Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00223: Permutations —runsort⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
St000291: Binary words ⟶ ℤ
Values
[.,[.,.]] => [2,1] => [1,2] => 0 => 0
[[.,.],.] => [1,2] => [1,2] => 0 => 0
[.,[.,[.,.]]] => [3,2,1] => [1,2,3] => 00 => 0
[.,[[.,.],.]] => [2,3,1] => [1,2,3] => 00 => 0
[[.,.],[.,.]] => [3,1,2] => [1,2,3] => 00 => 0
[[.,[.,.]],.] => [2,1,3] => [1,3,2] => 01 => 0
[[[.,.],.],.] => [1,2,3] => [1,2,3] => 00 => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,2,3,4] => 000 => 0
[.,[.,[[.,.],.]]] => [3,4,2,1] => [1,2,3,4] => 000 => 0
[.,[[.,.],[.,.]]] => [4,2,3,1] => [1,2,3,4] => 000 => 0
[.,[[.,[.,.]],.]] => [3,2,4,1] => [1,2,4,3] => 001 => 0
[.,[[[.,.],.],.]] => [2,3,4,1] => [1,2,3,4] => 000 => 0
[[.,.],[.,[.,.]]] => [4,3,1,2] => [1,2,3,4] => 000 => 0
[[.,.],[[.,.],.]] => [3,4,1,2] => [1,2,3,4] => 000 => 0
[[.,[.,.]],[.,.]] => [4,2,1,3] => [1,3,2,4] => 010 => 1
[[[.,.],.],[.,.]] => [4,1,2,3] => [1,2,3,4] => 000 => 0
[[.,[.,[.,.]]],.] => [3,2,1,4] => [1,4,2,3] => 001 => 0
[[.,[[.,.],.]],.] => [2,3,1,4] => [1,4,2,3] => 001 => 0
[[[.,.],[.,.]],.] => [3,1,2,4] => [1,2,4,3] => 001 => 0
[[[.,[.,.]],.],.] => [2,1,3,4] => [1,3,4,2] => 001 => 0
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => 000 => 0
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,2,3,4,5] => 0000 => 0
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [1,2,3,4,5] => 0000 => 0
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [1,2,3,4,5] => 0000 => 0
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [1,2,3,5,4] => 0001 => 0
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [1,2,3,4,5] => 0000 => 0
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [1,2,3,4,5] => 0000 => 0
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [1,2,3,4,5] => 0000 => 0
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [1,2,4,3,5] => 0010 => 1
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [1,2,3,4,5] => 0000 => 0
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [1,2,5,3,4] => 0001 => 0
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [1,2,5,3,4] => 0001 => 0
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [1,2,3,5,4] => 0001 => 0
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [1,2,4,5,3] => 0001 => 0
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,2,3,4,5] => 0000 => 0
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [1,2,3,4,5] => 0000 => 0
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [1,2,3,4,5] => 0000 => 0
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [1,2,3,4,5] => 0000 => 0
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [1,2,3,5,4] => 0001 => 0
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [1,2,3,4,5] => 0000 => 0
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [1,3,2,4,5] => 0100 => 1
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [1,3,2,4,5] => 0100 => 1
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [1,2,3,4,5] => 0000 => 0
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [1,2,3,4,5] => 0000 => 0
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [1,4,2,3,5] => 0010 => 1
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [1,4,2,3,5] => 0010 => 1
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [1,2,4,3,5] => 0010 => 1
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [1,3,4,2,5] => 0010 => 1
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,2,3,4,5] => 0000 => 0
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [1,5,2,3,4] => 0001 => 0
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [1,5,2,3,4] => 0001 => 0
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [1,5,2,3,4] => 0001 => 0
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [1,5,2,4,3] => 0011 => 0
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [1,5,2,3,4] => 0001 => 0
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [1,2,5,3,4] => 0001 => 0
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [1,2,5,3,4] => 0001 => 0
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [1,3,5,2,4] => 0001 => 0
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [1,2,3,5,4] => 0001 => 0
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [1,4,5,2,3] => 0001 => 0
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [1,4,5,2,3] => 0001 => 0
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [1,2,4,5,3] => 0001 => 0
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [1,3,4,5,2] => 0001 => 0
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => 0000 => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [1,2,3,4,6,5] => 00001 => 0
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [1,2,3,5,4,6] => 00010 => 1
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [1,2,3,6,4,5] => 00001 => 0
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [1,2,3,6,4,5] => 00001 => 0
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [1,2,3,4,6,5] => 00001 => 0
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [1,2,3,5,6,4] => 00001 => 0
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [1,2,3,4,6,5] => 00001 => 0
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [1,2,4,3,5,6] => 00100 => 1
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [1,2,4,3,5,6] => 00100 => 1
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [1,2,5,3,4,6] => 00010 => 1
