Identifier
Values
[[]] => [.,.] => [1] => [1] => 1
[[],[]] => [.,[.,.]] => [2,1] => [1,2] => 2
[[[]]] => [[.,.],.] => [1,2] => [2,1] => 2
[[],[],[]] => [.,[.,[.,.]]] => [3,2,1] => [1,2,3] => 3
[[],[[]]] => [.,[[.,.],.]] => [2,3,1] => [3,1,2] => 3
[[[]],[]] => [[.,.],[.,.]] => [3,1,2] => [1,3,2] => 3
[[[],[]]] => [[.,[.,.]],.] => [2,1,3] => [3,2,1] => 2
[[[[]]]] => [[[.,.],.],.] => [1,2,3] => [2,3,1] => 3
[[],[],[],[]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,2,3,4] => 4
[[],[],[[]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => [4,1,2,3] => 4
[[],[[]],[]] => [.,[[.,.],[.,.]]] => [4,2,3,1] => [1,4,2,3] => 4
[[],[[],[]]] => [.,[[.,[.,.]],.]] => [3,2,4,1] => [4,3,1,2] => 3
[[],[[[]]]] => [.,[[[.,.],.],.]] => [2,3,4,1] => [3,4,1,2] => 4
[[[]],[],[]] => [[.,.],[.,[.,.]]] => [4,3,1,2] => [1,2,4,3] => 4
[[[]],[[]]] => [[.,.],[[.,.],.]] => [3,4,1,2] => [4,1,3,2] => 3
[[[],[]],[]] => [[.,[.,.]],[.,.]] => [4,2,1,3] => [1,4,3,2] => 3
[[[[]]],[]] => [[[.,.],.],[.,.]] => [4,1,2,3] => [1,3,4,2] => 4
[[[],[],[]]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => [4,3,2,1] => 2
[[[],[[]]]] => [[.,[[.,.],.]],.] => [2,3,1,4] => [3,4,2,1] => 3
[[[[]],[]]] => [[[.,.],[.,.]],.] => [3,1,2,4] => [4,2,3,1] => 2
[[[[],[]]]] => [[[.,[.,.]],.],.] => [2,1,3,4] => [3,2,4,1] => 3
[[[[[]]]]] => [[[[.,.],.],.],.] => [1,2,3,4] => [2,3,4,1] => 4
[[],[],[],[],[]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,2,3,4,5] => 5
[[],[],[],[[]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [5,1,2,3,4] => 5
[[],[],[[]],[]] => [.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [1,5,2,3,4] => 5
[[],[],[[],[]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [5,4,1,2,3] => 4
[[],[],[[[]]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [4,5,1,2,3] => 5
[[],[[]],[],[]] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [1,2,5,3,4] => 5
[[],[[]],[[]]] => [.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [5,1,4,2,3] => 4
[[],[[],[]],[]] => [.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [1,5,4,2,3] => 4
[[],[[[]]],[]] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [1,4,5,2,3] => 5
[[],[[],[],[]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [5,4,3,1,2] => 3
[[],[[],[[]]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [4,5,3,1,2] => 4
[[],[[[]],[]]] => [.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [5,3,4,1,2] => 3
[[],[[[],[]]]] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [4,3,5,1,2] => 4
[[],[[[[]]]]] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [3,4,5,1,2] => 5
[[[]],[],[],[]] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [1,2,3,5,4] => 5
[[[]],[],[[]]] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [5,1,2,4,3] => 4
[[[]],[[]],[]] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [1,5,2,4,3] => 4
[[[]],[[],[]]] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [5,4,1,3,2] => 3
[[[]],[[[]]]] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [4,5,1,3,2] => 4
[[[],[]],[],[]] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [1,2,5,4,3] => 4
[[[[]]],[],[]] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [1,2,4,5,3] => 5
[[[],[]],[[]]] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [5,1,4,3,2] => 3
[[[[]]],[[]]] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [5,1,3,4,2] => 3
[[[],[],[]],[]] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [1,5,4,3,2] => 3
[[[],[[]]],[]] => [[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [1,4,5,3,2] => 4
[[[[]],[]],[]] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [1,5,3,4,2] => 3
[[[[],[]]],[]] => [[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [1,4,3,5,2] => 4
[[[[[]]]],[]] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,3,4,5,2] => 5
[[[],[],[],[]]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [5,4,3,2,1] => 2
[[[],[],[[]]]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [4,5,3,2,1] => 3
[[[],[[]],[]]] => [[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [5,3,4,2,1] => 2
[[[],[[],[]]]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [4,3,5,2,1] => 3
[[[],[[[]]]]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [3,4,5,2,1] => 4
[[[[]],[],[]]] => [[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [5,4,2,3,1] => 2
[[[[]],[[]]]] => [[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [4,5,2,3,1] => 3
[[[[],[]],[]]] => [[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [5,3,2,4,1] => 2
[[[[[]]],[]]] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [5,2,3,4,1] => 2
[[[[],[],[]]]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [4,3,2,5,1] => 3
