Identifier
Values
[.,.] => [1] => 0
[.,[.,.]] => [2,1] => 0
[[.,.],.] => [1,2] => 1
[.,[.,[.,.]]] => [3,2,1] => 0
[.,[[.,.],.]] => [2,3,1] => 1
[[.,.],[.,.]] => [3,1,2] => 1
[[.,[.,.]],.] => [2,1,3] => 1
[[[.,.],.],.] => [1,2,3] => 2
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 0
[.,[.,[[.,.],.]]] => [3,4,2,1] => 1
[.,[[.,.],[.,.]]] => [4,2,3,1] => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => 1
[.,[[[.,.],.],.]] => [2,3,4,1] => 2
[[.,.],[.,[.,.]]] => [4,3,1,2] => 1
[[.,.],[[.,.],.]] => [3,4,1,2] => 2
[[.,[.,.]],[.,.]] => [4,2,1,3] => 1
[[[.,.],.],[.,.]] => [4,1,2,3] => 2
[[.,[.,[.,.]]],.] => [3,2,1,4] => 1
[[.,[[.,.],.]],.] => [2,3,1,4] => 2
[[[.,.],[.,.]],.] => [3,1,2,4] => 2
[[[.,[.,.]],.],.] => [2,1,3,4] => 2
[[[[.,.],.],.],.] => [1,2,3,4] => 3
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 0
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 1
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => 1
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 2
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => 1
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => 2
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => 1
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => 2
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 1
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 2
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => 2
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 2
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 3
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 1
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 2
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 2
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 2
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 3
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 1
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 2
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 2
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 3
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 1
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 2
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 2
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 2
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 3
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 2
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => 2
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 2
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 3
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => 2
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 3
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 2
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 3
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 2
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 3
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => 3
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 3
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 4
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 0
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 1
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => 1
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 1
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 2
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => 1
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => 2
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => 1
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 1
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 2
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => 2
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 2
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 3
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => 1
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => 2
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 2
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => 2
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 3
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 1
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 2
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 2
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 3
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 1
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 2
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 2
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 2
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 3
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 1
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 2
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => 2
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 2
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 3
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => 2
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => 3
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => 2
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => 3
>>> Load all 445 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 2
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 3
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => 3
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 3
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 4
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 1
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 2
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 2
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 2
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 3
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 2
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 3
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 2
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 3
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 2
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 3
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 3
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 3
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 4
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 1
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 2
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 2
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 2
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 3
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 2
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 3
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 3
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 3
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 4
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 1
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 2
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 2
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 3
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 2
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 3
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 2
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 3
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 3
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 4
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 1
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 2
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 2
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 2
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 3
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 2
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 3
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 2
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 3
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 2
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 3
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 3
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 3
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 4
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 1
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 2
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => 2
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 2
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 3
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => 2
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => 3
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => 2
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => 3
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 2
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 3
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => 3
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 3
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 4
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 2
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 3
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 3
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 3
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 4
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 2
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 3
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 3
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 4
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 2
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 3
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 3
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 3
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 4
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 2
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 3
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => 3
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 3
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 4
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => 3
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 4
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 3
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 4
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 3
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 4
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => 4
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 4
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 5
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 0
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 4
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => 4
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 3
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 4
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => 4
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => 3
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => 4
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 3
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 4
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => 4
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 4
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 5
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => 1
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => 2
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => 3
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => 3
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => 5
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => 2
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => 3
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => 4
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => 4
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => 4
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => 4
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => 3
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => 4
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => 5
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => 4
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => 4
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => 5
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => 4
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => 4
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => 3
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => 4
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => 4
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => 3
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => 4
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => 3
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => 4
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => 4
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => 4
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => 5
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 1
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 2
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 2
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 3
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => 2
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => 2
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => 3
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 2
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 3
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => 2
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => 3
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 2
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 5
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => 4
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => 5
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => 5
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => 5
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 2
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 5
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => 5
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 3
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 5
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => 5
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => 5
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 4
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 5
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => 5
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 5
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 6
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 0
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 1
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => 2
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => 2
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => 2
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 1
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 2
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => 2
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => 2
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => 2
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => 4
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => 2
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => 2
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => 2
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => 2
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => 2
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => 4
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => 4
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => 4
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 1
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 2
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 2
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 3
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 5
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => 5
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 4
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 5
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => 5
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 5
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 6
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => 1
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => 2
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => 2
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => 2
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => 2
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => 2
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => 3
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => 4
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => 5
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => 5
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => 6
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => 1
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => 2
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => 2
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => 4
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => 4
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => 3
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => 4
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => 4
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => 5
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => 5
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => 2
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => 4
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => 4
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => 4
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => 3
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => 4
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => 5
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => 5
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => 6
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => 1
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => 2
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => 4
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => 5
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => 6
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => 3
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => 4
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => 5
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => 6
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => 1
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => 2
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => 4
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => 2
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => 2
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => 3
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => 5
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => 5
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => 4
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => 5
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => 5
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => 5
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => 6
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 1
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 2
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 2
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 3
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => 2
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 2
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => 3
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => 2
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => 3
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => 2
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => 3
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => 3
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => 5
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 6
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => 6
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => 6
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => 6
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 2
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 6
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => 5
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => 6
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => 6
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 3
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 6
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => 6
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 4
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => 6
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 5
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 6
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 7
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 0
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 7
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 8
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 0
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 8
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 9
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 1
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => 5
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => 7
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => 8
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => 6
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 6
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => 9
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => 7
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => 6
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [9,2,3,1,4,5,6,7,8] => 6
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => 6
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 6
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 7
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 9
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => 7
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => 7
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => 7
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => 6
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => 8
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => 8
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => 8
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => 8
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => 1
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 2
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => 1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 1
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 2
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 2
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => 2
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 2
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 3
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 4
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 5
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 6
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 7
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 2
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 3
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 4
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 5
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 6
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 7
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 8
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 9
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 7
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 7
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 8
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => 7
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => 7
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => 8
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => 2
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => 7
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => 5
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => 4
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => 3
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => 6
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => 5
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => 4
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => 3
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => 7
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Description
The number of ascents of a permutation.
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the Sylvester class.