Identifier
Values
[[]] => [.,.] => [1] => [1] => 1
[[],[]] => [[.,.],.] => [1,2] => [2,1] => 2
[[[]]] => [.,[.,.]] => [2,1] => [1,2] => 2
[[],[],[]] => [[[.,.],.],.] => [1,2,3] => [3,2,1] => 2
[[],[[]]] => [[.,.],[.,.]] => [1,3,2] => [2,3,1] => 3
[[[]],[]] => [[.,[.,.]],.] => [2,1,3] => [3,1,2] => 3
[[[],[]]] => [.,[[.,.],.]] => [2,3,1] => [1,3,2] => 3
[[[[]]]] => [.,[.,[.,.]]] => [3,2,1] => [1,2,3] => 3
[[],[],[],[]] => [[[[.,.],.],.],.] => [1,2,3,4] => [4,3,2,1] => 2
[[],[],[[]]] => [[[.,.],.],[.,.]] => [1,2,4,3] => [3,4,2,1] => 3
[[],[[]],[]] => [[[.,.],[.,.]],.] => [1,3,2,4] => [4,2,3,1] => 2
[[],[[],[]]] => [[.,.],[[.,.],.]] => [1,3,4,2] => [2,4,3,1] => 3
[[],[[[]]]] => [[.,.],[.,[.,.]]] => [1,4,3,2] => [2,3,4,1] => 4
[[[]],[],[]] => [[[.,[.,.]],.],.] => [2,1,3,4] => [4,3,1,2] => 3
[[[]],[[]]] => [[.,[.,.]],[.,.]] => [2,1,4,3] => [3,4,1,2] => 4
[[[],[]],[]] => [[.,[[.,.],.]],.] => [2,3,1,4] => [4,1,3,2] => 3
[[[[]]],[]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => [4,1,2,3] => 4
[[[],[],[]]] => [.,[[[.,.],.],.]] => [2,3,4,1] => [1,4,3,2] => 3
[[[],[[]]]] => [.,[[.,.],[.,.]]] => [2,4,3,1] => [1,3,4,2] => 4
[[[[]],[]]] => [.,[[.,[.,.]],.]] => [3,2,4,1] => [1,4,2,3] => 4
[[[[],[]]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => [1,2,4,3] => 4
[[[[[]]]]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,2,3,4] => 4
[[],[],[],[],[]] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [5,4,3,2,1] => 2
[[],[],[],[[]]] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [4,5,3,2,1] => 3
[[],[],[[]],[]] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [5,3,4,2,1] => 2
[[],[],[[],[]]] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [3,5,4,2,1] => 3
[[],[],[[[]]]] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [3,4,5,2,1] => 4
[[],[[]],[],[]] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [5,4,2,3,1] => 2
[[],[[]],[[]]] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [4,5,2,3,1] => 3
[[],[[],[]],[]] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [5,2,4,3,1] => 2
[[],[[[]]],[]] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [5,2,3,4,1] => 2
[[],[[],[],[]]] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [2,5,4,3,1] => 3
[[],[[],[[]]]] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [2,4,5,3,1] => 4
[[],[[[]],[]]] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [2,5,3,4,1] => 3
[[],[[[],[]]]] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [2,3,5,4,1] => 4
[[],[[[[]]]]] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [2,3,4,5,1] => 5
[[[]],[],[],[]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [5,4,3,1,2] => 3
[[[]],[],[[]]] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [4,5,3,1,2] => 4
[[[]],[[]],[]] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [5,3,4,1,2] => 3
[[[]],[[],[]]] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [3,5,4,1,2] => 4
[[[]],[[[]]]] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [3,4,5,1,2] => 5
[[[],[]],[],[]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [5,4,1,3,2] => 3
[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [5,4,1,2,3] => 4
[[[],[]],[[]]] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [4,5,1,3,2] => 4
[[[[]]],[[]]] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [4,5,1,2,3] => 5
[[[],[],[]],[]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [5,1,4,3,2] => 3
[[[],[[]]],[]] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [5,1,3,4,2] => 3
[[[[]],[]],[]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [5,1,4,2,3] => 4
[[[[],[]]],[]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [5,1,2,4,3] => 4
[[[[[]]]],[]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [5,1,2,3,4] => 5
[[[],[],[],[]]] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,5,4,3,2] => 3
[[[],[],[[]]]] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [1,4,5,3,2] => 4
[[[],[[]],[]]] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [1,5,3,4,2] => 3
[[[],[[],[]]]] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [1,3,5,4,2] => 4
[[[],[[[]]]]] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [1,3,4,5,2] => 5
[[[[]],[],[]]] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [1,5,4,2,3] => 4
[[[[]],[[]]]] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [1,4,5,2,3] => 5
[[[[],[]],[]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [1,5,2,4,3] => 4
[[[[[]]],[]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [1,5,2,3,4] => 5
[[[[],[],[]]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [1,2,5,4,3] => 4
[[[[],[[]]]]] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [1,2,4,5,3] => 5
