Identifier
Values
[.,.] => [.,.] => [1] => 0
[.,[.,.]] => [.,[.,.]] => [2,1] => 1
[[.,.],.] => [[.,.],.] => [1,2] => 0
[.,[.,[.,.]]] => [.,[.,[.,.]]] => [3,2,1] => 3
[.,[[.,.],.]] => [.,[[.,.],.]] => [2,3,1] => 2
[[.,.],[.,.]] => [[.,[.,.]],.] => [2,1,3] => 1
[[.,[.,.]],.] => [[.,.],[.,.]] => [1,3,2] => 1
[[[.,.],.],.] => [[[.,.],.],.] => [1,2,3] => 0
[.,[.,[.,[.,.]]]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 6
[.,[.,[[.,.],.]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => 5
[.,[[.,.],[.,.]]] => [.,[[.,[.,.]],.]] => [3,2,4,1] => 4
[.,[[.,[.,.]],.]] => [.,[[.,.],[.,.]]] => [2,4,3,1] => 4
[.,[[[.,.],.],.]] => [.,[[[.,.],.],.]] => [2,3,4,1] => 3
[[.,.],[.,[.,.]]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 3
[[.,.],[[.,.],.]] => [[.,[[.,.],.]],.] => [2,3,1,4] => 2
[[.,[.,.]],[.,.]] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 2
[[[.,.],.],[.,.]] => [[[.,[.,.]],.],.] => [2,1,3,4] => 1
[[.,[.,[.,.]]],.] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 3
[[.,[[.,.],.]],.] => [[.,.],[[.,.],.]] => [1,3,4,2] => 2
[[[.,.],[.,.]],.] => [[[.,.],[.,.]],.] => [1,3,2,4] => 1
[[[.,[.,.]],.],.] => [[[.,.],.],[.,.]] => [1,2,4,3] => 1
[[[[.,.],.],.],.] => [[[[.,.],.],.],.] => [1,2,3,4] => 0
[.,[.,[.,[.,[.,.]]]]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 10
[.,[.,[.,[[.,.],.]]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 9
[.,[.,[[.,.],[.,.]]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 8
[.,[.,[[.,[.,.]],.]]] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 8
[.,[.,[[[.,.],.],.]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 7
[.,[[.,.],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 7
[.,[[.,.],[[.,.],.]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 6
[.,[[.,[.,.]],[.,.]]] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 6
[.,[[[.,.],.],[.,.]]] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 5
[.,[[.,[.,[.,.]]],.]] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 7
[.,[[.,[[.,.],.]],.]] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 6
[.,[[[.,.],[.,.]],.]] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 5
[.,[[[.,[.,.]],.],.]] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 5
[.,[[[[.,.],.],.],.]] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 4
[[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 6
[[.,.],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 5
[[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 4
[[.,.],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 4
[[.,.],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 3
[[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 4
[[.,[.,.]],[[.,.],.]] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 3
[[[.,.],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 3
[[[.,.],.],[[.,.],.]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 2
[[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 4
[[.,[[.,.],.]],[.,.]] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 3
[[[.,.],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 2
[[[.,[.,.]],.],[.,.]] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 2
[[[[.,.],.],.],[.,.]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1
[[.,[.,[.,[.,.]]]],.] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 6
[[.,[.,[[.,.],.]]],.] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 5
[[.,[[.,.],[.,.]]],.] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 4
[[.,[[.,[.,.]],.]],.] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 4
[[.,[[[.,.],.],.]],.] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 3
[[[.,.],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 3
[[[.,.],[[.,.],.]],.] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 2
[[[.,[.,.]],[.,.]],.] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 2
[[[[.,.],.],[.,.]],.] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 1
[[[.,[.,[.,.]]],.],.] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 3
[[[.,[[.,.],.]],.],.] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 2
[[[[.,.],[.,.]],.],.] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 1
[[[[.,[.,.]],.],.],.] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 1
[[[[[.,.],.],.],.],.] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 15
[.,[.,[.,[.,[[.,.],.]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 14
[.,[.,[.,[[.,.],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 13
[.,[.,[.,[[.,[.,.]],.]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 13
[.,[.,[.,[[[.,.],.],.]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 12
[.,[.,[[.,.],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 12
[.,[.,[[.,.],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 11
[.,[.,[[.,[.,.]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 11
[.,[.,[[[.,.],.],[.,.]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 10
[.,[.,[[.,[.,[.,.]]],.]]] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 12
[.,[.,[[.,[[.,.],.]],.]]] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 11
[.,[.,[[[.,.],[.,.]],.]]] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 10
[.,[.,[[[.,[.,.]],.],.]]] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 10
[.,[.,[[[[.,.],.],.],.]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 9
[.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 11
[.,[[.,.],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 10
[.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 9
[.,[[.,.],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 9
[.,[[.,.],[[[.,.],.],.]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 8
[.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 9
[.,[[.,[.,.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 8
[.,[[[.,.],.],[.,[.,.]]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 8
[.,[[[.,.],.],[[.,.],.]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 7
[.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 9
[.,[[.,[[.,.],.]],[.,.]]] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 8
[.,[[[.,.],[.,.]],[.,.]]] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 7
[.,[[[.,[.,.]],.],[.,.]]] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 7
[.,[[[[.,.],.],.],[.,.]]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 6
[.,[[.,[.,[.,[.,.]]]],.]] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 11
[.,[[.,[.,[[.,.],.]]],.]] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 10
[.,[[.,[[.,.],[.,.]]],.]] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 9
[.,[[.,[[.,[.,.]],.]],.]] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 9
[.,[[.,[[[.,.],.],.]],.]] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 8
[.,[[[.,.],[.,[.,.]]],.]] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 8
[.,[[[.,.],[[.,.],.]],.]] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 7
[.,[[[.,[.,.]],[.,.]],.]] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 7
[.,[[[[.,.],.],[.,.]],.]] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 6
>>> Load all 389 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 8
[.,[[[.,[[.,.],.]],.],.]] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 7
[.,[[[[.,.],[.,.]],.],.]] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 6
[.,[[[[.,[.,.]],.],.],.]] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 6
[.,[[[[[.,.],.],.],.],.]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 5
[[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 10
[[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 9
[[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 8
[[.,.],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 8
[[.,.],[.,[[[.,.],.],.]]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 7
[[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 7
[[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 6
[[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 6
[[.,.],[[[.,.],.],[.,.]]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 5
[[.,.],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 7
[[.,.],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 6
[[.,.],[[[.,.],[.,.]],.]] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 5
[[.,.],[[[.,[.,.]],.],.]] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 5
