Identifier
Values
[.,.] => [1] => 0
[.,[.,.]] => [2,1] => 0
[[.,.],.] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => 0
[.,[[.,.],.]] => [2,3,1] => 0
[[.,.],[.,.]] => [1,3,2] => 0
[[.,[.,.]],.] => [2,1,3] => 0
[[[.,.],.],.] => [1,2,3] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 0
[.,[.,[[.,.],.]]] => [3,4,2,1] => 0
[.,[[.,.],[.,.]]] => [2,4,3,1] => 0
[.,[[.,[.,.]],.]] => [3,2,4,1] => 0
[.,[[[.,.],.],.]] => [2,3,4,1] => 0
[[.,.],[.,[.,.]]] => [1,4,3,2] => 0
[[.,.],[[.,.],.]] => [1,3,4,2] => 0
[[.,[.,.]],[.,.]] => [2,1,4,3] => 0
[[[.,.],.],[.,.]] => [1,2,4,3] => 0
[[.,[.,[.,.]]],.] => [3,2,1,4] => 0
[[.,[[.,.],.]],.] => [2,3,1,4] => 0
[[[.,.],[.,.]],.] => [1,3,2,4] => 0
[[[.,[.,.]],.],.] => [2,1,3,4] => 0
[[[[.,.],.],.],.] => [1,2,3,4] => 0
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 0
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 0
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 0
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 0
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 1
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 0
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 0
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 0
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 0
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 0
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 0
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 0
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 0
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 0
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 0
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 0
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 0
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 0
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 0
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 0
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 0
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 0
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 0
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 0
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 0
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 0
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 0
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 0
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 0
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 0
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 0
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 0
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 0
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 0
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 0
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 0
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 0
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 0
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 0
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 0
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 0
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 0
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 0
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 0
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 0
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 1
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 0
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 1
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 0
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 1
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 0
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 1
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 1
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 1
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 0
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 0
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 0
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 0
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 1
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 0
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 0
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 0
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 0
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 0
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 0
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 0
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 0
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 0
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 0
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 0
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 0
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 0
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 1
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 0
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 0
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 0
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 0
>>> Load all 304 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 0
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 0
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 0
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 0
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 0
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 0
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 0
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 0
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 0
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 1
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 0
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 0
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 0
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => 0
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 0
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 0
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => 0
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 0
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => 0
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 0
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 0
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 0
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 0
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => 0
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 0
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 0
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 0
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 0
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 0
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 0
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 0
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 0
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => 0
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 0
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 0
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 0
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 0
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 0
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 0
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 0
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => 0
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => 0
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => 0
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => 0
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 0
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 0
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 0
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 0
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 0
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => 0
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 0
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 0
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 0
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 0
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 0
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 0
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 0
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 1
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 0
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 0
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 0
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 0
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 0
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 0
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 0
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 0
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 0
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 0
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 0
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 0
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 0
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => 0
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 0
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 0
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 0
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 0
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 0
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => 0
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 0
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 0
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 0
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 0
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 0
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 0
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 0
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 0
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 0
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 0
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 0
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 0
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 0
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 0
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 0
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 0
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 0
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => 1
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => 1
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 0
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 0
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => 1
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 0
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 0
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => 0
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => 0
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => 0
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => 0
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => 0
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => 0
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => 1
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => 0
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => 0
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => 0
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => 0
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => 0
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => 0
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => 0
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => 0
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => 0
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => 0
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => 0
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => 0
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => 1
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => 0
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => 0
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => 0
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => 0
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => 0
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => 0
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => 0
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => 0
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => 0
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => 0
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => 0
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => 0
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => 0
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => 0
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => 0
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => 0
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => 0
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => 0
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => 0
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => 0
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => 0
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => 0
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => 0
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => 0
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => 0
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => 0
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => 0
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => 0
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => 0
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => 0
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => 0
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => 0
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => 0
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => 0
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => 0
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => 0
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => 0
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => 0
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => 0
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => 0
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => 0
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 0
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => 0
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => 1
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => 0
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => 0
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => 0
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => 0
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => 0
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => 0
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => 0
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => 0
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => 0
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => 0
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => 0
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => 0
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => 0
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => 0
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => 0
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => 0
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => 0
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => 0
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => 0
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => 0
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => 0
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 0
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => 0
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => 0
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => 0
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => 0
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => 0
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => 0
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => 0
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => 0
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => 0
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => 0
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => 0
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 0
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 0
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Description
Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation.
Let $\pi$ be a permutation. Its total displacement St000830The total displacement of a permutation. is $D(\pi) = \sum_i |\pi(i) - i|$, and its absolute length St000216The absolute length of a permutation. is the minimal number $T(\pi)$ of transpositions whose product is $\pi$. Finally, let $I(\pi)$ be the number of inversions St000018The number of inversions of a permutation. of $\pi$.
This statistic equals $\left(D(\pi)-T(\pi)-I(\pi)\right)/2$.
Diaconis and Graham [1] proved that this statistic is always nonnegative.
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.