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [1,2,5,3,4,6] => 00010 => 1
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [1,2,3,5,4,6] => 00010 => 1
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [1,2,4,5,3,6] => 00010 => 1
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [1,2,6,3,4,5] => 00001 => 0
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [1,2,6,3,4,5] => 00001 => 0
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [1,2,6,3,4,5] => 00001 => 0
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [1,2,6,3,5,4] => 00011 => 0
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [1,2,6,3,4,5] => 00001 => 0
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [1,2,3,6,4,5] => 00001 => 0
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [1,2,3,6,4,5] => 00001 => 0
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [1,2,4,6,3,5] => 00001 => 0
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [1,2,3,4,6,5] => 00001 => 0
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [1,2,5,6,3,4] => 00001 => 0
>>> Load all 1039 entries. <<<[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [1,2,5,6,3,4] => 00001 => 0
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [1,2,3,5,6,4] => 00001 => 0
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [1,2,4,5,6,3] => 00001 => 0
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 00000 => 0
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [1,2,3,4,5,6] => 00000 => 0
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [1,2,3,4,5,6] => 00000 => 0
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [1,2,3,4,5,6] => 00000 => 0
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [1,2,3,4,6,5] => 00001 => 0
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [1,2,3,4,5,6] => 00000 => 0
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [1,2,3,4,5,6] => 00000 => 0
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [1,2,3,4,5,6] => 00000 => 0
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [1,2,3,5,4,6] => 00010 => 1
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [1,2,3,4,5,6] => 00000 => 0
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [1,2,3,6,4,5] => 00001 => 0
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [1,2,3,6,4,5] => 00001 => 0
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [1,2,3,4,6,5] => 00001 => 0
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [1,2,3,5,6,4] => 00001 => 0
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [1,2,3,4,5,6] => 00000 => 0
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [1,3,2,4,5,6] => 01000 => 1
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [1,3,2,4,5,6] => 01000 => 1
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [1,3,2,4,5,6] => 01000 => 1
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [1,3,2,4,6,5] => 01001 => 1
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [1,3,2,4,5,6] => 01000 => 1
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [1,2,3,4,5,6] => 00000 => 0
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [1,2,3,4,5,6] => 00000 => 0
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [1,2,3,4,5,6] => 00000 => 0
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [1,2,3,4,6,5] => 00001 => 0
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [1,2,3,4,5,6] => 00000 => 0
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [1,4,2,3,5,6] => 00100 => 1
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [1,4,2,3,5,6] => 00100 => 1
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [1,4,2,3,5,6] => 00100 => 1
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [1,4,2,3,5,6] => 00100 => 1
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [1,2,4,3,5,6] => 00100 => 1
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [1,2,4,3,5,6] => 00100 => 1
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [1,3,4,2,5,6] => 00100 => 1
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [1,3,4,2,5,6] => 00100 => 1
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [1,2,3,4,5,6] => 00000 => 0
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [1,2,3,4,5,6] => 00000 => 0
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [1,5,2,3,4,6] => 00010 => 1
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [1,5,2,3,4,6] => 00010 => 1
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [1,5,2,3,4,6] => 00010 => 1
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [1,5,2,4,3,6] => 00110 => 1
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [1,5,2,3,4,6] => 00010 => 1
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [1,2,5,3,4,6] => 00010 => 1
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [1,2,5,3,4,6] => 00010 => 1
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [1,3,5,2,4,6] => 00010 => 1
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [1,2,3,5,4,6] => 00010 => 1
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [1,4,5,2,3,6] => 00010 => 1
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [1,4,5,2,3,6] => 00010 => 1
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [1,2,4,5,3,6] => 00010 => 1
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [1,3,4,5,2,6] => 00010 => 1
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,2,3,4,5,6] => 00000 => 0
