Identifier
Values
[.,.] => [1] => [1] => 0
[.,[.,.]] => [2,1] => [2,1] => 0
[[.,.],.] => [1,2] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => [3,2,1] => 1
[.,[[.,.],.]] => [2,3,1] => [1,3,2] => 0
[[.,.],[.,.]] => [1,3,2] => [1,3,2] => 0
[[.,[.,.]],.] => [2,1,3] => [2,1,3] => 0
[[[.,.],.],.] => [1,2,3] => [1,2,3] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,3,2,1] => 2
[.,[.,[[.,.],.]]] => [3,4,2,1] => [1,4,3,2] => 1
[.,[[.,.],[.,.]]] => [2,4,3,1] => [1,4,3,2] => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => [2,1,4,3] => 0
[.,[[[.,.],.],.]] => [2,3,4,1] => [1,2,4,3] => 0
[[.,.],[.,[.,.]]] => [1,4,3,2] => [1,4,3,2] => 1
[[.,.],[[.,.],.]] => [1,3,4,2] => [1,2,4,3] => 0
[[.,[.,.]],[.,.]] => [2,1,4,3] => [2,1,4,3] => 0
[[[.,.],.],[.,.]] => [1,2,4,3] => [1,2,4,3] => 0
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1,4] => 1
[[.,[[.,.],.]],.] => [2,3,1,4] => [1,3,2,4] => 0
[[[.,.],[.,.]],.] => [1,3,2,4] => [1,3,2,4] => 0
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => 0
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => 0
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,4,3,2,1] => 3
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [1,5,4,3,2] => 2
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [1,5,4,3,2] => 2
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [2,1,5,4,3] => 1
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [1,2,5,4,3] => 1
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [1,5,4,3,2] => 2
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [1,2,5,4,3] => 1
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [2,1,5,4,3] => 1
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [1,2,5,4,3] => 1
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [3,2,1,5,4] => 1
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [1,3,2,5,4] => 0
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [1,3,2,5,4] => 0
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [2,1,3,5,4] => 0
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,2,3,5,4] => 0
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [1,5,4,3,2] => 2
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [1,2,5,4,3] => 1
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [1,2,5,4,3] => 1
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [1,3,2,5,4] => 0
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [1,2,3,5,4] => 0
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [2,1,5,4,3] => 1
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [2,1,3,5,4] => 0
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [1,2,5,4,3] => 1
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [1,2,3,5,4] => 0
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [3,2,1,5,4] => 1
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [1,3,2,5,4] => 0
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [2,1,3,5,4] => 0
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1,5] => 2
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [1,4,3,2,5] => 1
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [1,4,3,2,5] => 1
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [2,1,4,3,5] => 0
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [1,2,4,3,5] => 0
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [1,4,3,2,5] => 1
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [1,2,4,3,5] => 0
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [2,1,4,3,5] => 0
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4,5] => 1
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [1,3,2,4,5] => 0
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => 0
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 4
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [1,6,5,4,3,2] => 3
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [1,6,5,4,3,2] => 3
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [2,1,6,5,4,3] => 2
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [1,2,6,5,4,3] => 2
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [1,6,5,4,3,2] => 3
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [1,2,6,5,4,3] => 2
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [2,1,6,5,4,3] => 2
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [1,2,6,5,4,3] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [3,2,1,6,5,4] => 2
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [1,3,2,6,5,4] => 1
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [1,3,2,6,5,4] => 1
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [2,1,3,6,5,4] => 1
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [1,2,3,6,5,4] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [1,6,5,4,3,2] => 3
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [1,2,6,5,4,3] => 2
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [1,2,6,5,4,3] => 2
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [1,3,2,6,5,4] => 1
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [1,2,3,6,5,4] => 1
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [2,1,6,5,4,3] => 2
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [2,1,3,6,5,4] => 1
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [1,2,6,5,4,3] => 2
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [1,2,3,6,5,4] => 1
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [3,2,1,6,5,4] => 2
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [1,3,2,6,5,4] => 1
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [1,3,2,6,5,4] => 1
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [2,1,3,6,5,4] => 1
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [1,2,3,6,5,4] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [4,3,2,1,6,5] => 2
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [1,4,3,2,6,5] => 1
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [1,4,3,2,6,5] => 1
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [2,1,4,3,6,5] => 0
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [1,2,4,3,6,5] => 0
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [1,4,3,2,6,5] => 1
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [1,2,4,3,6,5] => 0
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [2,1,4,3,6,5] => 0
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [1,2,4,3,6,5] => 0
>>> Load all 525 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [3,2,1,4,6,5] => 1
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [1,3,2,4,6,5] => 0
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [1,3,2,4,6,5] => 0
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [2,1,3,4,6,5] => 0
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [1,2,3,4,6,5] => 0
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 3
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [1,2,6,5,4,3] => 2
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [1,2,6,5,4,3] => 2
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [1,3,2,6,5,4] => 1
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [1,2,3,6,5,4] => 1
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [1,2,6,5,4,3] => 2
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [1,2,3,6,5,4] => 1
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [1,3,2,6,5,4] => 1