[[[[],[[]]]]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [3,4,2,5,1] => 4
[[[[[]],[]]]] => [[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [4,2,3,5,1] => 3
[[[[[],[]]]]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [3,2,4,5,1] => 4
[[[[[[]]]]]] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [2,3,4,5,1] => 5
[[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => 6
[[],[],[],[],[[]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [6,1,2,3,4,5] => 6
[[],[],[],[[]],[]] => [.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [1,6,2,3,4,5] => 6
[[],[],[],[[],[]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [6,5,1,2,3,4] => 5
[[],[],[],[[[]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [5,6,1,2,3,4] => 6
[[],[],[[]],[],[]] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [1,2,6,3,4,5] => 6
[[],[],[[]],[[]]] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [6,1,5,2,3,4] => 5
[[],[],[[],[]],[]] => [.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [1,6,5,2,3,4] => 5
[[],[],[[[]]],[]] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [1,5,6,2,3,4] => 6
[[],[],[[],[],[]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [6,5,4,1,2,3] => 4
[[],[],[[],[[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [5,6,4,1,2,3] => 5
[[],[],[[[]],[]]] => [.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [6,4,5,1,2,3] => 4
[[],[],[[[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [5,4,6,1,2,3] => 5
[[],[],[[[[]]]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [4,5,6,1,2,3] => 6
[[],[[]],[],[],[]] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [1,2,3,6,4,5] => 6
[[],[[]],[],[[]]] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [6,1,2,5,3,4] => 5
[[],[[]],[[]],[]] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [1,6,2,5,3,4] => 5
[[],[[]],[[],[]]] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [6,5,1,4,2,3] => 4
[[],[[]],[[[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [5,6,1,4,2,3] => 5
[[],[[],[]],[],[]] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [1,2,6,5,3,4] => 5
[[],[[[]]],[],[]] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [1,2,5,6,3,4] => 6
[[],[[],[]],[[]]] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [6,1,5,4,2,3] => 4
[[],[[[]]],[[]]] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [6,1,4,5,2,3] => 4
[[],[[],[],[]],[]] => [.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [1,6,5,4,2,3] => 4
[[],[[],[[]]],[]] => [.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [1,5,6,4,2,3] => 5
[[],[[[]],[]],[]] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [1,6,4,5,2,3] => 4
[[],[[[],[]]],[]] => [.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [1,5,4,6,2,3] => 5
[[],[[[[]]]],[]] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [1,4,5,6,2,3] => 6
[[],[[],[],[],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [6,5,4,3,1,2] => 3
[[],[[],[],[[]]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [5,6,4,3,1,2] => 4
[[],[[],[[]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [6,4,5,3,1,2] => 3
[[],[[],[[],[]]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [5,4,6,3,1,2] => 4
[[],[[],[[[]]]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [4,5,6,3,1,2] => 5
[[],[[[]],[],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [6,5,3,4,1,2] => 3
[[],[[[]],[[]]]] => [.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [5,6,3,4,1,2] => 4
[[],[[[],[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [6,4,3,5,1,2] => 3
[[],[[[[]]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [6,3,4,5,1,2] => 3
>>> Load all 387 entries. <<<
[[],[[[],[],[]]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [5,4,3,6,1,2] => 4
[[],[[[],[[]]]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [4,5,3,6,1,2] => 5
[[],[[[[]],[]]]] => [.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [5,3,4,6,1,2] => 4
[[],[[[[],[]]]]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [4,3,5,6,1,2] => 5
[[],[[[[[]]]]]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[[[]],[],[],[],[]] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [1,2,3,4,6,5] => 6
[[[]],[],[],[[]]] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [6,1,2,3,5,4] => 5
[[[]],[],[[]],[]] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [1,6,2,3,5,4] => 5
[[[]],[],[[],[]]] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [6,5,1,2,4,3] => 4
[[[]],[],[[[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [5,6,1,2,4,3] => 5
[[[]],[[]],[],[]] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [1,2,6,3,5,4] => 5