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [1,6,2,3,4,5] => 00001 => 0
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [1,6,2,3,4,5] => 00001 => 0
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [1,6,2,3,4,5] => 00001 => 0
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [1,6,2,3,5,4] => 00011 => 0
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [1,6,2,3,4,5] => 00001 => 0
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [1,6,2,3,4,5] => 00001 => 0
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [1,6,2,3,4,5] => 00001 => 0
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [1,6,2,4,3,5] => 00101 => 1
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [1,6,2,3,4,5] => 00001 => 0
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [1,6,2,5,3,4] => 00011 => 0
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [1,6,2,5,3,4] => 00011 => 0
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [1,6,2,3,5,4] => 00011 => 0
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [1,6,2,4,5,3] => 00011 => 0
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [1,6,2,3,4,5] => 00001 => 0
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [1,2,6,3,4,5] => 00001 => 0
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [1,2,6,3,4,5] => 00001 => 0
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [1,2,6,3,4,5] => 00001 => 0
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [1,2,6,3,5,4] => 00011 => 0
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [1,2,6,3,4,5] => 00001 => 0
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [1,3,6,2,4,5] => 00001 => 0
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [1,3,6,2,4,5] => 00001 => 0
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [1,2,3,6,4,5] => 00001 => 0
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [1,2,3,6,4,5] => 00001 => 0
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [1,4,6,2,3,5] => 00001 => 0
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [1,4,6,2,3,5] => 00001 => 0
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [1,2,4,6,3,5] => 00001 => 0
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [1,3,4,6,2,5] => 00001 => 0
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [1,2,3,4,6,5] => 00001 => 0
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [1,5,6,2,3,4] => 00001 => 0
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [1,5,6,2,3,4] => 00001 => 0
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [1,5,6,2,3,4] => 00001 => 0
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [1,5,6,2,4,3] => 00101 => 1
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [1,5,6,2,3,4] => 00001 => 0
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [1,2,5,6,3,4] => 00001 => 0
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [1,2,5,6,3,4] => 00001 => 0
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [1,3,5,6,2,4] => 00001 => 0
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [1,2,3,5,6,4] => 00001 => 0
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [1,4,5,6,2,3] => 00001 => 0
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [1,4,5,6,2,3] => 00001 => 0
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [1,2,4,5,6,3] => 00001 => 0
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 00001 => 0
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 00000 => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [1,2,3,4,5,7,6] => 000001 => 0
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [1,2,3,4,6,5,7] => 000010 => 1
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [1,2,3,4,7,5,6] => 000001 => 0
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [1,2,3,4,7,5,6] => 000001 => 0
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [1,2,3,4,5,7,6] => 000001 => 0
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [1,2,3,4,6,7,5] => 000001 => 0
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [1,2,3,4,5,7,6] => 000001 => 0
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [1,2,3,5,4,6,7] => 000100 => 1
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [1,2,3,5,4,6,7] => 000100 => 1
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => [1,2,3,6,4,5,7] => 000010 => 1
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => [1,2,3,6,4,5,7] => 000010 => 1
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [1,2,3,4,6,5,7] => 000010 => 1
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => [1,2,3,5,6,4,7] => 000010 => 1
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [1,2,3,7,4,5,6] => 000001 => 0
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [1,2,3,7,4,5,6] => 000001 => 0
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [1,2,3,7,4,5,6] => 000001 => 0
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [1,2,3,7,4,6,5] => 000011 => 0
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [1,2,3,7,4,5,6] => 000001 => 0
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [1,2,3,4,7,5,6] => 000001 => 0
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [1,2,3,4,7,5,6] => 000001 => 0
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [1,2,3,5,7,4,6] => 000001 => 0
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [1,2,3,4,5,7,6] => 000001 => 0
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [1,2,3,6,7,4,5] => 000001 => 0
