7,8,11,12,1,2] => [[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]

[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [11,12,9,10,5,6,7,8,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]],[.,.]]

[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [12,9,4,3,8,7,6,5,2,11,10,1] => [1,10,11,2,5,6,7,8,3,4,9,12] => [.,[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]

[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [9,10,11,12,5,6,7,8,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]

[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [11,12,1,2,5,6,7,8,3,4,9,10] => [[.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]

[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [9,10,11,12,5,6,7,8,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]

[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [12,11,10,5,4,7,6,9,8,3,2,1] => [1,2,3,8,9,6,7,4,5,10,11,12] => [.,[.,[.,[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]]]]

[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,10,5,4,7,6,9,8,3,12,11] => [11,12,3,8,9,6,7,4,5,10,1,2] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],[.,[.,.]]]],[.,.]]

[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [12,3,2,5,4,7,6,9,8,11,10,1] => [1,10,11,8,9,6,7,4,5,2,3,12] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,[.,.]]]]

[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,12,5,4,7,6,9,8,11,10,3] => [3,10,11,8,9,6,7,4,5,12,1,2] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]]

[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [10,3,2,5,4,7,6,9,8,1,12,11] => [11,12,1,8,9,6,7,4,5,2,3,10] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]],[.,.]]

[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [12,11,4,3,10,7,6,9,8,5,2,1] => [1,2,5,8,9,6,7,10,3,4,11,12] => [.,[.,[[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]

[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,10,7,6,9,8,5,12,11] => [11,12,5,8,9,6,7,10,3,4,1,2] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],[.,[.,.]]]],[.,.]]

[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [12,3,2,11,10,7,6,9,8,5,4,1] => [1,4,5,8,9,6,7,10,11,2,3,12] => [.,[[.,[.,.]],[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]

[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [3,4,5,8,9,6,7,10,11,12,1,2] => [[.,[.,.]],[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]

[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [4,3,2,1,10,7,6,9,8,5,12,11] => [11,12,5,8,9,6,7,10,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,[.,.]]]],[.,.]]

[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [12,5,4,3,2,7,6,9,8,11,10,1] => [1,10,11,8,9,6,7,2,3,4,5,12] => [.,[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,[.,.]]]]

[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,12,7,6,9,8,11,10,5] => [5,10,11,8,9,6,7,12,3,4,1,2] => [[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],[.,[.,.]]]]

[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [10,5,4,3,2,7,6,9,8,1,12,11] => [11,12,1,8,9,6,7,2,3,4,5,10] => [[.,[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,.]]]],[.,.]]

[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [4,3,2,1,12,7,6,9,8,11,10,5] => [5,10,11,8,9,6,7,12,1,2,3,4] => [[.,[.,[.,[.,.]]]],[[[.,[.,.]],[.,.]],[.,[.,.]]]]

[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [12,11,8,5,4,7,6,3,10,9,2,1] => [1,2,9,10,3,6,7,4,5,8,11,12] => [.,[.,[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]]]]

[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,8,5,4,7,6,3,10,9,12,11] => [11,12,9,10,3,6,7,4,5,8,1,2] => [[[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,.]]

[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [12,3,2,5,4,7,6,11,10,9,8,1] => [1,8,9,10,11,6,7,4,5,2,3,12] => [.,[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]]

[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,12,5,4,7,6,11,10,9,8,3] => [3,8,9,10,11,6,7,4,5,12,1,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]]

[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [8,3,2,5,4,7,6,1,10,9,12,11] => [11,12,9,10,1,6,7,4,5,2,3,8] => [[[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]],[.,.]],[.,.]]

[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [12,9,8,5,4,7,6,3,2,11,10,1] => [1,10,11,2,3,6,7,4,5,8,9,12] => [.,[[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],[.,[.,.]]]]

[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,8,5,4,7,6,3,12,11,10,9] => [9,10,11,12,3,6,7,4,5,8,1,2] => [[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]]

[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [11,12,1,2,3,6,7,4,5,8,9,10] => [[.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]],[.,.]]