[[[[[]],[]]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [1,2,5,3,4] => 5
[[[[[],[]]]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [1,2,3,5,4] => 5
[[[[[[]]]]]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,2,3,4,5] => 5
[[],[],[],[],[],[]] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 2
[[],[],[],[],[[]]] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 3
[[],[],[],[[]],[]] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 2
[[],[],[],[[],[]]] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [4,6,5,3,2,1] => 3
[[],[],[],[[[]]]] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [4,5,6,3,2,1] => 4
[[],[],[[]],[],[]] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 2
[[],[],[[]],[[]]] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => 3
[[],[],[[],[]],[]] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [6,3,5,4,2,1] => 2
[[],[],[[[]]],[]] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [6,3,4,5,2,1] => 2
[[],[],[[],[],[]]] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [3,6,5,4,2,1] => 3
[[],[],[[],[[]]]] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [3,5,6,4,2,1] => 4
[[],[],[[[]],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [3,6,4,5,2,1] => 3
[[],[],[[[],[]]]] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [3,4,6,5,2,1] => 4
[[],[],[[[[]]]]] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [3,4,5,6,2,1] => 5
[[],[[]],[],[],[]] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 2
[[],[[]],[],[[]]] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 3
[[],[[]],[[]],[]] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => 2
[[],[[]],[[],[]]] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [4,6,5,2,3,1] => 3
[[],[[]],[[[]]]] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [4,5,6,2,3,1] => 4
[[],[[],[]],[],[]] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [6,5,2,4,3,1] => 2
[[],[[[]]],[],[]] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [6,5,2,3,4,1] => 2
[[],[[],[]],[[]]] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [5,6,2,4,3,1] => 3
[[],[[[]]],[[]]] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [5,6,2,3,4,1] => 3
[[],[[],[],[]],[]] => [[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [6,2,5,4,3,1] => 2
[[],[[],[[]]],[]] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [6,2,4,5,3,1] => 2
[[],[[[]],[]],[]] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [6,2,5,3,4,1] => 2
[[],[[[],[]]],[]] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [6,2,3,5,4,1] => 2
[[],[[[[]]]],[]] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [6,2,3,4,5,1] => 2
[[],[[],[],[],[]]] => [[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [2,6,5,4,3,1] => 3
[[],[[],[],[[]]]] => [[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [2,5,6,4,3,1] => 4
[[],[[],[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [2,6,4,5,3,1] => 3
[[],[[],[[],[]]]] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [2,4,6,5,3,1] => 4
[[],[[],[[[]]]]] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [2,4,5,6,3,1] => 5
[[],[[[]],[],[]]] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [2,6,5,3,4,1] => 3
[[],[[[]],[[]]]] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [2,5,6,3,4,1] => 4
[[],[[[],[]],[]]] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [2,6,3,5,4,1] => 3
[[],[[[[]]],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [2,6,3,4,5,1] => 3
>>> Load all 402 entries. <<<
[[],[[[],[],[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [2,3,6,5,4,1] => 4
[[],[[[],[[]]]]] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [2,3,5,6,4,1] => 5
[[],[[[[]],[]]]] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [2,3,6,4,5,1] => 4
[[],[[[[],[]]]]] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [2,3,4,6,5,1] => 5
[[],[[[[[]]]]]] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [2,3,4,5,6,1] => 6
[[[]],[],[],[],[]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => 3
[[[]],[],[],[[]]] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => 4
[[[]],[],[[]],[]] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [6,4,5,3,1,2] => 3
[[[]],[],[[],[]]] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [4,6,5,3,1,2] => 4
[[[]],[],[[[]]]] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [4,5,6,3,1,2] => 5
[[[]],[[]],[],[]] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [6,5,3,4,1,2] => 3
[[[]],[[]],[[]]] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => 4
[[[]],[[],[]],[]] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [6,3,5,4,1,2] => 3