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [1,2,3,6,5,4] => 1
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [1,4,3,2,6,5] => 1
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [1,2,4,3,6,5] => 0
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [1,2,4,3,6,5] => 0
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [1,3,2,4,6,5] => 0
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [1,2,3,4,6,5] => 0
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [2,1,3,6,5,4] => 1
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [2,1,3,6,5,4] => 1
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [2,1,4,3,6,5] => 0
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [2,1,3,4,6,5] => 0
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 2
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [1,2,3,6,5,4] => 1
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [1,2,3,6,5,4] => 1
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [1,2,4,3,6,5] => 0
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [1,2,3,4,6,5] => 0
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [3,2,1,4,6,5] => 1
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [1,3,2,6,5,4] => 1
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [1,3,2,4,6,5] => 0
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 1
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [1,3,2,4,6,5] => 0
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 1
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [2,1,3,4,6,5] => 0
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [1,2,3,4,6,5] => 0
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 2
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [1,4,3,2,6,5] => 1
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [1,4,3,2,6,5] => 1
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [2,1,4,3,6,5] => 0
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [1,2,4,3,6,5] => 0
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 1
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [1,2,4,3,6,5] => 0
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 0
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 0
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 1
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [1,3,2,4,6,5] => 0
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 0
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 0
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 0
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 3
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [1,5,4,3,2,6] => 2
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [1,5,4,3,2,6] => 2
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [2,1,5,4,3,6] => 1
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [1,2,5,4,3,6] => 1
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [1,5,4,3,2,6] => 2
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [1,2,5,4,3,6] => 1
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [2,1,5,4,3,6] => 1
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [1,2,5,4,3,6] => 1
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [3,2,1,5,4,6] => 1
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [1,3,2,5,4,6] => 0
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [1,3,2,5,4,6] => 0
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [2,1,3,5,4,6] => 0
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [1,2,3,5,4,6] => 0
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [1,2,5,4,3,6] => 1
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [1,2,5,4,3,6] => 1
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [1,3,2,5,4,6] => 0
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [1,2,3,5,4,6] => 0
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 1
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [2,1,3,5,4,6] => 0
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 1
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [1,2,3,5,4,6] => 0
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 1
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [1,3,2,5,4,6] => 0
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 0
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 0
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 0
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 2
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [1,4,3,2,5,6] => 1
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [1,4,3,2,5,6] => 1
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [2,1,4,3,5,6] => 0
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [1,2,4,3,5,6] => 0
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 1
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [1,2,4,3,5,6] => 0
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 0
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 0
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 1
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [1,3,2,4,5,6] => 0
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 0
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 0
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 5
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [1,7,6,5,4,3,2] => 4
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [1,7,6,5,4,3,2] => 4
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [2,1,7,6,5,4,3] => 3
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [1,2,7,6,5,4,3] => 3
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [1,7,6,5,4,3,2] => 4
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [1,2,7,6,5,4,3] => 3
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [2,1,7,6,5,4,3] => 3
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [1,2,7,6,5,4,3] => 3
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [1,3,2,7,6,5,4] => 2
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [1,3,2,7,6,5,4] => 2
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => 2
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [1,7,6,5,4,3,2] => 4
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [1,2,7,6,5,4,3] => 3
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [1,2,7,6,5,4,3] => 3
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [1,3,2,7,6,5,4] => 2
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [1,2,3,7,6,5,4] => 2
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [2,1,7,6,5,4,3] => 3
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [1,2,7,6,5,4,3] => 3
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [1,2,3,7,6,5,4] => 2
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [1,3,2,7,6,5,4] => 2
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [1,3,2,7,6,5,4] => 2
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [1,2,3,7,6,5,4] => 2
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [1,4,3,2,7,6,5] => 2
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [1,4,3,2,7,6,5] => 2
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [1,2,4,3,7,6,5] => 1
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [1,4,3,2,7,6,5] => 2
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [1,2,4,3,7,6,5] => 1