[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [8,3,2,5,4,7,6,1,12,11,10,9] => [9,10,11,12,1,6,7,4,5,2,3,8] => [[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]]

[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [12,5,4,3,2,7,6,11,10,9,8,1] => [1,8,9,10,11,6,7,2,3,4,5,12] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,[.,.]]]]]]

[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,12,7,6,11,10,9,8,5] => [5,8,9,10,11,6,7,12,3,4,1,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]

[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [8,5,4,3,2,7,6,1,10,9,12,11] => [11,12,9,10,1,6,7,2,3,4,5,8] => [[[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],[.,.]],[.,.]]

[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => [5,8,9,10,11,6,7,12,1,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]

[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [8,5,4,3,2,7,6,1,12,11,10,9] => [9,10,11,12,1,6,7,2,3,4,5,8] => [[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],[.,[.,[.,.]]]]

[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [1,2,3,4,7,8,5,6,9,10,11,12] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]]]

[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [11,12,3,4,7,8,5,6,9,10,1,2] => [[[.,[.,.]],[.,[[.,[.,.]],[.,[.,[.,.]]]]]],[.,.]]

[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [12,3,2,9,6,5,8,7,4,11,10,1] => [1,10,11,4,7,8,5,6,9,2,3,12] => [.,[[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]]

[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,12,9,6,5,8,7,4,11,10,3] => [3,10,11,4,7,8,5,6,9,12,1,2] => [[.,[.,.]],[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]]

[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [10,3,2,9,6,5,8,7,4,1,12,11] => [11,12,1,4,7,8,5,6,9,2,3,10] => [[.,[[.,[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]],[.,.]]

[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [12,11,4,3,6,5,8,7,10,9,2,1] => [1,2,9,10,7,8,5,6,3,4,11,12] => [.,[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]]]

[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,6,3,4,1,2] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]

[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [12,3,2,11,6,5,8,7,10,9,4,1] => [1,4,9,10,7,8,5,6,11,2,3,12] => [.,[[.,[.,.]],[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]]]

[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,12,11,6,5,8,7,10,9,4,3] => [3,4,9,10,7,8,5,6,11,12,1,2] => [[.,[.,.]],[.,[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]]]

[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,6,1,2,3,4] => [[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]],[.,.]]

[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [12,9,4,3,6,5,8,7,2,11,10,1] => [1,10,11,2,7,8,5,6,3,4,9,12] => [.,[[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]],[.,[.,.]]]]

[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [9,10,11,12,7,8,5,6,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]

[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [10,9,4,3,6,5,8,7,2,1,12,11] => [11,12,1,2,7,8,5,6,3,4,9,10] => [[.,[.,[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]]],[.,.]]

[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [9,10,11,12,7,8,5,6,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,[.,[.,.]]]]

[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [1,2,3,6,7,8,9,4,5,10,11,12] => [.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]]]

[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,10,5,4,9,8,7,6,3,12,11] => [11,12,3,6,7,8,9,4,5,10,1,2] => [[[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]],[.,.]]

[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [12,3,2,5,4,9,8,7,6,11,10,1] => [1,10,11,6,7,8,9,4,5,2,3,12] => [.,[[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]]

[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,12,5,4,9,8,7,6,11,10,3] => [3,10,11,6,7,8,9,4,5,12,1,2] => [[.,[.,.]],[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]]

[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [10,3,2,5,4,9,8,7,6,1,12,11] => [11,12,1,6,7,8,9,4,5,2,3,10] => [[.,[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]],[.,.]]

[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [1,2,5,6,7,8,9,10,3,4,11,12] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]

[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [11,12,5,6,7,8,9,10,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]

[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [12,3,2,11,10,9,8,7,6,5,4,1] => [1,4,5,6,7,8,9,10,11,2,3,12] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]

[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [3,4,5,6,7,8,9,10,11,12,1,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]

[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [11,12,5,6,7,8,9,10,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]

[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [12,5,4,3,2,9,8,7,6,11,10,1] => [1,10,11,6,7,8,9,2,3,4,5,12] => [.,[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,[.,.]]]]