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [1,2,3,6,7,4,5] => 000001 => 0
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [1,2,3,4,6,7,5] => 000001 => 0
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [1,2,3,5,6,7,4] => 000001 => 0
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [1,2,3,4,5,7,6] => 000001 => 0
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [1,2,3,4,6,5,7] => 000010 => 1
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [1,2,3,4,7,5,6] => 000001 => 0
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [1,2,3,4,7,5,6] => 000001 => 0
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [1,2,3,4,5,7,6] => 000001 => 0
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => [1,2,3,4,6,7,5] => 000001 => 0
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [1,2,4,3,5,6,7] => 001000 => 1
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [1,2,4,3,5,6,7] => 001000 => 1
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => [1,2,4,3,5,6,7] => 001000 => 1
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => [1,2,4,3,5,7,6] => 001001 => 1
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => [1,2,4,3,5,6,7] => 001000 => 1
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [1,2,3,4,5,7,6] => 000001 => 0
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [1,2,5,3,4,6,7] => 000100 => 1
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => [1,2,5,3,4,6,7] => 000100 => 1
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [1,2,5,3,4,6,7] => 000100 => 1
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => [1,2,5,3,4,6,7] => 000100 => 1
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [1,2,3,5,4,6,7] => 000100 => 1
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [1,2,3,5,4,6,7] => 000100 => 1
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [1,2,4,5,3,6,7] => 000100 => 1
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => [1,2,4,5,3,6,7] => 000100 => 1
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [1,2,6,3,4,5,7] => 000010 => 1
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [1,2,6,3,4,5,7] => 000010 => 1
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [1,2,6,3,4,5,7] => 000010 => 1
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [1,2,6,3,5,4,7] => 000110 => 1
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [1,2,6,3,4,5,7] => 000010 => 1
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [1,2,3,6,4,5,7] => 000010 => 1
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [1,2,3,6,4,5,7] => 000010 => 1
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [1,2,4,6,3,5,7] => 000010 => 1
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [1,2,3,4,6,5,7] => 000010 => 1
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [1,2,5,6,3,4,7] => 000010 => 1
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [1,2,5,6,3,4,7] => 000010 => 1
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [1,2,3,5,6,4,7] => 000010 => 1
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [1,2,4,5,6,3,7] => 000010 => 1
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [1,2,7,3,4,5,6] => 000001 => 0
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [1,2,7,3,4,5,6] => 000001 => 0
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [1,2,7,3,4,5,6] => 000001 => 0
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [1,2,7,3,4,6,5] => 000011 => 0
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [1,2,7,3,4,5,6] => 000001 => 0
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [1,2,7,3,4,5,6] => 000001 => 0
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [1,2,7,3,4,5,6] => 000001 => 0
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [1,2,7,3,5,4,6] => 000101 => 1
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [1,2,7,3,4,5,6] => 000001 => 0
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [1,2,7,3,6,4,5] => 000011 => 0
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [1,2,7,3,6,4,5] => 000011 => 0
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => [1,2,7,3,4,6,5] => 000011 => 0
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [1,2,7,3,5,6,4] => 000011 => 0
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [1,2,7,3,4,5,6] => 000001 => 0
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [1,2,3,7,4,5,6] => 000001 => 0
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [1,2,3,7,4,5,6] => 000001 => 0
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [1,2,3,7,4,5,6] => 000001 => 0
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [1,2,3,7,4,6,5] => 000011 => 0
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [1,2,3,7,4,5,6] => 000001 => 0
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [1,2,4,7,3,5,6] => 000001 => 0
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => [1,2,4,7,3,5,6] => 000001 => 0
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [1,2,3,4,7,5,6] => 000001 => 0
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [1,2,3,4,7,5,6] => 000001 => 0
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [1,2,5,7,3,4,6] => 000001 => 0
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => [1,2,5,7,3,4,6] => 000001 => 0
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => [1,2,3,5,7,4,6] => 000001 => 0
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => [1,2,4,5,7,3,6] => 000001 => 0