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [1,2,4,3,7,6,5] => 1
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [1,3,2,4,7,6,5] => 1
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [1,3,2,4,7,6,5] => 1
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [1,2,3,4,7,6,5] => 1
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [1,7,6,5,4,3,2] => 4
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [1,2,7,6,5,4,3] => 3
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [1,2,7,6,5,4,3] => 3
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [1,3,2,7,6,5,4] => 2
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [1,2,3,7,6,5,4] => 2
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [1,2,7,6,5,4,3] => 3
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [1,2,3,7,6,5,4] => 2
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [1,3,2,7,6,5,4] => 2
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [1,2,3,7,6,5,4] => 2
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [1,4,3,2,7,6,5] => 2
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [1,2,4,3,7,6,5] => 1
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [1,2,4,3,7,6,5] => 1
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [1,3,2,4,7,6,5] => 1
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [1,2,3,4,7,6,5] => 1
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [2,1,7,6,5,4,3] => 3
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [1,2,7,6,5,4,3] => 3
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [1,2,3,7,6,5,4] => 2
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [1,2,3,7,6,5,4] => 2
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [1,2,4,3,7,6,5] => 1
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [1,2,3,4,7,6,5] => 1
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [1,3,2,7,6,5,4] => 2
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [1,3,2,4,7,6,5] => 1
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [1,3,2,7,6,5,4] => 2
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [1,3,2,4,7,6,5] => 1
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [1,2,3,7,6,5,4] => 2
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [1,2,3,4,7,6,5] => 1
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [1,4,3,2,7,6,5] => 2
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [1,4,3,2,7,6,5] => 2
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [1,2,4,3,7,6,5] => 1
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [1,4,3,2,7,6,5] => 2
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [1,2,4,3,7,6,5] => 1
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [1,2,4,3,7,6,5] => 1
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [1,3,2,4,7,6,5] => 1
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [1,3,2,4,7,6,5] => 1
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [1,2,3,4,7,6,5] => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [5,4,3,2,1,7,6] => 3
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [1,2,5,4,3,7,6] => 1
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [1,2,5,4,3,7,6] => 1
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [1,2,5,4,3,7,6] => 1
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [1,3,2,5,4,7,6] => 0
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [1,3,2,5,4,7,6] => 0
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [1,2,3,5,4,7,6] => 0
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [1,2,5,4,3,7,6] => 1
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [1,2,5,4,3,7,6] => 1
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [1,3,2,5,4,7,6] => 0
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [1,2,3,5,4,7,6] => 0
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [1,2,5,4,3,7,6] => 1
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [1,2,3,5,4,7,6] => 0
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [1,3,2,5,4,7,6] => 0
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [1,3,2,5,4,7,6] => 0
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [1,2,3,5,4,7,6] => 0
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [1,4,3,2,5,7,6] => 1
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [1,4,3,2,5,7,6] => 1
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [1,2,4,3,5,7,6] => 0
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [1,4,3,2,5,7,6] => 1
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [1,2,4,3,5,7,6] => 0
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [1,2,4,3,5,7,6] => 0
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [1,3,2,4,5,7,6] => 0
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [1,3,2,4,5,7,6] => 0
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [1,2,3,4,5,7,6] => 0
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 4
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [1,2,7,6,5,4,3] => 3
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [1,2,7,6,5,4,3] => 3
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [1,3,2,7,6,5,4] => 2
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [1,2,3,7,6,5,4] => 2
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [1,2,7,6,5,4,3] => 3
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [1,2,3,7,6,5,4] => 2
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [1,3,2,7,6,5,4] => 2
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [1,2,3,7,6,5,4] => 2
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [1,4,3,2,7,6,5] => 2
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [1,2,4,3,7,6,5] => 1
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [1,2,4,3,7,6,5] => 1
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [1,3,2,4,7,6,5] => 1
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [1,2,3,4,7,6,5] => 1
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [1,2,7,6,5,4,3] => 3
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [1,2,3,7,6,5,4] => 2
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [1,2,3,7,6,5,4] => 2
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [1,2,4,3,7,6,5] => 1
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [1,2,3,4,7,6,5] => 1
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [1,3,2,7,6,5,4] => 2
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [1,3,2,4,7,6,5] => 1
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [1,2,3,7,6,5,4] => 2
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [1,2,3,4,7,6,5] => 1
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [1,4,3,2,7,6,5] => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [1,2,4,3,7,6,5] => 1
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [1,2,4,3,7,6,5] => 1
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [1,3,2,4,7,6,5] => 1
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [1,2,3,4,7,6,5] => 1
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [1,2,5,4,3,7,6] => 1
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [1,2,5,4,3,7,6] => 1
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [1,3,2,5,4,7,6] => 0
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [1,2,3,5,4,7,6] => 0
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [1,2,5,4,3,7,6] => 1