[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => [5,10,11,6,7,8,9,12,3,4,1,2] => [[[.,[.,.]],[.,.]],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]

[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => [11,12,1,6,7,8,9,2,3,4,5,10] => [[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]],[.,.]]

[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [4,3,2,1,12,9,8,7,6,11,10,5] => [5,10,11,6,7,8,9,12,1,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]

[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [12,11,6,5,4,3,8,7,10,9,2,1] => [1,2,9,10,7,8,3,4,5,6,11,12] => [.,[.,[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]]]

[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [11,12,9,10,7,8,3,4,5,6,1,2] => [[[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]]

[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [12,3,2,5,4,11,8,7,10,9,6,1] => [1,6,9,10,7,8,11,4,5,2,3,12] => [.,[[[.,[.,.]],[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]]

[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,12,5,4,11,8,7,10,9,6,3] => [3,6,9,10,7,8,11,4,5,12,1,2] => [[.,[.,.]],[[.,[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]]

[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [6,3,2,5,4,1,8,7,10,9,12,11] => [11,12,9,10,7,8,1,4,5,2,3,6] => [[[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,.]],[.,.]]

[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [12,9,6,5,4,3,8,7,2,11,10,1] => [1,10,11,2,7,8,3,4,5,6,9,12] => [.,[[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],[.,[.,.]]]]

[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [9,10,11,12,7,8,3,4,5,6,1,2] => [[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]

[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [11,12,1,2,7,8,3,4,5,6,9,10] => [[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]],[.,.]]

[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [6,3,2,5,4,1,8,7,12,11,10,9] => [9,10,11,12,7,8,1,4,5,2,3,6] => [[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]

[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [12,5,4,3,2,11,8,7,10,9,6,1] => [1,6,9,10,7,8,11,2,3,4,5,12] => [.,[[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,[.,[.,.]]]]]]

[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [5,6,9,10,7,8,11,12,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,[[.,[.,.]],[.,[.,[.,.]]]]]]

[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [11,12,9,10,7,8,1,2,3,4,5,6] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]],[.,.]]

[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [5,6,9,10,7,8,11,12,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[[.,[.,.]],[.,[.,[.,.]]]]]]

[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [9,10,11,12,7,8,1,2,3,4,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,[.,[.,.]]]]

[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [1,2,3,8,9,4,5,6,7,10,11,12] => [.,[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]]]

[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,10,7,6,5,4,9,8,3,12,11] => [11,12,3,8,9,4,5,6,7,10,1,2] => [[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,[.,.]]]],[.,.]]

[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [12,3,2,7,6,5,4,9,8,11,10,1] => [1,10,11,8,9,4,5,6,7,2,3,12] => [.,[[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]],[.,[.,.]]]]

[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,12,7,6,5,4,9,8,11,10,3] => [3,10,11,8,9,4,5,6,7,12,1,2] => [[.,[.,.]],[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,.]]]]

[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [10,3,2,7,6,5,4,9,8,1,12,11] => [11,12,1,8,9,4,5,6,7,2,3,10] => [[.,[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]],[.,.]]

[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [12,11,4,3,6,5,10,9,8,7,2,1] => [1,2,7,8,9,10,5,6,3,4,11,12] => [.,[.,[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]

[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [11,12,7,8,9,10,5,6,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]],[.,.]]

[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [12,3,2,11,6,5,10,9,8,7,4,1] => [1,4,7,8,9,10,5,6,11,2,3,12] => [.,[[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]

[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [3,4,7,8,9,10,5,6,11,12,1,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]

[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [11,12,7,8,9,10,5,6,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]],[.,.]]

[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [12,7,4,3,6,5,2,9,8,11,10,1] => [1,10,11,8,9,2,5,6,3,4,7,12] => [.,[[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,[.,.]]]]

[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,12,9,8,11,10,7] => [7,10,11,8,9,12,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],[.,[.,.]]]]

[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [10,7,4,3,6,5,2,9,8,1,12,11] => [11,12,1,8,9,2,5,6,3,4,7,10] => [[.,[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]],[.,.]]

[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [4,3,2,1,6,5,12,9,8,11,10,7] => [7,10,11,8,9,12,5,6,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,.]],[[.,[.,.]],[.,[.,.]]]]