[[[]],[[[]]],[]] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [6,3,4,5,1,2] => 3
[[[]],[[],[],[]]] => [[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [3,6,5,4,1,2] => 4
[[[]],[[],[[]]]] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [3,5,6,4,1,2] => 5
[[[]],[[[]],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [3,6,4,5,1,2] => 4
[[[]],[[[],[]]]] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [3,4,6,5,1,2] => 5
[[[]],[[[[]]]]] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => 6
[[[],[]],[],[],[]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => 3
[[[[]]],[],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => 4
[[[],[]],[],[[]]] => [[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [5,6,4,1,3,2] => 4
[[[[]]],[],[[]]] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [5,6,4,1,2,3] => 5
[[[],[]],[[]],[]] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [6,4,5,1,3,2] => 3
[[[[]]],[[]],[]] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [6,4,5,1,2,3] => 4
[[[],[]],[[],[]]] => [[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [4,6,5,1,3,2] => 4
[[[],[]],[[[]]]] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [4,5,6,1,3,2] => 5
[[[[]]],[[],[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [4,6,5,1,2,3] => 5
[[[[]]],[[[]]]] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [4,5,6,1,2,3] => 6
[[[],[],[]],[],[]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => 3
[[[],[[]]],[],[]] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [6,5,1,3,4,2] => 3
[[[[]],[]],[],[]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [6,5,1,4,2,3] => 4
[[[[],[]]],[],[]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [6,5,1,2,4,3] => 4
[[[[[]]]],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => 5
[[[],[],[]],[[]]] => [[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [5,6,1,4,3,2] => 4
[[[],[[]]],[[]]] => [[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [5,6,1,3,4,2] => 4
[[[[]],[]],[[]]] => [[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [5,6,1,4,2,3] => 5
[[[[],[]]],[[]]] => [[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [5,6,1,2,4,3] => 5
[[[[[]]]],[[]]] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [5,6,1,2,3,4] => 6
[[[],[],[],[]],[]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => 3
[[[],[],[[]]],[]] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [6,1,4,5,3,2] => 3
[[[],[[]],[]],[]] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [6,1,5,3,4,2] => 3
[[[],[[],[]]],[]] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [6,1,3,5,4,2] => 3
[[[],[[[]]]],[]] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [6,1,3,4,5,2] => 3
[[[[]],[],[]],[]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [6,1,5,4,2,3] => 4
[[[[]],[[]]],[]] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [6,1,4,5,2,3] => 4
[[[[],[]],[]],[]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [6,1,5,2,4,3] => 4
[[[[[]]],[]],[]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [6,1,5,2,3,4] => 5
[[[[],[],[]]],[]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [6,1,2,5,4,3] => 4
[[[[],[[]]]],[]] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [6,1,2,4,5,3] => 4
[[[[[]],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [6,1,2,5,3,4] => 5
[[[[[],[]]]],[]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [6,1,2,3,5,4] => 5
[[[[[[]]]]],[]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => 6
[[[],[],[],[],[]]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => 3
[[[],[],[],[[]]]] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [1,5,6,4,3,2] => 4
[[[],[],[[]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [1,6,4,5,3,2] => 3
[[[],[],[[],[]]]] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [1,4,6,5,3,2] => 4
[[[],[],[[[]]]]] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [1,4,5,6,3,2] => 5
[[[],[[]],[],[]]] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [1,6,5,3,4,2] => 3
[[[],[[]],[[]]]] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [1,5,6,3,4,2] => 4
[[[],[[],[]],[]]] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [1,6,3,5,4,2] => 3
[[[],[[[]]],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [1,6,3,4,5,2] => 3
[[[],[[],[],[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [1,3,6,5,4,2] => 4
[[[],[[],[[]]]]] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [1,3,5,6,4,2] => 5
[[[],[[[]],[]]]] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [1,3,6,4,5,2] => 4
[[[],[[[],[]]]]] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [1,3,4,6,5,2] => 5
