Identifier
Values
[.,.] => [1] => 0
[.,[.,.]] => [2,1] => 1
[[.,.],.] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => 3
[.,[[.,.],.]] => [2,3,1] => 2
[[.,.],[.,.]] => [3,1,2] => 2
[[.,[.,.]],.] => [2,1,3] => 1
[[[.,.],.],.] => [1,2,3] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 6
[.,[.,[[.,.],.]]] => [3,4,2,1] => 5
[.,[[.,.],[.,.]]] => [4,2,3,1] => 5
[.,[[.,[.,.]],.]] => [3,2,4,1] => 4
[.,[[[.,.],.],.]] => [2,3,4,1] => 3
[[.,.],[.,[.,.]]] => [4,3,1,2] => 5
[[.,.],[[.,.],.]] => [3,4,1,2] => 4
[[.,[.,.]],[.,.]] => [4,2,1,3] => 4
[[[.,.],.],[.,.]] => [4,1,2,3] => 3
[[.,[.,[.,.]]],.] => [3,2,1,4] => 3
[[.,[[.,.],.]],.] => [2,3,1,4] => 2
[[[.,.],[.,.]],.] => [3,1,2,4] => 2
[[[.,[.,.]],.],.] => [2,1,3,4] => 1
[[[[.,.],.],.],.] => [1,2,3,4] => 0
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 10
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 9
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => 9
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 8
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 7
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => 9
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => 8
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => 8
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => 7
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 7
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 6
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => 6
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 5
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 4
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 9
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 8
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 8
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 7
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 6
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 8
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 7
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 7
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 6
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 7
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 6
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 6
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 5
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 4
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 6
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 5
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => 5
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 4
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 3
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => 5
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 4
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 4
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 3
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 3
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 2
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => 2
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 15
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 14
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => 14
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 13
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 12
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => 14
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => 13
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => 13
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => 12
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 12
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 11
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => 11
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 10
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 9
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => 14
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => 13
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 13
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => 12
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 11
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 13
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 12
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 12
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 11
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 12
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 11
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 11
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 10
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 9
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 11
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 10
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => 10
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 9
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 8
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => 10
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => 9
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => 9
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => 8
>>> Load all 440 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 8
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 7
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => 7
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 6
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 5
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 14
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 13
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 13
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 12
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 11
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 13
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 12
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 12
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 11
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 11
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 10
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 10
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 9
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 8
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 13
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 12
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 12
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 11
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 10
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 12
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 11
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 11
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 10
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 9
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 12
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 11
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 11
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 10
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 11
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 10
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 10
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 9
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 9
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 8
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 11
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 10
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 10
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 9
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 8
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 10
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 9
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 9
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 8
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 8
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 7
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 7
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 6
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 5
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 10
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 9
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => 9
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 8
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 7
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => 9
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => 8
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => 8
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => 7
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 7
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 6
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => 6
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 5
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 4
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 9
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 8
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 8
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 7
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 6
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 8
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 7
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 7
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 6
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 7
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 6
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 6
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 5
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 4
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 6
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 5
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => 5
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 4
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 3
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => 5
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 4
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 4
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 3
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 3
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 2
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => 2
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 1
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 21
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 10
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => 10
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 10
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 9
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => 10
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => 10
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => 9
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 9
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 8
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => 8
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 7
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 6
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => 20
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => 19
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => 18
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => 10
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => 18
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => 17
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => 16
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => 15
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => 15
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => 14
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => 12
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => 11
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => 10
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => 10
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => 10
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => 10
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => 9
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => 10
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => 10
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => 9
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => 9
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => 8
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => 8
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => 7
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => 6
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 15
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 14
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 13
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 12
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => 14
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => 13
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => 12
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 12
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 11
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => 12
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => 11
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 11
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 5
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => 12
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => 9
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => 8
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => 5
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 10
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 4
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => 4
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 6
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 3
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => 4
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => 3
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 3
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 2
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => 2
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 1
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 0
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 28
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 26
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => 26
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => 26
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => 26
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 24
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 22
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => 26
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => 26
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => 26
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => 22
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => 26
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => 26
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => 26
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => 26
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => 24
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => 22
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => 22
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => 18
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 22
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 20
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 18
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 16
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 10
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => 10
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 10
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 9
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => 9
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 8
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 7
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => 27
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => 26
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => 26
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => 26
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => 26
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => 26
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => 25
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => 24
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => 20
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => 20
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => 12
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => 26
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => 24
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => 25
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => 22
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => 22
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => 24
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => 23
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => 22
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => 21
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => 22
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => 20
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => 20
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => 18
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => 22
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => 21
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => 20
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => 19
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => 16
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => 24
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => 22
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => 18
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => 17
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => 15
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => 20
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => 19
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => 13
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => 12
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => 22
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => 21
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => 19
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => 20
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => 18
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => 16
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => 10
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => 10
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => 10
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => 9
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => 9
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => 8
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => 7
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 21
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 20
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 19
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 18
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => 20
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 18
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => 19
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => 19
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => 18
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => 18
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => 19
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => 17
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => 15
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 6
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => 12
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => 10
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => 6
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 15
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 5
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => 12
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => 9
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => 5
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 10
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 4
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => 4
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 6
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => 4
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 3
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 1
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 0
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 36
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 8
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 0
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 45
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 9
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 0
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 28
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 36
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => 40
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => 8
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => 9
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => 9
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 9
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => 10
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => 10
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => 10
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [9,2,3,1,4,5,6,7,8] => 10
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => 10
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 10
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 10
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 10
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => 14
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => 18
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => 20
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => 15
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => 16
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => 21
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => 24
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => 25
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => 35
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 27
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => 44
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 45
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 35
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 26
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => 33
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 21
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 15
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 10
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 6
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 3
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 1
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 28
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 21
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 15
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 10
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 6
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 3
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 1
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 1
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 7
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 6
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 8
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => 6
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [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] => 42
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => 17
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => 21
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => 26
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => 30
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => 24
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => 30
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => 35
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => 39
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => 4
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Description
The number of inversions of a permutation.
This equals the minimal number of simple transpositions $(i,i+1)$ needed to write $\pi$. Thus, it is also the Coxeter length of $\pi$.
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.