[[[]],[[]],[[]]] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [6,1,5,2,4,3] => 4
[[[]],[[],[]],[]] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [1,6,5,2,4,3] => 4
[[[]],[[[]]],[]] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [1,5,6,2,4,3] => 5
[[[]],[[],[],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [6,5,4,1,3,2] => 3
[[[]],[[],[[]]]] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [5,6,4,1,3,2] => 4
[[[]],[[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [6,4,5,1,3,2] => 3
[[[]],[[[],[]]]] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [5,4,6,1,3,2] => 4
[[[]],[[[[]]]]] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [4,5,6,1,3,2] => 5
[[[],[]],[],[],[]] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [1,2,3,6,5,4] => 5
[[[[]]],[],[],[]] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [1,2,3,5,6,4] => 6
[[[],[]],[],[[]]] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [6,1,2,5,4,3] => 4
[[[[]]],[],[[]]] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [6,1,2,4,5,3] => 4
[[[],[]],[[]],[]] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [1,6,2,5,4,3] => 4
[[[[]]],[[]],[]] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [1,6,2,4,5,3] => 4
[[[],[]],[[],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [6,5,1,4,3,2] => 3
[[[],[]],[[[]]]] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [5,6,1,4,3,2] => 4
[[[[]]],[[],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [6,5,1,3,4,2] => 3
[[[[]]],[[[]]]] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [5,6,1,3,4,2] => 4
[[[],[],[]],[],[]] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [1,2,6,5,4,3] => 4
[[[],[[]]],[],[]] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [1,2,5,6,4,3] => 5
[[[[]],[]],[],[]] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [1,2,6,4,5,3] => 4
[[[[],[]]],[],[]] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [1,2,5,4,6,3] => 5
[[[[[]]]],[],[]] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [1,2,4,5,6,3] => 6
[[[],[],[]],[[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [6,1,5,4,3,2] => 3
[[[],[[]]],[[]]] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [6,1,4,5,3,2] => 3
[[[[]],[]],[[]]] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [6,1,5,3,4,2] => 3
[[[[],[]]],[[]]] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [6,1,4,3,5,2] => 3
[[[[[]]]],[[]]] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [6,1,3,4,5,2] => 3
[[[],[],[],[]],[]] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [1,6,5,4,3,2] => 3
[[[],[],[[]]],[]] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [1,5,6,4,3,2] => 4
[[[],[[]],[]],[]] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [1,6,4,5,3,2] => 3
[[[],[[],[]]],[]] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [1,5,4,6,3,2] => 4
[[[],[[[]]]],[]] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [1,4,5,6,3,2] => 5
[[[[]],[],[]],[]] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [1,6,5,3,4,2] => 3
[[[[]],[[]]],[]] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [1,5,6,3,4,2] => 4
[[[[],[]],[]],[]] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [1,6,4,3,5,2] => 3
[[[[[]]],[]],[]] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [1,6,3,4,5,2] => 3
[[[[],[],[]]],[]] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [1,5,4,3,6,2] => 4
[[[[],[[]]]],[]] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [1,4,5,3,6,2] => 5
[[[[[]],[]]],[]] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [1,5,3,4,6,2] => 4
[[[[[],[]]]],[]] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [1,4,3,5,6,2] => 5
[[[[[[]]]]],[]] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,3,4,5,6,2] => 6
[[[],[],[],[],[]]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => 2
[[[],[],[],[[]]]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [5,6,4,3,2,1] => 3
[[[],[],[[]],[]]] => [[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [6,4,5,3,2,1] => 2
[[[],[],[[],[]]]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [5,4,6,3,2,1] => 3
[[[],[],[[[]]]]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [4,5,6,3,2,1] => 4
[[[],[[]],[],[]]] => [[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [6,5,3,4,2,1] => 2
[[[],[[]],[[]]]] => [[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [5,6,3,4,2,1] => 3
[[[],[[],[]],[]]] => [[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [6,4,3,5,2,1] => 2
[[[],[[[]]],[]]] => [[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [6,3,4,5,2,1] => 2
[[[],[[],[],[]]]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [5,4,3,6,2,1] => 3
