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] => 2
[[[.,.],.],.] => [1,2,3] => 3
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 0
[.,[.,[[.,.],.]]] => [3,4,2,1] => 1
[.,[[.,.],[.,.]]] => [4,2,3,1] => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => 2
[.,[[[.,.],.],.]] => [2,3,4,1] => 3
[[.,.],[.,[.,.]]] => [4,3,1,2] => 1
[[.,.],[[.,.],.]] => [3,4,1,2] => 2
[[.,[.,.]],[.,.]] => [4,2,1,3] => 2
[[[.,.],.],[.,.]] => [4,1,2,3] => 3
[[.,[.,[.,.]]],.] => [3,2,1,4] => 3
[[.,[[.,.],.]],.] => [2,3,1,4] => 4
[[[.,.],[.,.]],.] => [3,1,2,4] => 4
[[[.,[.,.]],.],.] => [2,1,3,4] => 5
[[[[.,.],.],.],.] => [1,2,3,4] => 6
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 0
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 1
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => 1
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 2
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 3
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => 1
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => 2
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => 2
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => 3
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 3
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 4
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => 4
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 5
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 6
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 1
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 2
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 2
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 3
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 4
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 2
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 3
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 3
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 4
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 3
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 4
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 4
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 5
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 6
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 4
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 5
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => 5
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 6
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 7
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => 5
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 6
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 6
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 7
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 7
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 8
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => 8
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 9
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 10
[.,[.,[.,[.,[.,[.,.]]]]]] => [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] => 2
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 3
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => 1
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => 2
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => 2
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => 3
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 3
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 4
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => 4
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 5
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 6
[.,[[.,.],[.,[.,[.,.]]]]] => [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] => 3
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 4
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 2
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 3
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 3
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 4
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 3
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 4
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 4
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 5
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 6
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 4
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 5
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => 5
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 6
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 7
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => 5
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => 6
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => 6
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => 7
>>> Load all 445 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 7
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 8
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => 8
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 9
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 10
[[.,.],[.,[.,[.,[.,.]]]]] => [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] => 3
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 4
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 2
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 3
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 3
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 4
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 4
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 5
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 5
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 6
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 7
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 3
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 3
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 4
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 5
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 3
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 4
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 4
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 5
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 6
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 3
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 4
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 4
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 5
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 4
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 5
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 5
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 6
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 6
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 7
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 4
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 5
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 5
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 6
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 7
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 5
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 6
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 6
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 7
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 7
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 8
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 8
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 9
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 10
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 5
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 6
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => 6
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 7
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 8
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => 6
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => 7
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => 7
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => 8
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 8
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 9
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => 9
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 10
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 11
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 6
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 7
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 7
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 8
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 9
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 7
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 8
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 8
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 9
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 8
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 9
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 9
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 10
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 11
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 9
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 10
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => 10
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 11
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 12
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => 10
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 11
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 11
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 12
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 12
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 13
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => 13
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 14
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 15
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 0
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 11
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => 11
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 11
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 12
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => 11
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => 11
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => 12
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 12
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 13
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => 13
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 14
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 15
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [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] => 4
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => 11
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => 3
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => 4
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => 5
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => 6
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => 7
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => 8
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => 6
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => 7
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => 9
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => 7
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => 10
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => 11
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => 11
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => 11
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => 11
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => 12
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => 11
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => 11
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => 12
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => 12
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => 13
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => 13
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => 14
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => 15
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 6
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 7
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 8
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 9
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => 7
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => 8
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => 9
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 9
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 10
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => 9
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => 10
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 10
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 16
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => 9
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => 12
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => 13
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => 16
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 11
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 17
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => 17
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 15
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 18
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => 17
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => 18
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 18
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 19
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => 19
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 20
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 21
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 0
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 2
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [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] => 4
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 6
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [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] => 6
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [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] => 4
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => 6
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => 6
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => 10
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 6
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 8
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 10
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 12
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 18
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => 18
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 18
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 19
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => 19
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 20
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 21
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [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] => 8
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => 8
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => 16
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => 2
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => 4
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => 3
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => 6
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => 6
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => 4
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => 5
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => 6
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => 7
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => 9
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => 6
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => 8
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => 8
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => 10
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => 6
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => 7
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => 8
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => 9
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => 12
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => 4
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => 6
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => 10
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => 11
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => 13
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => 8
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => 9
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => 15
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => 16
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => 6
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => 7
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => 9
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => 8
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => 10
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => 12
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => 18
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => 18
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => 18
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => 19
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => 19
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => 20
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => 21
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 7
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 8
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 9
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 10
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => 8
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 10
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => 9
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => 9
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => 10
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => 10
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => 9
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => 11
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => 13
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 22
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => 16
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => 18
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => 22
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 13
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 23
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => 16
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => 19
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => 23
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 18
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 24
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => 24
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 22
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => 24
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 25
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 27
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 28
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 0
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 28
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 36
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 0
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 36
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 45
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 8
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 9
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => 5
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => 28
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => 36
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => 27
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 27
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => 45
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => 35
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => 26
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [9,2,3,1,4,5,6,7,8] => 26
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => 26
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 26
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 35
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 45
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => 22
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => 18
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => 16
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => 21
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => 29
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => 24
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => 21
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => 20
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => 1
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 9
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => 1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 10
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 10
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 10
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => 3
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 15
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 21
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 26
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 30
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 33
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 35
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 17
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 24
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 30
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 35
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 39
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 42
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 44
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 54
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 29
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 30
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 37
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => 30
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => 29
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => 37
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => 3
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => 28
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => 15
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => 10
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => 6
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => 21
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => 15
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => 10
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => 6
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => 32
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Description
The number of non-inversions of a permutation.
For a permutation of $\{1,\ldots,n\}$, this is given by $\operatorname{noninv}(\pi) = \binom{n}{2}-\operatorname{inv}(\pi)$.
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.