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [1,2,3,5,4,7,6] => 0
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [1,3,2,5,4,7,6] => 0
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [1,2,3,5,4,7,6] => 0
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [1,4,3,2,5,7,6] => 1
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [1,2,4,3,5,7,6] => 0
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [1,2,4,3,5,7,6] => 0
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [1,3,2,4,5,7,6] => 0
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [1,2,3,4,5,7,6] => 0
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 3
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 3
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [1,2,3,7,6,5,4] => 2
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [1,2,3,7,6,5,4] => 2
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [1,2,4,3,7,6,5] => 1
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [1,2,3,4,7,6,5] => 1
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [1,2,3,7,6,5,4] => 2
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [1,2,3,4,7,6,5] => 1
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [1,2,4,3,7,6,5] => 1
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [1,2,3,4,7,6,5] => 1
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [1,2,5,4,3,7,6] => 1
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [1,2,3,5,4,7,6] => 0
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [1,2,3,5,4,7,6] => 0
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [1,2,4,3,5,7,6] => 0
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [1,2,3,4,5,7,6] => 0
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [1,3,2,7,6,5,4] => 2
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [1,3,2,4,7,6,5] => 1
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [1,3,2,4,7,6,5] => 1
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [1,3,2,5,4,7,6] => 0
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [1,3,2,4,5,7,6] => 0
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => 2
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [1,3,2,4,7,6,5] => 1
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [1,3,2,4,7,6,5] => 1
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [1,3,2,5,4,7,6] => 0
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [1,3,2,4,5,7,6] => 0
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => 2
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [1,2,3,4,7,6,5] => 1
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [1,2,3,4,7,6,5] => 1
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [1,2,3,5,4,7,6] => 0
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [1,2,3,4,5,7,6] => 0
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [1,4,3,2,7,6,5] => 2
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [1,4,3,2,5,7,6] => 1
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [1,4,3,2,7,6,5] => 2
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [1,4,3,2,5,7,6] => 1
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [1,2,4,3,7,6,5] => 1
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [1,2,4,3,5,7,6] => 0
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => 2
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [1,4,3,2,5,7,6] => 1
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [1,2,4,3,7,6,5] => 1
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [1,2,4,3,5,7,6] => 0
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => 1
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [1,2,4,3,5,7,6] => 0
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [1,3,2,4,7,6,5] => 1
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [1,3,2,4,5,7,6] => 0
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => 1
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [1,3,2,4,5,7,6] => 0
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => 1
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [1,2,3,4,5,7,6] => 0
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 3
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [1,2,5,4,3,7,6] => 1
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [1,2,5,4,3,7,6] => 1
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [1,2,5,4,3,7,6] => 1
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [1,3,2,5,4,7,6] => 0
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [1,3,2,5,4,7,6] => 0
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [1,2,3,5,4,7,6] => 0
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [1,2,5,4,3,7,6] => 1
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [1,2,5,4,3,7,6] => 1
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [1,3,2,5,4,7,6] => 0
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [1,2,3,5,4,7,6] => 0
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => 1
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [1,2,3,5,4,7,6] => 0
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [1,3,2,5,4,7,6] => 0
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => 0
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => 0
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [1,4,3,2,5,7,6] => 1
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [1,4,3,2,5,7,6] => 1
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [1,2,4,3,5,7,6] => 0
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => 1
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [1,2,4,3,5,7,6] => 0
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => 0
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [1,3,2,4,5,7,6] => 0
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => 0
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 4
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [1,2,6,5,4,3,7] => 2
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [1,2,6,5,4,3,7] => 2
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [1,2,6,5,4,3,7] => 2
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [1,3,2,6,5,4,7] => 1
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [1,3,2,6,5,4,7] => 1
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [1,2,3,6,5,4,7] => 1
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [1,2,6,5,4,3,7] => 2
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [1,2,6,5,4,3,7] => 2
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [1,3,2,6,5,4,7] => 1
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [1,2,3,6,5,4,7] => 1
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [1,2,6,5,4,3,7] => 2
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [1,2,3,6,5,4,7] => 1
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [1,3,2,6,5,4,7] => 1
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [1,3,2,6,5,4,7] => 1
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [1,2,3,6,5,4,7] => 1
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [1,4,3,2,6,5,7] => 1
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [1,4,3,2,6,5,7] => 1
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [1,2,4,3,6,5,7] => 0
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [1,4,3,2,6,5,7] => 1
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [1,2,4,3,6,5,7] => 0