[[[],[[],[[]]]]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [4,5,3,6,2,1] => 4
[[[],[[[]],[]]]] => [[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [5,3,4,6,2,1] => 3
[[[],[[[],[]]]]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [4,3,5,6,2,1] => 4
[[[],[[[[]]]]]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[[[[]],[],[],[]]] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [6,5,4,2,3,1] => 2
[[[[]],[],[[]]]] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [5,6,4,2,3,1] => 3
[[[[]],[[]],[]]] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [6,4,5,2,3,1] => 2
[[[[]],[[],[]]]] => [[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [5,4,6,2,3,1] => 3
[[[[]],[[[]]]]] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [4,5,6,2,3,1] => 4
[[[[],[]],[],[]]] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [6,5,3,2,4,1] => 2
[[[[[]]],[],[]]] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [6,5,2,3,4,1] => 2
[[[[],[]],[[]]]] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [5,6,3,2,4,1] => 3
[[[[[]]],[[]]]] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [5,6,2,3,4,1] => 3
[[[[],[],[]],[]]] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [6,4,3,2,5,1] => 2
[[[[],[[]]],[]]] => [[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [6,3,4,2,5,1] => 2
[[[[[]],[]],[]]] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [6,4,2,3,5,1] => 2
[[[[[],[]]],[]]] => [[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [6,3,2,4,5,1] => 2
[[[[[[]]]],[]]] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [6,2,3,4,5,1] => 2
[[[[],[],[],[]]]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [5,4,3,2,6,1] => 3
[[[[],[],[[]]]]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [4,5,3,2,6,1] => 4
[[[[],[[]],[]]]] => [[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [5,3,4,2,6,1] => 3
[[[[],[[],[]]]]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [4,3,5,2,6,1] => 4
[[[[],[[[]]]]]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [3,4,5,2,6,1] => 5
[[[[[]],[],[]]]] => [[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [5,4,2,3,6,1] => 3
[[[[[]],[[]]]]] => [[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [4,5,2,3,6,1] => 4
[[[[[],[]],[]]]] => [[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [5,3,2,4,6,1] => 3
[[[[[[]]],[]]]] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [5,2,3,4,6,1] => 3
[[[[[],[],[]]]]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [4,3,2,5,6,1] => 4
[[[[[],[[]]]]]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [3,4,2,5,6,1] => 5
[[[[[[]],[]]]]] => [[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [4,2,3,5,6,1] => 4
[[[[[[],[]]]]]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [3,2,4,5,6,1] => 5
[[[[[[[]]]]]]] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 6
[[],[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 7
[[],[],[],[],[],[[]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [7,1,2,3,4,5,6] => 7
[[],[],[],[],[[]],[]] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [1,7,2,3,4,5,6] => 7
[[],[],[],[],[[],[]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [7,6,1,2,3,4,5] => 6
[[],[],[],[],[[[]]]] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [6,7,1,2,3,4,5] => 7
[[],[],[],[[]],[],[]] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [1,2,7,3,4,5,6] => 7
[[],[],[],[[[]]],[]] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [1,6,7,2,3,4,5] => 7
[[],[],[],[[],[],[]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [7,6,5,1,2,3,4] => 5
[[],[],[],[[[]],[]]] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [7,5,6,1,2,3,4] => 5
[[],[],[],[[[[]]]]] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [5,6,7,1,2,3,4] => 7
[[],[],[[]],[],[],[]] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [1,2,3,7,4,5,6] => 7
[[],[],[[],[]],[],[]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [1,2,7,6,3,4,5] => 6
[[],[],[[[]]],[],[]] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [1,2,6,7,3,4,5] => 7
[[],[],[[[[]]]],[]] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [1,5,6,7,2,3,4] => 7
[[],[],[[],[],[],[]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [7,6,5,4,1,2,3] => 4
[[],[],[[[]],[],[]]] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [7,6,4,5,1,2,3] => 4
[[],[],[[[]],[[]]]] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [6,7,4,5,1,2,3] => 5
[[],[],[[[[]]],[]]] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [7,4,5,6,1,2,3] => 4
[[],[],[[[[]],[]]]] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [6,4,5,7,1,2,3] => 5