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [1,2,3,4,5,7,6] => 000001 => 0
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [1,2,6,7,3,4,5] => 000001 => 0
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [1,2,6,7,3,4,5] => 000001 => 0
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [1,2,6,7,3,4,5] => 000001 => 0
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [1,2,6,7,3,5,4] => 000101 => 1
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [1,2,6,7,3,4,5] => 000001 => 0
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [1,2,3,6,7,4,5] => 000001 => 0
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [1,2,3,6,7,4,5] => 000001 => 0
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [1,2,4,6,7,3,5] => 000001 => 0
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [1,2,3,4,6,7,5] => 000001 => 0
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [1,2,5,6,7,3,4] => 000001 => 0
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [1,2,5,6,7,3,4] => 000001 => 0
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [1,2,3,5,6,7,4] => 000001 => 0
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [1,2,4,5,6,7,3] => 000001 => 0
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [1,2,3,4,5,7,6] => 000001 => 0
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [1,2,3,4,6,5,7] => 000010 => 1
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [1,2,3,4,7,5,6] => 000001 => 0
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [1,2,3,4,7,5,6] => 000001 => 0
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [1,2,3,4,5,7,6] => 000001 => 0
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => [1,2,3,4,6,7,5] => 000001 => 0
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [1,2,3,4,5,7,6] => 000001 => 0
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [1,2,3,5,4,6,7] => 000100 => 1
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [1,2,3,5,4,6,7] => 000100 => 1
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [1,2,3,6,4,5,7] => 000010 => 1
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [1,2,3,6,4,5,7] => 000010 => 1
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [1,2,3,4,6,5,7] => 000010 => 1
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [1,2,3,5,6,4,7] => 000010 => 1
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [1,2,3,7,4,5,6] => 000001 => 0
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [1,2,3,7,4,5,6] => 000001 => 0
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [1,2,3,7,4,5,6] => 000001 => 0
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => [1,2,3,7,4,6,5] => 000011 => 0
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [1,2,3,7,4,5,6] => 000001 => 0
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [1,2,3,4,7,5,6] => 000001 => 0
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [1,2,3,4,7,5,6] => 000001 => 0
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => [1,2,3,5,7,4,6] => 000001 => 0
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [1,2,3,4,5,7,6] => 000001 => 0
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => [1,2,3,6,7,4,5] => 000001 => 0
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [1,2,3,6,7,4,5] => 000001 => 0
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [1,2,3,4,6,7,5] => 000001 => 0
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [1,2,3,5,6,7,4] => 000001 => 0
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [1,3,2,4,5,6,7] => 010000 => 1
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [1,3,2,4,5,6,7] => 010000 => 1
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => [1,3,2,4,5,6,7] => 010000 => 1
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => [1,3,2,4,5,7,6] => 010001 => 1
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => [1,3,2,4,5,6,7] => 010000 => 1
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [1,3,2,4,5,6,7] => 010000 => 1
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => [1,3,2,4,5,6,7] => 010000 => 1
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => [1,3,2,4,6,5,7] => 010010 => 2
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [1,3,2,4,5,6,7] => 010000 => 1
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [1,3,2,4,7,5,6] => 010001 => 1
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => [1,3,2,4,7,5,6] => 010001 => 1
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => [1,3,2,4,5,7,6] => 010001 => 1
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => [1,3,2,4,6,7,5] => 010001 => 1
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [1,3,2,4,5,6,7] => 010000 => 1
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [1,2,3,4,5,6,7] => 000000 => 0
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [1,2,3,4,5,6,7] => 000000 => 0
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [1,2,3,4,5,6,7] => 000000 => 0
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [1,2,3,4,5,7,6] => 000001 => 0
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => 000000 => 0
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [1,2,3,4,5,6,7] => 000000 => 0
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [1,2,3,4,5,6,7] => 000000 => 0
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [1,2,3,4,6,5,7] => 000010 => 1
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => 000000 => 0
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [1,2,3,4,7,5,6] => 000001 => 0