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [1,2,4,3,6,5,7] => 0
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [1,3,2,4,6,5,7] => 0
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [1,3,2,4,6,5,7] => 0
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [1,2,3,4,6,5,7] => 0
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [1,2,6,5,4,3,7] => 2
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [1,2,6,5,4,3,7] => 2
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [1,3,2,6,5,4,7] => 1
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [1,2,3,6,5,4,7] => 1
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [1,2,6,5,4,3,7] => 2
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [1,2,3,6,5,4,7] => 1
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [1,3,2,6,5,4,7] => 1
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [1,2,3,6,5,4,7] => 1
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [1,4,3,2,6,5,7] => 1
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [1,2,4,3,6,5,7] => 0
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [1,2,4,3,6,5,7] => 0
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [1,3,2,4,6,5,7] => 0
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [1,2,3,4,6,5,7] => 0
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => 2
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [1,2,3,6,5,4,7] => 1
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [1,2,3,6,5,4,7] => 1
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [1,2,4,3,6,5,7] => 0
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [1,2,3,4,6,5,7] => 0
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [1,3,2,6,5,4,7] => 1
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [1,3,2,4,6,5,7] => 0
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => 1
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [1,3,2,4,6,5,7] => 0
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => 1
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [1,2,3,4,6,5,7] => 0
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [1,4,3,2,6,5,7] => 1
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [1,4,3,2,6,5,7] => 1
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [1,2,4,3,6,5,7] => 0
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => 1
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [1,2,4,3,6,5,7] => 0
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => 0
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [1,3,2,4,6,5,7] => 0
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 0
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 0
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 3
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [1,2,5,4,3,6,7] => 1
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [1,2,5,4,3,6,7] => 1
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [1,2,5,4,3,6,7] => 1
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [1,3,2,5,4,6,7] => 0
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [1,3,2,5,4,6,7] => 0
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [1,2,3,5,4,6,7] => 0
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [1,2,5,4,3,6,7] => 1
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [1,2,5,4,3,6,7] => 1
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [1,3,2,5,4,6,7] => 0
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [1,2,3,5,4,6,7] => 0
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 1
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [1,2,3,5,4,6,7] => 0
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [1,3,2,5,4,6,7] => 0
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => 0
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 0
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 2
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [1,4,3,2,5,6,7] => 1
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [1,4,3,2,5,6,7] => 1
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [1,2,4,3,5,6,7] => 0
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => 1
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [1,2,4,3,5,6,7] => 0
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 0
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 1
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 0
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 6
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [2,1,4,3,6,5,8,7] => 0
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => [2,1,4,3,6,5,8,7] => 0
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => [2,1,4,3,6,5,8,7] => 0
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => [2,1,4,3,6,5,8,7] => 0
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => [2,1,4,3,6,5,8,7] => 0
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,8,7] => 0
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 5
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 4
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => [2,1,4,3,6,5,8,7] => 0
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => [2,1,4,3,6,5,8,7] => 0
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => [2,1,3,4,5,6,8,7] => 0
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 4
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => [1,2,3,4,5,6,8,7] => 0
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 4
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => [4,3,2,1,6,5,8,7] => 2
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => [2,1,4,3,8,7,6,5] => 2
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => [2,1,4,3,6,5,8,7] => 0
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 2
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [2,1,4,3,6,5,8,7] => 0
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 4
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6] => 2
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 4
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [2,1,4,3,6,5,8,7] => 0
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [2,1,4,3,6,5,8,7] => 0
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => 2
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [2,1,4,3,6,5,8,7] => 0
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 2
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [2,1,4,3,6,5,8,7] => 0
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 0
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => 0
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 5
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => 2
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => 0
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => 0
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 2
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
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Description
The number of double descents of a permutation.
A double descent of a permutation $\pi$ is a position $i$ such that $\pi(i) > \pi(i+1) > \pi(i+2)$.
Map
Inverse fireworks map
Description
Sends a permutation to an inverse fireworks permutation.
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..
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.