- FindStat

Identifier

Mp00019: Binary trees —right rotate⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
St001004: Permutations ⟶ ℤ

Values

[.,.] => [.,.] => [1] => [1] => 1

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

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

[.,[.,[.,.]]] => [[.,[.,.]],.] => [2,1,3] => [3,2,1] => 2

[.,[[.,.],.]] => [[[.,.],.],.] => [1,2,3] => [2,3,1] => 3

[[.,.],[.,.]] => [.,[.,[.,.]]] => [3,2,1] => [1,2,3] => 3

[[.,[.,.]],.] => [.,[[.,.],.]] => [2,3,1] => [3,1,2] => 3

[[[.,.],.],.] => [[.,.],[.,.]] => [1,3,2] => [2,1,3] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[.,[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [5,4,3,2,1] => 2

[.,[.,[.,[[.,.],.]]]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [4,5,3,2,1] => 3

[.,[.,[[.,.],[.,.]]]] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [3,5,4,2,1] => 3

[.,[.,[[.,[.,.]],.]]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [4,3,5,2,1] => 3

[.,[.,[[[.,.],.],.]]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [3,4,5,2,1] => 4

[.,[[.,.],[.,[.,.]]]] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [2,5,4,3,1] => 3

[.,[[.,.],[[.,.],.]]] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [2,4,5,3,1] => 4

[.,[[.,[.,.]],[.,.]]] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [3,2,5,4,1] => 3

[.,[[[.,.],.],[.,.]]] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [2,3,5,4,1] => 4

[.,[[.,[.,[.,.]]],.]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [4,3,2,5,1] => 3

[.,[[.,[[.,.],.]],.]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [3,4,2,5,1] => 4

[.,[[[.,.],[.,.]],.]] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [2,4,3,5,1] => 4

[.,[[[.,[.,.]],.],.]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [3,2,4,5,1] => 4

[.,[[[[.,.],.],.],.]] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [2,3,4,5,1] => 5

[[.,.],[.,[.,[.,.]]]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,2,3,4,5] => 5

[[.,.],[.,[[.,.],.]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [5,1,2,3,4] => 5

[[.,.],[[.,.],[.,.]]] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [4,1,2,3,5] => 5

[[.,.],[[.,[.,.]],.]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [5,4,1,2,3] => 4

[[.,.],[[[.,.],.],.]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [4,5,1,2,3] => 5

[[.,[.,.]],[.,[.,.]]] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [3,1,2,4,5] => 5

[[.,[.,.]],[[.,.],.]] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [3,5,1,2,4] => 5

[[[.,.],.],[.,[.,.]]] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [2,1,3,4,5] => 5

[[[.,.],.],[[.,.],.]] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [2,5,1,3,4] => 5

[[.,[.,[.,.]]],[.,.]] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [4,3,1,2,5] => 4

[[.,[[.,.],.]],[.,.]] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [3,4,1,2,5] => 5

[[[.,.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [2,4,1,3,5] => 5

[[[.,[.,.]],.],[.,.]] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [3,2,1,4,5] => 4

[[[[.,.],.],.],[.,.]] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [2,3,1,4,5] => 5

[[.,[.,[.,[.,.]]]],.] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [5,4,3,1,2] => 3

[[.,[.,[[.,.],.]]],.] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [4,5,3,1,2] => 4

[[.,[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [3,5,4,1,2] => 4

[[.,[[.,[.,.]],.]],.] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [4,3,5,1,2] => 4

[[.,[[[.,.],.],.]],.] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [3,4,5,1,2] => 5

[[[.,.],[.,[.,.]]],.] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [2,5,4,1,3] => 4

[[[.,.],[[.,.],.]],.] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [2,4,5,1,3] => 5

[[[.,[.,.]],[.,.]],.] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [3,2,5,1,4] => 4

[[[[.,.],.],[.,.]],.] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [2,3,5,1,4] => 5

[[[.,[.,[.,.]]],.],.] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [4,3,2,1,5] => 3

[[[.,[[.,.],.]],.],.] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [3,4,2,1,5] => 4

[[[[.,.],[.,.]],.],.] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [2,4,3,1,5] => 4

[[[[.,[.,.]],.],.],.] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [3,2,4,1,5] => 4

[[[[[.,.],.],.],.],.] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [2,3,4,1,5] => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 383 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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searching the database for the individual values of this statistic

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searching the database for statistics with the same generating function

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$F_{1} = q$

$F_{2} = 2\ q^{2}$

$F_{3} = q^{2} + 4\ q^{3}$

$F_{4} = q^{2} + 5\ q^{3} + 8\ q^{4}$

$F_{5} = q^{2} + 8\ q^{3} + 17\ q^{4} + 16\ q^{5}$

$F_{6} = q^{2} + 12\ q^{3} + 38\ q^{4} + 49\ q^{5} + 32\ q^{6}$

Description

The number of indices that are either left-to-right maxima or right-to-left minima.
The (bivariate) generating function for this statistic is (essentially) given in [1], the mid points of a

$321$ pattern in the permutation are those elements which are neither left-to-right maxima nor a right-to-left minima, see St000371The number of mid points of decreasing subsequences of length 3 in a permutation. and St000372The number of mid points of increasing subsequences of length 3 in a permutation..

Map

right rotate

Description

Return the result of right rotation applied to a binary tree.
Right rotation on binary trees is defined as follows: Let

$T$ be a binary tree such that the left child of the root of

$T$ is a node. Let

$C$ be the right child of the root of

$T$ , and let

$A$ and

$B$ be the left and right children of the left child of the root of

$T$ . (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the right rotation of

$T$ is the binary tree in which the left child of the root is

$A$ , whereas the right child of the root is a node whose left and right children are

$B$ and

$C$ .

Map

to 312-avoiding permutation

Description

Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.

Map

Lehmer code rotation

Description

Sends a permutation

$\pi$ to the unique permutation

$\tau$ (of the same length) such that every entry in the Lehmer code of

$\tau$ is cyclically one larger than the Lehmer code of

$\pi$ .