[[[],[[[[]]]]]] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [1,3,4,5,6,2] => 6
[[[[]],[],[],[]]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [1,6,5,4,2,3] => 4
[[[[]],[],[[]]]] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [1,5,6,4,2,3] => 5
[[[[]],[[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [1,6,4,5,2,3] => 4
[[[[]],[[],[]]]] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [1,4,6,5,2,3] => 5
[[[[]],[[[]]]]] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [1,4,5,6,2,3] => 6
[[[[],[]],[],[]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [1,6,5,2,4,3] => 4
[[[[[]]],[],[]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [1,6,5,2,3,4] => 5
[[[[],[]],[[]]]] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [1,5,6,2,4,3] => 5
[[[[[]]],[[]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [1,5,6,2,3,4] => 6
[[[[],[],[]],[]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [1,6,2,5,4,3] => 4
[[[[],[[]]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [1,6,2,4,5,3] => 4
[[[[[]],[]],[]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [1,6,2,5,3,4] => 5
[[[[[],[]]],[]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [1,6,2,3,5,4] => 5
[[[[[[]]]],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [1,6,2,3,4,5] => 6
[[[[],[],[],[]]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [1,2,6,5,4,3] => 4
[[[[],[],[[]]]]] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [1,2,5,6,4,3] => 5
[[[[],[[]],[]]]] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [1,2,6,4,5,3] => 4
[[[[],[[],[]]]]] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [1,2,4,6,5,3] => 5
[[[[],[[[]]]]]] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [1,2,4,5,6,3] => 6
[[[[[]],[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [1,2,6,5,3,4] => 5
[[[[[]],[[]]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [1,2,5,6,3,4] => 6
[[[[[],[]],[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [1,2,6,3,5,4] => 5
[[[[[[]]],[]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [1,2,6,3,4,5] => 6
[[[[[],[],[]]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => 5
[[[[[],[[]]]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [1,2,3,5,6,4] => 6
[[[[[[]],[]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [1,2,3,6,4,5] => 6
[[[[[[],[]]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [1,2,3,4,6,5] => 6
[[[[[[[]]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => 6
[[],[],[],[],[],[],[]] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => 2
[[],[[[[[[]]]]]]] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [2,3,4,5,6,7,1] => 7
[[[]],[],[],[],[],[]] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [7,6,5,4,3,1,2] => 3
[[[]],[[]],[],[],[]] => [[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [7,6,5,3,4,1,2] => 3
[[[]],[[]],[[]],[]] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [7,5,6,3,4,1,2] => 3
[[[]],[[[[[]]]]]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [3,4,5,6,7,1,2] => 7
[[[[]]],[],[],[],[]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [7,6,5,4,1,2,3] => 4
[[[[]]],[[]],[],[]] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [7,6,4,5,1,2,3] => 4
[[[[]]],[[]],[[]]] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [6,7,4,5,1,2,3] => 5
[[[[]]],[[[]]],[]] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [7,4,5,6,1,2,3] => 4
[[[[[]]]],[],[],[]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [7,6,5,1,2,3,4] => 5
[[[[[]]]],[[]],[]] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [7,5,6,1,2,3,4] => 5
[[[[[]]]],[[[]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [5,6,7,1,2,3,4] => 7
[[[[[[]]]]],[],[]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [7,6,1,2,3,4,5] => 6
[[[[[[]]]]],[[]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [6,7,1,2,3,4,5] => 7
[[[[[[[]]]]]],[]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [7,1,2,3,4,5,6] => 7
[[[],[],[],[],[],[]]] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => 3
[[[],[],[],[],[[]]]] => [.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [1,6,7,5,4,3,2] => 4
[[[],[],[],[[],[]]]] => [.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [1,5,7,6,4,3,2] => 4
[[[],[],[],[[[]]]]] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [1,5,6,7,4,3,2] => 5
[[[],[],[[]],[],[]]] => [.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [1,7,6,4,5,3,2] => 3
[[[],[],[[],[]],[]]] => [.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [1,7,4,6,5,3,2] => 3
[[[],[],[[[]]],[]]] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [1,7,4,5,6,3,2] => 3