[[.,.],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 4
[[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 7
[[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => 6
[[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => 5
[[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => 5
[[.,[.,.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => 4
[[[.,.],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 6
[[[.,.],.],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 5
[[[.,.],.],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 4
[[[.,.],.],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 4
[[[.,.],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 3
[[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 6
[[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 5
[[.,[[.,.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 5
[[.,[[.,.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => 4
[[[.,.],[.,.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 4
[[[.,.],[.,.]],[[.,.],.]] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => 3
[[[.,[.,.]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 4
[[[.,[.,.]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => 3
[[[[.,.],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 3
[[[[.,.],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 2
[[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 7
[[.,[.,[[.,.],.]]],[.,.]] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 6
[[.,[[.,.],[.,.]]],[.,.]] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 5
[[.,[[.,[.,.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 5
[[.,[[[.,.],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => 4
[[[.,.],[.,[.,.]]],[.,.]] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 4
[[[.,.],[[.,.],.]],[.,.]] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 3
[[[.,[.,.]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 3
[[[[.,.],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 2
[[[.,[.,[.,.]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 4
[[[.,[[.,.],.]],.],[.,.]] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 3
[[[[.,.],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 2
[[[[.,[.,.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 2
[[[[[.,.],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 10
[[.,[.,[.,[[.,.],.]]]],.] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 9
[[.,[.,[[.,.],[.,.]]]],.] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 8
[[.,[.,[[.,[.,.]],.]]],.] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 8
[[.,[.,[[[.,.],.],.]]],.] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 7
[[.,[[.,.],[.,[.,.]]]],.] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 7
[[.,[[.,.],[[.,.],.]]],.] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 6
[[.,[[.,[.,.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 6
[[.,[[[.,.],.],[.,.]]],.] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 5
[[.,[[.,[.,[.,.]]],.]],.] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 7
[[.,[[.,[[.,.],.]],.]],.] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 6
[[.,[[[.,.],[.,.]],.]],.] => [[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => 5
[[.,[[[.,[.,.]],.],.]],.] => [[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => 5
[[.,[[[[.,.],.],.],.]],.] => [[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => 4
[[[.,.],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 6
[[[.,.],[.,[[.,.],.]]],.] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 5
[[[.,.],[[.,.],[.,.]]],.] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 4
[[[.,.],[[.,[.,.]],.]],.] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 4
[[[.,.],[[[.,.],.],.]],.] => [[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => 3
[[[.,[.,.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 4
[[[.,[.,.]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 3
[[[[.,.],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 3
[[[[.,.],.],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 2
[[[.,[.,[.,.]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 4
[[[.,[[.,.],.]],[.,.]],.] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 3
[[[[.,.],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 2
[[[[.,[.,.]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 2
[[[[[.,.],.],.],[.,.]],.] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 1
[[[.,[.,[.,[.,.]]]],.],.] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 6
[[[.,[.,[[.,.],.]]],.],.] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 5
[[[.,[[.,.],[.,.]]],.],.] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 4
[[[.,[[.,[.,.]],.]],.],.] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 4
[[[.,[[[.,.],.],.]],.],.] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 3
[[[[.,.],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 3
[[[[.,.],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 2
[[[[.,[.,.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 2
[[[[[.,.],.],[.,.]],.],.] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 1
[[[[.,[.,[.,.]]],.],.],.] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 3
[[[[.,[[.,.],.]],.],.],.] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 2
[[[[[.,.],[.,.]],.],.],.] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 1
[[[[[.,[.,.]],.],.],.],.] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 1
[[[[[[.,.],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 21
[.,[[.,.],[[[[.,.],.],.],.]]] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 10
[.,[[[.,.],.],[[.,.],[.,.]]]] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 10
[.,[[[.,.],.],[[[.,.],.],.]]] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 9
[.,[[[[.,.],.],.],[.,[.,.]]]] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 9
[.,[[[[.,.],.],.],[[.,.],.]]] => [.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 8
[.,[[[[[.,.],.],.],.],[.,.]]] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 7
[.,[[[[[[.,.],.],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 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
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => 13
[[.,.],[.,[.,[[[.,.],.],.]]]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 12
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 12
[[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 11
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => 11
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => 12
[[.,.],[.,[[.,[[.,.],.]],.]]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => 11
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 11
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => 11
[[.,.],[[[[[.,.],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 5
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => 11
[[.,[.,.]],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => 5
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 10
[[[.,.],.],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 4
[[[.,[.,.]],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => 4
[[[[.,.],.],.],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 6
[[[[.,.],.],.],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 3
[[[[[.,.],.],.],.],[.,[.,.]]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 3
[[[[[.,.],.],.],.],[[.,.],.]] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 2
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => 11
[[[[[[.,.],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => 15
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => 14
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => 13
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => 13
[[.,[.,[.,[[[.,.],.],.]]]],.] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => 12
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => 12
[[.,[.,[[.,.],[[.,.],.]]]],.] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => 11
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => 11
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => 12
[[.,[.,[[.,[[.,.],.]],.]]],.] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => 11
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => 11
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 11