[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [1,2,9,10,3,4,5,6,7,8,11,12] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]]]

[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [11,12,9,10,3,4,5,6,7,8,1,2] => [[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]]

[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [12,3,2,7,6,5,4,11,10,9,8,1] => [1,8,9,10,11,4,5,6,7,2,3,12] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]

[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,12,7,6,5,4,11,10,9,8,3] => [3,8,9,10,11,4,5,6,7,12,1,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]

[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => [11,12,9,10,1,4,5,6,7,2,3,8] => [[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]]

[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [12,9,8,7,6,5,4,3,2,11,10,1] => [1,10,11,2,3,4,5,6,7,8,9,12] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,[.,.]]]]

[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [9,10,11,12,3,4,5,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]

[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [11,12,1,2,3,4,5,6,7,8,9,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]

[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => [9,10,11,12,1,4,5,6,7,2,3,8] => [[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]

[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [12,7,4,3,6,5,2,11,10,9,8,1] => [1,8,9,10,11,2,5,6,3,4,7,12] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]

[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [7,8,9,10,11,12,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]

[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [11,12,9,10,1,2,5,6,3,4,7,8] => [[[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],[.,.]],[.,.]]

[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [7,8,9,10,11,12,5,6,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]

[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [9,10,11,12,1,2,5,6,3,4,7,8] => [[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]

[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [1,2,7,8,9,10,3,4,5,6,11,12] => [.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]]]

[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [11,12,7,8,9,10,3,4,5,6,1,2] => [[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]]

[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [12,3,2,5,4,11,10,9,8,7,6,1] => [1,6,7,8,9,10,11,4,5,2,3,12] => [.,[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]

[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,12,5,4,11,10,9,8,7,6,3] => [3,6,7,8,9,10,11,4,5,12,1,2] => [[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]

[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [6,3,2,5,4,1,10,9,8,7,12,11] => [11,12,7,8,9,10,1,4,5,2,3,6] => [[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]]

[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [12,7,6,5,4,3,2,9,8,11,10,1] => [1,10,11,8,9,2,3,4,5,6,7,12] => [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,[.,.]]]]

[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,6,5,4,3,12,9,8,11,10,7] => [7,10,11,8,9,12,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[[.,[.,.]],[.,[.,.]]]]

[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [10,7,6,5,4,3,2,9,8,1,12,11] => [11,12,1,8,9,2,3,4,5,6,7,10] => [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]],[.,.]]

[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [6,3,2,5,4,1,12,9,8,11,10,7] => [7,10,11,8,9,12,1,4,5,2,3,6] => [[.,[[.,[.,.]],[.,[.,.]]]],[[.,[.,.]],[.,[.,.]]]]

[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => [1,6,7,8,9,10,11,2,3,4,5,12] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,[.,.]]]]]]]]

[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [5,6,7,8,9,10,11,12,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]

[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [11,12,7,8,9,10,1,2,3,4,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]],[.,.]]

[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [5,6,7,8,9,10,11,12,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]

[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [6,5,4,3,2,1,12,9,8,11,10,7] => [7,10,11,8,9,12,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],[.,[.,.]]]]

[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [12,7,6,5,4,3,2,11,10,9,8,1] => [1,8,9,10,11,2,3,4,5,6,7,12] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,.]]]]]]

[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [7,8,9,10,11,12,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]

[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [11,12,9,10,1,2,3,4,5,6,7,8] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],[.,.]]

[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => [7,8,9,10,11,12,1,4,5,2,3,6] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]

[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [9,10,11,12,1,2,3,4,5,6,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,[.,[.,.]]]]

[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [7,8,9,10,11,12,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,[.,.]]]]]]

[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [6,5,4,3,2,1,12,11,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]

Map

to permutation

Description

Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.

Map

reverse

Description

Sends a permutation to its reverse.
The reverse of a permutation

$\sigma$ of length

$n$ is given by

$\tau$ with

$\tau(i) = \sigma(n+1-i)$ .

Map

binary search tree: left to right

Description

Return the shape of the binary search tree of the permutation as a non labelled binary tree.