[[[],[],[[],[],[]]]] => [.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [1,4,7,6,5,3,2] => 4
[[[],[],[[],[[]]]]] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [1,4,6,7,5,3,2] => 5
[[[],[],[[[],[]]]]] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [1,4,5,7,6,3,2] => 5
[[[],[],[[[[]]]]]] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [1,4,5,6,7,3,2] => 6
[[[],[[],[],[]],[]]] => [.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [1,7,3,6,5,4,2] => 3
[[[],[[],[[]]],[]]] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [1,7,3,5,6,4,2] => 3
[[[],[[],[],[],[]]]] => [.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [1,3,7,6,5,4,2] => 4
[[[],[[],[],[[]]]]] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [1,3,6,7,5,4,2] => 5
[[[],[[],[[]],[]]]] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [1,3,7,5,6,4,2] => 4
[[[],[[],[[],[]]]]] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [1,3,5,7,6,4,2] => 5
[[[],[[],[[[]]]]]] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [1,3,5,6,7,4,2] => 6
[[[],[[[]],[],[]]]] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [1,3,7,6,4,5,2] => 4
[[[],[[[]],[[]]]]] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [1,3,6,7,4,5,2] => 5
[[[],[[[],[]],[]]]] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [1,3,7,4,6,5,2] => 4
[[[],[[[[]]],[]]]] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [1,3,7,4,5,6,2] => 4
[[[],[[[],[],[]]]]] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [1,3,4,7,6,5,2] => 5
[[[],[[[],[[]]]]]] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [1,3,4,6,7,5,2] => 6
[[[],[[[[]],[]]]]] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [1,3,4,7,5,6,2] => 5
[[[],[[[[],[]]]]]] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [1,3,4,5,7,6,2] => 6
[[[],[[[[[]]]]]]] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [1,3,4,5,6,7,2] => 7
[[[[]],[[[],[]]]]] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [1,4,5,7,6,2,3] => 6
[[[[]],[[[[]]]]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [1,4,5,6,7,2,3] => 7
[[[[[]]],[[[]]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [1,5,6,7,2,3,4] => 7
[[[[[[]]]],[[]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [1,6,7,2,3,4,5] => 7
[[[[[[[]]]]],[]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [1,7,2,3,4,5,6] => 7
[[[[],[],[],[],[]]]] => [.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [1,2,7,6,5,4,3] => 4
[[[[],[],[],[[]]]]] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [1,2,6,7,5,4,3] => 5
[[[[],[],[[]],[]]]] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [1,2,7,5,6,4,3] => 4
[[[[],[],[[],[]]]]] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [1,2,5,7,6,4,3] => 5
[[[[],[],[[[]]]]]] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [1,2,5,6,7,4,3] => 6
[[[[],[[]],[],[]]]] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [1,2,7,6,4,5,3] => 4
[[[[],[[]],[[]]]]] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [1,2,6,7,4,5,3] => 5
[[[[],[[],[]],[]]]] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [1,2,7,4,6,5,3] => 4
[[[[],[[[]]],[]]]] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [1,2,7,4,5,6,3] => 4
[[[[],[[],[],[]]]]] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [1,2,4,7,6,5,3] => 5
[[[[],[[],[[]]]]]] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [1,2,4,6,7,5,3] => 6
[[[[],[[[]],[]]]]] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [1,2,4,7,5,6,3] => 5
[[[[],[[[],[]]]]]] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [1,2,4,5,7,6,3] => 6
[[[[],[[[[]]]]]]] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [1,2,4,5,6,7,3] => 7
[[[[[]],[],[],[]]]] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [1,2,7,6,5,3,4] => 5
[[[[[]],[],[[]]]]] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [1,2,6,7,5,3,4] => 6
[[[[[]],[[]],[]]]] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [1,2,7,5,6,3,4] => 5
[[[[[]],[[],[]]]]] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [1,2,5,7,6,3,4] => 6
[[[[[]],[[[]]]]]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [1,2,5,6,7,3,4] => 7
[[[[[],[]],[],[]]]] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [1,2,7,6,3,5,4] => 5
[[[[[[]]],[],[]]]] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [1,2,7,6,3,4,5] => 6
[[[[[],[]],[[]]]]] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [1,2,6,7,3,5,4] => 6
[[[[[[]]],[[]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [1,2,6,7,3,4,5] => 7
[[[[[],[],[]],[]]]] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [1,2,7,3,6,5,4] => 5
[[[[[],[[]]],[]]]] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [1,2,7,3,5,6,4] => 5