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [1,2,3,4,7,5,6] => 000001 => 0
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [1,2,3,4,5,7,6] => 000001 => 0
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => [1,2,3,4,6,7,5] => 000001 => 0
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [1,4,2,3,5,6,7] => 001000 => 1
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => [1,4,2,3,5,6,7] => 001000 => 1
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => [1,4,2,3,5,6,7] => 001000 => 1
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => [1,4,2,3,5,7,6] => 001001 => 1
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => [1,4,2,3,5,6,7] => 001000 => 1
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [1,4,2,3,5,6,7] => 001000 => 1
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => [1,4,2,3,5,6,7] => 001000 => 1
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => [1,4,2,3,5,6,7] => 001000 => 1
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => [1,4,2,3,5,7,6] => 001001 => 1
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => [1,4,2,3,5,6,7] => 001000 => 1
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [1,2,4,3,5,6,7] => 001000 => 1
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [1,2,4,3,5,6,7] => 001000 => 1
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [1,2,4,3,5,6,7] => 001000 => 1
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [1,2,4,3,5,7,6] => 001001 => 1
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [1,2,4,3,5,6,7] => 001000 => 1
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [1,3,4,2,5,6,7] => 001000 => 1
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => [1,3,4,2,5,6,7] => 001000 => 1
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => [1,3,4,2,5,6,7] => 001000 => 1
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => [1,3,4,2,5,7,6] => 001001 => 1
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => [1,3,4,2,5,6,7] => 001000 => 1
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [1,2,3,4,5,6,7] => 000000 => 0
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [1,2,3,4,5,6,7] => 000000 => 0
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [1,2,3,4,5,6,7] => 000000 => 0
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [1,2,3,4,5,7,6] => 000001 => 0
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [1,5,2,3,4,6,7] => 000100 => 1
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [1,5,2,3,4,6,7] => 000100 => 1
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [1,5,2,3,4,6,7] => 000100 => 1
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [1,5,2,3,4,6,7] => 000100 => 1
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [1,5,2,3,4,6,7] => 000100 => 1
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [1,5,2,3,4,6,7] => 000100 => 1
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [1,5,2,4,3,6,7] => 001100 => 1
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [1,5,2,4,3,6,7] => 001100 => 1
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [1,5,2,3,4,6,7] => 000100 => 1
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [1,5,2,3,4,6,7] => 000100 => 1
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [1,2,5,3,4,6,7] => 000100 => 1
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [1,2,5,3,4,6,7] => 000100 => 1
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [1,2,5,3,4,6,7] => 000100 => 1
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [1,2,5,3,4,6,7] => 000100 => 1
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [1,3,5,2,4,6,7] => 000100 => 1
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [1,3,5,2,4,6,7] => 000100 => 1
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [1,2,3,5,4,6,7] => 000100 => 1
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [1,2,3,5,4,6,7] => 000100 => 1
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [1,4,5,2,3,6,7] => 000100 => 1
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [1,4,5,2,3,6,7] => 000100 => 1
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [1,4,5,2,3,6,7] => 000100 => 1
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [1,4,5,2,3,6,7] => 000100 => 1
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [1,2,4,5,3,6,7] => 000100 => 1
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [1,2,4,5,3,6,7] => 000100 => 1
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [1,3,4,5,2,6,7] => 000100 => 1
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => [1,3,4,5,2,6,7] => 000100 => 1
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [1,2,3,4,5,6,7] => 000000 => 0
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [1,6,2,3,4,5,7] => 000010 => 1
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [1,6,2,3,4,5,7] => 000010 => 1
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [1,6,2,3,4,5,7] => 000010 => 1
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [1,6,2,3,5,4,7] => 000110 => 1
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [1,6,2,3,4,5,7] => 000010 => 1
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [1,6,2,3,4,5,7] => 000010 => 1
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [1,6,2,3,4,5,7] => 000010 => 1
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [1,6,2,4,3,5,7] => 001010 => 2
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [1,6,2,3,4,5,7] => 000010 => 1