[[],[],[[[[],[]]]]] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [5,4,6,7,1,2,3] => 6
[[],[[]],[],[],[],[]] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [1,2,3,4,7,5,6] => 7
[[],[[]],[[]],[],[]] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,2,7,3,6,4,5] => 6
[[],[[],[]],[],[],[]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [1,2,3,7,6,4,5] => 6
[[],[[[]]],[],[],[]] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [1,2,3,6,7,4,5] => 7
[[],[[],[],[]],[],[]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [1,2,7,6,5,3,4] => 5
[[],[[],[[]]],[],[]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [1,2,6,7,5,3,4] => 6
[[],[[[]],[]],[],[]] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [1,2,7,5,6,3,4] => 5
[[],[[[],[]]],[],[]] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [1,2,6,5,7,3,4] => 6
[[],[[[[]]]],[],[]] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [1,2,5,6,7,3,4] => 7
[[],[[[[[]]]]],[]] => [.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [1,4,5,6,7,2,3] => 7
[[],[[],[],[],[],[]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [7,6,5,4,3,1,2] => 3
[[],[[[]],[],[],[]]] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [7,6,5,3,4,1,2] => 3
[[],[[[]],[[]],[]]] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [7,5,6,3,4,1,2] => 3
[[],[[[]],[[],[]]]] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [6,5,7,3,4,1,2] => 4
[[],[[[[[[]]]]]]] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [3,4,5,6,7,1,2] => 7
[[[]],[],[],[],[],[]] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [1,2,3,4,5,7,6] => 7
[[[]],[],[[]],[],[]] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,2,7,3,4,6,5] => 6
[[[]],[[]],[],[],[]] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,2,3,7,4,6,5] => 6
[[[]],[[],[]],[],[]] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [1,2,7,6,3,5,4] => 5
[[[]],[[[]]],[],[]] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [1,2,6,7,3,5,4] => 6
[[[],[]],[],[],[],[]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [1,2,3,4,7,6,5] => 6
[[[[]]],[],[],[],[]] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [1,2,3,4,6,7,5] => 7
[[[],[]],[[]],[],[]] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [1,2,7,3,6,5,4] => 5
[[[[]]],[[]],[],[]] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [1,2,7,3,5,6,4] => 5
[[[],[],[]],[],[],[]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [1,2,3,7,6,5,4] => 5
[[[],[[]]],[],[],[]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [1,2,3,6,7,5,4] => 6
[[[[]],[]],[],[],[]] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [1,2,3,7,5,6,4] => 5
[[[[],[]]],[],[],[]] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [1,2,3,6,5,7,4] => 6
[[[[[]]]],[],[],[]] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [1,2,3,5,6,7,4] => 7
[[[],[],[],[]],[],[]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [1,2,7,6,5,4,3] => 4
[[[],[],[[]]],[],[]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [1,2,6,7,5,4,3] => 5
[[[],[[]],[]],[],[]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [1,2,7,5,6,4,3] => 4
[[[],[[],[]]],[],[]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [1,2,6,5,7,4,3] => 5
[[[],[[[]]]],[],[]] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [1,2,5,6,7,4,3] => 6
[[[[]],[],[]],[],[]] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [1,2,7,6,4,5,3] => 4
[[[[]],[[]]],[],[]] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [1,2,6,7,4,5,3] => 5
[[[[],[]],[]],[],[]] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [1,2,7,5,4,6,3] => 4
[[[[[]]],[]],[],[]] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [1,2,7,4,5,6,3] => 4
[[[[],[],[]]],[],[]] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [1,2,6,5,4,7,3] => 5
[[[[],[[]]]],[],[]] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [1,2,5,6,4,7,3] => 6
[[[[[]],[]]],[],[]] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [1,2,6,4,5,7,3] => 5
[[[[[],[]]]],[],[]] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [1,2,5,4,6,7,3] => 6
[[[[[[]]]]],[],[]] => [[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [1,2,4,5,6,7,3] => 7
[[[],[],[],[],[]],[]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [1,7,6,5,4,3,2] => 3
[[[],[],[],[[]]],[]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [1,6,7,5,4,3,2] => 4
[[[],[],[[],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [1,6,5,7,4,3,2] => 4
[[[],[],[[[]]]],[]] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [1,5,6,7,4,3,2] => 5
[[[],[[]],[],[]],[]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [1,7,6,4,5,3,2] => 3
[[[],[[],[]],[]],[]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [1,7,5,4,6,3,2] => 3