[[[[[[]],[]],[]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [1,2,7,3,6,4,5] => 6
[[[[[[],[]]],[]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [1,2,7,3,4,6,5] => 6
[[[[[[[]]]],[]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [1,2,7,3,4,5,6] => 7
[[[[[],[],[],[]]]]] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => 5
[[[[[],[],[[]]]]]] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [1,2,3,6,7,5,4] => 6
[[[[[],[[]],[]]]]] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [1,2,3,7,5,6,4] => 5
[[[[[],[[],[]]]]]] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [1,2,3,5,7,6,4] => 6
[[[[[],[[[]]]]]]] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [1,2,3,5,6,7,4] => 7
[[[[[[]],[],[]]]]] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [1,2,3,7,6,4,5] => 6
[[[[[[]],[[]]]]]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [1,2,3,6,7,4,5] => 7
[[[[[[],[]],[]]]]] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [1,2,3,7,4,6,5] => 6
[[[[[[[]]],[]]]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [1,2,3,7,4,5,6] => 7
[[[[[[],[],[]]]]]] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [1,2,3,4,7,6,5] => 6
[[[[[[],[[]]]]]]] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [1,2,3,4,6,7,5] => 7
[[[[[[[]],[]]]]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [1,2,3,4,7,5,6] => 7
[[[[[[[],[]]]]]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [1,2,3,4,5,7,6] => 7
[[[[[[[[]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 7
[[],[],[],[],[],[],[],[]] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => 2
[[],[],[],[],[[]],[[]]] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => [7,8,5,6,4,3,2,1] => 3
[[],[],[],[],[[[]],[]]] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => [5,8,6,7,4,3,2,1] => 3
[[],[],[],[[]],[],[[]]] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => [7,8,6,4,5,3,2,1] => 3
[[],[],[],[[]],[[]],[]] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [8,6,7,4,5,3,2,1] => 2
[[],[],[],[[[]],[],[]]] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => [4,8,7,5,6,3,2,1] => 3
[[],[],[[]],[],[],[[]]] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => [7,8,6,5,3,4,2,1] => 3
[[],[],[[]],[],[[]],[]] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => [8,6,7,5,3,4,2,1] => 2
[[],[],[[]],[[]],[],[]] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [8,7,5,6,3,4,2,1] => 2
[[],[],[[[]]],[[[]]]] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => [6,7,8,3,4,5,2,1] => 4
[[],[],[[[],[]],[]],[]] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,2,5,6,4,7,3,8] => [8,3,7,4,6,5,2,1] => 2
[[],[],[[],[[],[],[]]]] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => [3,5,8,7,6,4,2,1] => 4
[[],[],[[[]],[],[],[]]] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => [3,8,7,6,4,5,2,1] => 3
[[],[],[[[],[],[]],[]]] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => [3,8,4,7,6,5,2,1] => 3
[[],[],[[[[[]]],[]]]] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => [3,4,8,5,6,7,2,1] => 4
[[],[[]],[],[],[],[[]]] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => [7,8,6,5,4,2,3,1] => 3
[[],[[]],[],[],[[]],[]] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [8,6,7,5,4,2,3,1] => 2
[[],[[]],[],[[]],[],[]] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => [8,7,5,6,4,2,3,1] => 2
[[],[[]],[[]],[],[],[]] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [8,7,6,4,5,2,3,1] => 2
[[],[[[]]],[],[[[]]]] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => [6,7,8,5,2,3,4,1] => 4
[[],[[],[]],[[],[]],[]] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [8,5,7,6,2,4,3,1] => 2
[[],[[[]]],[[[]]],[]] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [8,5,6,7,2,3,4,1] => 2
[[],[[[],[]],[]],[],[]] => [[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,4,5,3,6,2,7,8] => [8,7,2,6,3,5,4,1] => 2
[[],[[],[],[[],[]]],[]] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => [8,2,5,7,6,4,3,1] => 2
[[],[[],[[],[]],[]],[]] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => [8,2,7,4,6,5,3,1] => 2
[[],[[[],[]],[],[]],[]] => [[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,4,5,3,6,7,2,8] => [8,2,7,6,3,5,4,1] => 2
[[],[[],[],[],[[],[]]]] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => [2,6,8,7,5,4,3,1] => 4
[[],[[],[],[[],[]],[]]] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,3,4,6,7,5,8,2] => [2,8,5,7,6,4,3,1] => 3
[[],[[[]],[],[],[],[]]] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => [2,8,7,6,5,3,4,1] => 3