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [1,6,2,5,3,4,7] => 000110 => 1
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [1,6,2,5,3,4,7] => 000110 => 1
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [1,6,2,3,5,4,7] => 000110 => 1
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [1,6,2,4,5,3,7] => 000110 => 1
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [1,6,2,3,4,5,7] => 000010 => 1
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [1,2,6,3,4,5,7] => 000010 => 1
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [1,2,6,3,4,5,7] => 000010 => 1
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [1,2,6,3,4,5,7] => 000010 => 1
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [1,2,6,3,5,4,7] => 000110 => 1
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [1,2,6,3,4,5,7] => 000010 => 1
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [1,3,6,2,4,5,7] => 000010 => 1
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [1,3,6,2,4,5,7] => 000010 => 1
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [1,2,3,6,4,5,7] => 000010 => 1
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [1,2,3,6,4,5,7] => 000010 => 1
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [1,4,6,2,3,5,7] => 000010 => 1
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [1,4,6,2,3,5,7] => 000010 => 1
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [1,2,4,6,3,5,7] => 000010 => 1
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => [1,3,4,6,2,5,7] => 000010 => 1
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [1,2,3,4,6,5,7] => 000010 => 1
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [1,5,6,2,3,4,7] => 000010 => 1
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [1,5,6,2,3,4,7] => 000010 => 1
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [1,5,6,2,3,4,7] => 000010 => 1
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [1,5,6,2,4,3,7] => 001010 => 2
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [1,5,6,2,3,4,7] => 000010 => 1
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [1,2,5,6,3,4,7] => 000010 => 1
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [1,2,5,6,3,4,7] => 000010 => 1
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => [1,3,5,6,2,4,7] => 000010 => 1
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [1,2,3,5,6,4,7] => 000010 => 1
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => [1,4,5,6,2,3,7] => 000010 => 1
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [1,4,5,6,2,3,7] => 000010 => 1
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [1,2,4,5,6,3,7] => 000010 => 1
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [1,3,4,5,6,2,7] => 000010 => 1
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6,7] => 000000 => 0
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [1,7,2,3,4,6,5] => 000011 => 0
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [1,7,2,3,5,4,6] => 000101 => 1
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [1,7,2,3,6,4,5] => 000011 => 0
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [1,7,2,3,6,4,5] => 000011 => 0
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => [1,7,2,3,4,6,5] => 000011 => 0
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [1,7,2,3,5,6,4] => 000011 => 0
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => [1,7,2,3,4,6,5] => 000011 => 0
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [1,7,2,4,3,5,6] => 001001 => 1
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => [1,7,2,4,3,5,6] => 001001 => 1
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [1,7,2,5,3,4,6] => 000101 => 1
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => [1,7,2,5,3,4,6] => 000101 => 1
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [1,7,2,3,5,4,6] => 000101 => 1
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => [1,7,2,4,5,3,6] => 000101 => 1
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [1,7,2,6,3,4,5] => 000011 => 0
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [1,7,2,6,3,4,5] => 000011 => 0
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [1,7,2,6,3,4,5] => 000011 => 0
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [1,7,2,6,3,5,4] => 000111 => 0
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [1,7,2,6,3,4,5] => 000011 => 0
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [1,7,2,3,6,4,5] => 000011 => 0
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [1,7,2,3,6,4,5] => 000011 => 0
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [1,7,2,4,6,3,5] => 000011 => 0
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [1,7,2,3,4,6,5] => 000011 => 0
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [1,7,2,5,6,3,4] => 000011 => 0
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [1,7,2,5,6,3,4] => 000011 => 0
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [1,7,2,3,5,6,4] => 000011 => 0
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [1,7,2,4,5,6,3] => 000011 => 0
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [1,7,2,3,4,5,6] => 000001 => 0
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [1,2,7,3,4,5,6] => 000001 => 0
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [1,2,7,3,4,5,6] => 000001 => 0
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [1,2,7,3,4,5,6] => 000001 => 0