[[[],[[[]]],[]],[]] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [1,7,4,5,6,3,2] => 3
[[[],[[],[],[]]],[]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [1,6,5,4,7,3,2] => 4
[[[],[[],[[]]]],[]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [1,5,6,4,7,3,2] => 5
[[[],[[[[]]]]],[]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [1,4,5,6,7,3,2] => 6
[[[[],[],[]],[]],[]] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [1,7,5,4,3,6,2] => 3
[[[[],[[]]],[]],[]] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [1,7,4,5,3,6,2] => 3
[[[[],[],[],[]]],[]] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [1,6,5,4,3,7,2] => 4
[[[[],[[[]]]]],[]] => [[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [1,4,5,6,3,7,2] => 6
[[[[[],[[]]]]],[]] => [[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [1,4,5,3,6,7,2] => 6
[[[[[[],[]]]]],[]] => [[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [1,4,3,5,6,7,2] => 6
[[[[[[[]]]]]],[]] => [[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [1,3,4,5,6,7,2] => 7
[[[],[],[],[],[],[]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => 2
[[[[],[[[[]]]]]]] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [3,4,5,6,2,7,1] => 6
[[[[[[[]]]],[]]]] => [[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [6,2,3,4,5,7,1] => 3
[[[[[],[[],[]]]]]] => [[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [4,3,5,2,6,7,1] => 5
[[[[[],[[[]]]]]]] => [[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [3,4,5,2,6,7,1] => 6
[[[[[[]],[[]]]]]] => [[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [4,5,2,3,6,7,1] => 5
[[[[[[],[]],[]]]]] => [[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [5,3,2,4,6,7,1] => 4
[[[[[[[]]],[]]]]] => [[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [5,2,3,4,6,7,1] => 4
[[[[[[],[],[]]]]]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [4,3,2,5,6,7,1] => 5
[[[[[[],[[]]]]]]] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [3,4,2,5,6,7,1] => 6
[[[[[[[]],[]]]]]] => [[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [4,2,3,5,6,7,1] => 5
[[[[[[[],[]]]]]]] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [3,2,4,5,6,7,1] => 6
[[[[[[[[]]]]]]]] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => 7
[[],[],[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 8
[[],[],[],[],[],[],[[]]] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [8,1,2,3,4,5,6,7] => 8
[[],[],[],[],[],[[]],[]] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [8,6,7,5,4,3,2,1] => [1,8,2,3,4,5,6,7] => 8
[[],[],[],[],[],[[],[]]] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [8,7,1,2,3,4,5,6] => 7
[[],[],[],[],[],[[[]]]] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [7,8,1,2,3,4,5,6] => 8
[[],[],[],[],[[[]]],[]] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [8,5,6,7,4,3,2,1] => [1,7,8,2,3,4,5,6] => 8
[[],[],[],[],[[],[],[]]] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [8,7,6,1,2,3,4,5] => 6
[[],[],[],[],[[[]],[]]] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => [8,6,7,1,2,3,4,5] => 6
[[],[],[],[],[[[[]]]]] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [6,7,8,1,2,3,4,5] => 8
[[],[],[],[[]],[],[],[]] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [1,2,3,8,4,5,6,7] => 8
[[],[],[],[[]],[[]],[]] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [1,8,2,7,3,4,5,6] => 7
[[],[],[],[[[[]]]],[]] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [8,4,5,6,7,3,2,1] => [1,6,7,8,2,3,4,5] => 8
[[],[],[],[[],[],[],[]]] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [8,7,6,5,1,2,3,4] => 5
[[],[],[],[[[]],[],[]]] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => [8,7,5,6,1,2,3,4] => 5
[[],[],[],[[[]],[[]]]] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [6,7,4,5,8,3,2,1] => [7,8,5,6,1,2,3,4] => 6
[[],[],[],[[[[]]],[]]] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [8,5,6,7,1,2,3,4] => 5
[[],[],[],[[[[[]]]]]] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [5,6,7,8,1,2,3,4] => 8
[[],[],[[],[]],[],[[]]] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [7,8,6,4,3,5,2,1] => [8,1,2,7,6,3,4,5] => 6
[[],[],[[],[]],[[[]]]] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [6,7,8,4,3,5,2,1] => [7,8,1,6,5,2,3,4] => 6
[[],[],[[],[],[]],[],[]] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => [1,2,8,7,6,3,4,5] => 6
[[],[],[[[],[]]],[],[]] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [8,7,4,3,5,6,2,1] => [1,2,7,6,8,3,4,5] => 7
[[],[],[[],[],[],[],[]]] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [8,7,6,5,4,1,2,3] => 4