[[],[[[],[[[],[]]]]]] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => [2,3,5,6,8,7,4,1] => 6
[[],[[[[[]]],[],[]]]] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,6,5,4,7,8,3,2] => [2,3,8,7,4,5,6,1] => 4
[[],[[[[[[]]],[]]]]] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => [2,3,4,8,5,6,7,1] => 5
[[],[[[[[[[]]]]]]]] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [2,3,4,5,6,7,8,1] => 8
[[[]],[],[],[],[],[],[]] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [8,7,6,5,4,3,1,2] => 3
[[[]],[],[],[],[],[[]]] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [7,8,6,5,4,3,1,2] => 4
[[[]],[],[],[],[[]],[]] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => [8,6,7,5,4,3,1,2] => 3
[[[]],[],[],[[]],[],[]] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => [8,7,5,6,4,3,1,2] => 3
[[[]],[],[[]],[],[],[]] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8] => [8,7,6,4,5,3,1,2] => 3
[[[]],[[]],[],[],[],[]] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => [8,7,6,5,3,4,1,2] => 3
[[[]],[[]],[[]],[],[]] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => [8,7,5,6,3,4,1,2] => 3
[[[]],[[]],[[]],[[]]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => 4
[[[]],[[]],[[],[[]]]] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => [5,7,8,6,3,4,1,2] => 5
[[[]],[[]],[[[[]]]]] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [5,6,7,8,3,4,1,2] => 6
[[[]],[[[[]]]],[[]]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [7,8,3,4,5,6,1,2] => 4
[[[]],[[[[[[]]]]]]] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [3,4,5,6,7,8,1,2] => 8
[[[[]]],[],[],[],[],[]] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [8,7,6,5,4,1,2,3] => 4
[[[],[]],[],[],[[],[]]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => [6,8,7,5,4,1,3,2] => 4
[[[[]]],[],[],[[[]]]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [6,7,8,5,4,1,2,3] => 6
[[[[]]],[],[[[]]],[]] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => [8,5,6,7,4,1,2,3] => 4
[[[[]]],[[]],[],[],[]] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [3,2,1,5,4,6,7,8] => [8,7,6,4,5,1,2,3] => 4
[[[[]]],[[]],[[]],[]] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => [8,6,7,4,5,1,2,3] => 4
[[[[]]],[[[]]],[],[]] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [3,2,1,6,5,4,7,8] => [8,7,4,5,6,1,2,3] => 4
[[[[]]],[[[]]],[[]]] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [3,2,1,6,5,4,8,7] => [7,8,4,5,6,1,2,3] => 5
[[[],[]],[[],[],[]],[]] => [[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => [8,4,7,6,5,1,3,2] => 3
[[[[]],[]],[],[],[],[]] => [[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [8,7,6,5,1,4,2,3] => 4
[[[[[]]]],[],[],[],[]] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [8,7,6,5,1,2,3,4] => 5
[[[[[]]]],[[]],[],[]] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => [8,7,5,6,1,2,3,4] => 5
[[[[[]]]],[[]],[[]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [7,8,5,6,1,2,3,4] => 6
[[[[[]]]],[[[]]],[]] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => [8,5,6,7,1,2,3,4] => 5
[[[],[],[]],[[],[],[]]] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => [5,8,7,6,1,4,3,2] => 4
[[[],[[]]],[[[]],[]]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => [5,8,6,7,1,3,4,2] => 4
[[[[]],[]],[[],[[]]]] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => [5,7,8,6,1,4,2,3] => 6
[[[[],[]]],[[[],[]]]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => [5,6,8,7,1,2,4,3] => 6
[[[[[]]]],[[[[]]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [5,6,7,8,1,2,3,4] => 8
[[[],[[]],[]],[],[],[]] => [[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => [8,7,6,1,5,3,4,2] => 3
[[[[[[]]]]],[],[],[]] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [8,7,6,1,2,3,4,5] => 6
[[[[[[]]]]],[[]],[]] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8] => [8,6,7,1,2,3,4,5] => 6
[[[[[[]]]]],[[[]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => [6,7,8,1,2,3,4,5] => 8
[[[],[],[],[[]]],[],[]] => [[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => [8,7,1,5,6,4,3,2] => 3
[[[],[],[[]],[]],[],[]] => [[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => [8,7,1,6,4,5,3,2] => 3
[[[[],[],[]],[]],[],[]] => [[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => [8,7,1,6,2,5,4,3] => 4
[[[[[[[]]]]]],[],[]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [8,7,1,2,3,4,5,6] => 7
[[[[[]]],[],[]],[[]]] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [4,3,2,5,6,1,8,7] => [7,8,1,6,5,2,3,4] => 6
[[[[],[[]]],[]],[[]]] => [[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [3,5,4,2,6,1,8,7] => [7,8,1,6,2,4,5,3] => 5