[[[[[[.,.],.],.],.],[.,.]],.] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 1
[[[[[[.,.],[.,.]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 1
[[[[[[.,[.,.]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 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
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => 24
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 24
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 22
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => 16
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => 20
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [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
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => 14
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => 12
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 10
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 10
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 9
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => 12
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => 12
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => 10
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 8
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => 20
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => 12
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 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
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => 19
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 18
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 18
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => 18
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => 13
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => 13
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => 9
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 6
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => 16
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => 10
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => 8
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => 6
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 15
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 5
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => 13
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => 9
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 10
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 4
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => 12
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => 10
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => 8
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => 8
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => 8
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => 8
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => 6
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => 8
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => 6
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => 6
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 6
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => 13
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => 9
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => 6
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => 4
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 3
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => 16
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => 10
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => 8
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => 8
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => 6
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => 6
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => 8
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => 6
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => 6
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => 4
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => 2
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 1
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => 21
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => 20
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => 19
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => 19
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => 18
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => 18
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => 18
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => 13
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => 13
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => 9
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => 12
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => 6
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => 4
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => 3
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => 2
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => 2
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => 1
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => 12
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => 2
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => 4
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => 2
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => 1
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => 1
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => 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
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 7
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 9
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 0
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => 28
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => 36
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => 5
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => 6
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 1
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 1
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 1
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 10
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 6
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 3
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 8
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 28
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => 27
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 27
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 36
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => 45
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,9,10,8,7,6,5,4,3,2] => 35
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,8,7,9,6,5,4,3,2] => 26
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 26
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 35
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 45
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 21
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => 29
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => 21
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => 21
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => 29
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => 1
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => 1
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 9
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 10
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 10
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 28
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 3
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 6
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 10
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 15
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 6
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 10
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 15
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 21
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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
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
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.