[[],[],[[],[],[[[]]]]] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => [6,7,8,5,4,1,2,3] => 6
[[],[],[[],[[[]]],[]]] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [7,4,5,6,3,8,2,1] => [8,5,6,7,4,1,2,3] => 4
[[],[],[[[]],[],[],[]]] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => [8,7,6,4,5,1,2,3] => 4
[[],[],[[[[]]],[],[]]] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [8,7,4,5,6,1,2,3] => 4
[[],[[]],[],[],[],[],[]] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [1,2,3,4,5,8,6,7] => 8
[[],[[]],[],[],[[]],[]] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,8,2,3,4,7,5,6] => 7
[[],[[]],[[]],[],[],[]] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [1,2,3,8,4,7,5,6] => 7
[[],[[]],[[]],[[]],[]] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,8,2,7,3,6,4,5] => 6
[[],[[]],[[],[],[],[]]] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,2,3,1] => [8,7,6,5,1,4,2,3] => 4
[[],[[],[],[],[]],[[]]] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [7,8,5,4,3,2,6,1] => [8,1,7,6,5,4,2,3] => 4
[[],[[],[],[],[],[]],[]] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [8,6,5,4,3,2,7,1] => [1,8,7,6,5,4,2,3] => 4
[[],[[],[],[[],[]]],[]] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [8,5,4,6,3,2,7,1] => [1,7,6,8,5,4,2,3] => 5
[[],[[[],[],[],[]]],[]] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [8,5,4,3,2,6,7,1] => [1,7,6,5,4,8,2,3] => 5
[[],[[],[],[],[],[],[]]] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [8,7,6,5,4,3,1,2] => 3
[[],[[],[],[],[],[[]]]] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [7,8,6,5,4,3,1,2] => 4
[[],[[],[],[],[[]],[]]] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [7,5,6,4,3,2,8,1] => [8,6,7,5,4,3,1,2] => 3
[[],[[],[],[[]],[],[]]] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [7,6,4,5,3,2,8,1] => [8,7,5,6,4,3,1,2] => 3
[[],[[],[[]],[],[],[]]] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [7,6,5,3,4,2,8,1] => [8,7,6,4,5,3,1,2] => 3
[[],[[[]],[],[],[],[]]] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [8,7,6,5,3,4,1,2] => 3
[[],[[[]],[[]],[],[]]] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,2,3,8,1] => [8,7,5,6,3,4,1,2] => 3
[[],[[[]],[[]],[[]]]] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => [7,8,5,6,3,4,1,2] => 4
[[],[[[]],[[[[]]]]]] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => [5,6,7,8,3,4,1,2] => 6
[[],[[[[[]]]],[[]]]] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => [7,8,3,4,5,6,1,2] => 4
[[],[[[[[[[]]]]]]]] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [3,4,5,6,7,8,1,2] => 8
[[[]],[],[],[],[],[],[]] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,8,7] => 8
[[[]],[],[[]],[],[[]]] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [8,1,2,7,3,4,6,5] => 6
[[[]],[[],[],[]],[[]]] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => [8,1,7,6,5,2,4,3] => 4
[[[]],[[[],[]]],[[]]] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => [8,1,6,5,7,2,4,3] => 4
[[[],[]],[[]],[[],[]]] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [7,6,8,4,5,2,1,3] => [8,7,1,6,2,5,4,3] => 4
[[[[]]],[[]],[[[]]]] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [6,7,8,4,5,1,2,3] => [7,8,1,6,2,4,5,3] => 5
[[[[]],[]],[[],[],[]]] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,1,2,4] => [8,7,6,1,5,3,4,2] => 3
[[[[[[]]]]],[],[],[]] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [1,2,3,5,6,7,8,4] => 8
[[[],[[]],[]],[[],[]]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [7,6,8,4,2,3,1,5] => [8,7,1,6,4,5,3,2] => 3
[[[],[],[[[]]]],[],[]] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [8,7,3,4,5,2,1,6] => [1,2,6,7,8,5,4,3] => 6
[[[[[]]],[],[]],[],[]] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => [1,2,8,7,4,5,6,3] => 4
[[[],[],[],[[]]],[[]]] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [7,8,4,5,3,2,1,6] => [8,1,6,7,5,4,3,2] => 3
[[[],[],[],[],[],[]],[]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => [1,8,7,6,5,4,3,2] => 3
[[[],[],[],[],[[]]],[]] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [8,5,6,4,3,2,1,7] => [1,7,8,6,5,4,3,2] => 4
[[[],[],[],[[]],[]],[]] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [8,6,4,5,3,2,1,7] => [1,8,6,7,5,4,3,2] => 3
[[[],[],[],[[],[]]],[]] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [8,5,4,6,3,2,1,7] => [1,7,6,8,5,4,3,2] => 4
[[[],[],[],[[[]]]],[]] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => [1,6,7,8,5,4,3,2] => 5
[[[],[],[[]],[],[]],[]] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [8,6,5,3,4,2,1,7] => [1,8,7,5,6,4,3,2] => 3
[[[],[[]],[[]],[]],[]] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,2,3,1,7] => [1,8,6,7,4,5,3,2] => 3