[[[[[[[]]]]]],[[]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [7,8,1,2,3,4,5,6] => 8
[[[],[],[],[],[[]]],[]] => [[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => [8,1,6,7,5,4,3,2] => 3
[[[],[],[],[[]],[]],[]] => [[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => [8,1,7,5,6,4,3,2] => 3
[[[[]],[],[],[],[]],[]] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [8,1,7,6,5,4,2,3] => 4
[[[[]],[[]],[[]]],[]] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => [8,1,6,7,4,5,2,3] => 4
[[[[],[]],[],[],[]],[]] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => [8,1,7,6,5,2,4,3] => 4
[[[[],[],[[[]]]]],[]] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => [8,1,2,5,6,7,4,3] => 4
[[[[[[]]],[],[]]],[]] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => [8,1,2,7,6,3,4,5] => 6
[[[[[[],[]]],[]]],[]] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => [8,1,2,7,3,4,6,5] => 6
[[[[[[[[]]]]]]],[]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7] => 8
[[[],[],[],[],[],[],[]]] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2] => 3
[[[],[],[],[],[],[[]]]] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => [1,7,8,6,5,4,3,2] => 4
[[[],[],[],[],[[]],[]]] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => [1,8,6,7,5,4,3,2] => 3
[[[],[],[],[],[[],[]]]] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [2,3,4,5,7,8,6,1] => [1,6,8,7,5,4,3,2] => 4
[[[],[],[],[],[[[]]]]] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [2,3,4,5,8,7,6,1] => [1,6,7,8,5,4,3,2] => 5
[[[],[],[],[[]],[],[]]] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [2,3,4,6,5,7,8,1] => [1,8,7,5,6,4,3,2] => 3
[[[],[],[],[[],[],[]]]] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [2,3,4,6,7,8,5,1] => [1,5,8,7,6,4,3,2] => 4
[[[],[],[[]],[[]],[]]] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [2,3,5,4,7,6,8,1] => [1,8,6,7,4,5,3,2] => 3
[[[],[],[[],[]],[],[]]] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => [2,3,5,6,4,7,8,1] => [1,8,7,4,6,5,3,2] => 3
[[[],[],[[[]]],[],[]]] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [2,3,6,5,4,7,8,1] => [1,8,7,4,5,6,3,2] => 3
[[[],[],[[],[],[]],[]]] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => [2,3,5,6,7,4,8,1] => [1,8,4,7,6,5,3,2] => 3
[[[],[[]],[],[],[[]]]] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => [1,7,8,6,5,3,4,2] => 4
[[[],[[],[]],[[],[]]]] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [2,4,5,3,7,8,6,1] => [1,6,8,7,3,5,4,2] => 4
[[[],[[[]]],[[[]]]]] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => [1,6,7,8,3,4,5,2] => 5
[[[],[[],[[],[[]]]]]] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => [1,3,5,7,8,6,4,2] => 6
[[[[]],[],[],[],[],[]]] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [1,8,7,6,5,4,2,3] => 4
[[[[]],[[],[[]],[]]]] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [3,2,5,7,6,8,4,1] => [1,4,8,6,7,5,2,3] => 5
[[[[[[]]]],[[[]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [5,4,3,2,8,7,6,1] => [1,6,7,8,2,3,4,5] => 8
[[[[[[[]]]]],[[]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [6,5,4,3,2,8,7,1] => [1,7,8,2,3,4,5,6] => 8
[[[[[[]],[]],[]],[]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [1,8,2,7,3,6,4,5] => 6
[[[[[[[]]]],[]],[]]] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [1,8,2,7,3,4,5,6] => 7
[[[[[[[]],[]]]],[]]] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [1,8,2,3,4,7,5,6] => 7
[[[[[[[[]]]]]],[]]] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [1,8,2,3,4,5,6,7] => 8
[[[[],[],[],[[[]]]]]] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [3,4,5,8,7,6,2,1] => [1,2,6,7,8,5,4,3] => 6
[[[[],[[[]]],[],[]]]] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [3,6,5,4,7,8,2,1] => [1,2,8,7,4,5,6,3] => 4
[[[[[[]]],[],[],[]]]] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => [1,2,8,7,6,3,4,5] => 6
[[[[[],[[[[]]]]]]]] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => [1,2,3,5,6,7,8,4] => 8
[[[[[[[]],[]],[]]]]] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [1,2,3,8,4,7,5,6] => 7
[[[[[[[[]]]],[]]]]] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [1,2,3,8,4,5,6,7] => 8
[[[[[[[[]],[]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [1,2,3,4,5,8,6,7] => 8
[[[[[[[[],[]]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,7] => 8
[[[[[[[[[]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 8
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
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
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
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.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.