[[[],[[],[]],[],[]],[]] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [8,6,5,3,2,4,1,7] => [1,8,7,5,4,6,3,2] => 3
[[[],[[[]]],[],[]],[]] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [8,6,5,2,3,4,1,7] => [1,8,7,4,5,6,3,2] => 3
[[[],[[],[],[]],[]],[]] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [8,6,4,3,2,5,1,7] => [1,8,6,5,4,7,3,2] => 3
[[[[[]]],[[[]]]],[]] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [8,4,5,6,1,2,3,7] => [1,6,7,8,3,4,5,2] => 5
[[[],[],[],[],[],[],[]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [8,7,6,5,4,3,2,1] => 2
[[[],[],[],[],[[],[]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [7,6,8,5,4,3,2,1] => 3
[[[],[],[],[[]],[[]]]] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [6,7,4,5,3,2,1,8] => [7,8,5,6,4,3,2,1] => 3
[[[],[],[[]],[],[[]]]] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [6,7,5,3,4,2,1,8] => [7,8,6,4,5,3,2,1] => 3
[[[],[],[[]],[[]],[]]] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => [8,6,7,4,5,3,2,1] => 2
[[[],[],[[],[],[],[]]]] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => [7,6,5,4,8,3,2,1] => 3
[[[],[],[[],[[],[]]]]] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => [6,5,7,4,8,3,2,1] => 4
[[[],[[]],[],[],[[]]]] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => [7,8,6,5,3,4,2,1] => 3
[[[],[[]],[],[[]],[]]] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,2,3,1,8] => [8,6,7,5,3,4,2,1] => 2
[[[],[[]],[[]],[],[]]] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => [8,7,5,6,3,4,2,1] => 2
[[[],[[[]]],[[[]]]]] => [[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => [6,7,8,3,4,5,2,1] => 4
[[[[]],[],[],[],[[]]]] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,3,1,2,8] => [7,8,6,5,4,2,3,1] => 3
[[[[]],[],[],[[]],[]]] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => [8,6,7,5,4,2,3,1] => 2
[[[[]],[],[[]],[],[]]] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,3,1,2,8] => [8,7,5,6,4,2,3,1] => 2
[[[[]],[[]],[],[],[]]] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [7,6,5,3,4,1,2,8] => [8,7,6,4,5,2,3,1] => 2
[[[[[]]],[],[[[]]]]] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => [6,7,8,5,2,3,4,1] => 4
[[[[],[]],[[],[]],[]]] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => [8,6,5,7,3,2,4,1] => 2
[[[[[]]],[[[]]],[]]] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => [8,5,6,7,2,3,4,1] => 2
[[[[],[],[],[],[],[]]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [7,6,5,4,3,2,8,1] => 3
[[[[],[],[],[[],[]]]]] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => [6,5,7,4,3,2,8,1] => 4
[[[[],[[],[],[],[]]]]] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [6,5,4,3,7,2,8,1] => 4
[[[[],[[],[[],[]]]]]] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [5,4,6,3,7,2,8,1] => 5
[[[[[[],[[[]]]]]]]] => [[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [3,4,5,2,6,7,8,1] => 7
[[[[[[[[]]],[]]]]]] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => [5,2,3,4,6,7,8,1] => 5
[[[[[[[],[],[]]]]]]] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [4,3,2,5,6,7,8,1] => 6
[[[[[[[],[[]]]]]]]] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [3,4,2,5,6,7,8,1] => 7
[[[[[[[[]],[]]]]]]] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => [4,2,3,5,6,7,8,1] => 6
[[[[[[[[],[]]]]]]]] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [3,2,4,5,6,7,8,1] => 7
[[[[[[[[[]]]]]]]]] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,1] => 8
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
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Description
The number of indices that are either left-to-right maxima or right-to-left minima.
The (bivariate) generating function for this statistic is (essentially) given in [1], the mid points of a $321$ pattern in the permutation are those elements which are neither left-to-right maxima nor a right-to-left minima, see St000371The number of mid points of decreasing subsequences of length 3 in a permutation. and St000372The number of mid points of increasing subsequences of length 3 in a permutation..
Map
Lehmer code rotation
Description
Sends a permutation $\pi$ to the unique permutation $\tau$ (of the same length) such that every entry in the Lehmer code of $\tau$ is cyclically one larger than the Lehmer code of $\pi$.
Map
to binary tree: right brother = right child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of an ordered tree $t$) obtained from $t$ by the following recursive rule:
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.
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.