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => [1,2,7,3,4,6,5] => 000011 => 0
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [1,2,7,3,4,5,6] => 000001 => 0
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [1,2,7,3,4,5,6] => 000001 => 0
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [1,2,7,3,4,5,6] => 000001 => 0
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => [1,2,7,3,5,4,6] => 000101 => 1
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [1,2,7,3,4,5,6] => 000001 => 0
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => [1,2,7,3,6,4,5] => 000011 => 0
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [1,2,7,3,6,4,5] => 000011 => 0
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [1,2,7,3,4,6,5] => 000011 => 0
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [1,2,7,3,5,6,4] => 000011 => 0
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [1,2,7,3,4,5,6] => 000001 => 0
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [1,3,7,2,4,5,6] => 000001 => 0
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => [1,3,7,2,4,5,6] => 000001 => 0
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => [1,3,7,2,4,5,6] => 000001 => 0
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => [1,3,7,2,4,6,5] => 000011 => 0
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [1,3,7,2,4,5,6] => 000001 => 0
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [1,2,3,7,4,5,6] => 000001 => 0
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [1,2,3,7,4,5,6] => 000001 => 0
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [1,2,3,7,4,5,6] => 000001 => 0
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [1,2,3,7,4,6,5] => 000011 => 0
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [1,2,3,7,4,5,6] => 000001 => 0
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [1,4,7,2,3,5,6] => 000001 => 0
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => [1,4,7,2,3,5,6] => 000001 => 0
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => [1,4,7,2,3,5,6] => 000001 => 0
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => [1,4,7,2,3,5,6] => 000001 => 0
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [1,2,4,7,3,5,6] => 000001 => 0
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => [1,2,4,7,3,5,6] => 000001 => 0
[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => [1,3,4,7,2,5,6] => 000001 => 0
[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => [1,3,4,7,2,5,6] => 000001 => 0
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [1,2,3,4,7,5,6] => 000001 => 0
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [1,2,3,4,7,5,6] => 000001 => 0
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [1,5,7,2,3,4,6] => 000001 => 0
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [1,5,7,2,3,4,6] => 000001 => 0
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [1,5,7,2,3,4,6] => 000001 => 0
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [1,5,7,2,4,3,6] => 001001 => 1
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [1,5,7,2,3,4,6] => 000001 => 0
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [1,2,5,7,3,4,6] => 000001 => 0
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [1,2,5,7,3,4,6] => 000001 => 0
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => [1,3,5,7,2,4,6] => 000001 => 0
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [1,2,3,5,7,4,6] => 000001 => 0
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => [1,4,5,7,2,3,6] => 000001 => 0
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => [1,4,5,7,2,3,6] => 000001 => 0
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [1,2,4,5,7,3,6] => 000001 => 0
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [1,3,4,5,7,2,6] => 000001 => 0
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [1,2,3,4,5,7,6] => 000001 => 0
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [1,6,7,2,3,4,5] => 000001 => 0
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [1,6,7,2,3,4,5] => 000001 => 0
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [1,6,7,2,3,4,5] => 000001 => 0
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [1,6,7,2,3,5,4] => 000101 => 1
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [1,6,7,2,3,4,5] => 000001 => 0
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [1,6,7,2,3,4,5] => 000001 => 0
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [1,6,7,2,3,4,5] => 000001 => 0
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [1,6,7,2,4,3,5] => 001001 => 1
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [1,6,7,2,3,4,5] => 000001 => 0
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [1,6,7,2,5,3,4] => 000101 => 1
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [1,6,7,2,5,3,4] => 000101 => 1
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [1,6,7,2,3,5,4] => 000101 => 1
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [1,6,7,2,4,5,3] => 000101 => 1
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [1,6,7,2,3,4,5] => 000001 => 0
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [1,2,6,7,3,4,5] => 000001 => 0
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [1,2,6,7,3,4,5] => 000001 => 0
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [1,2,6,7,3,4,5] => 000001 => 0
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [1,2,6,7,3,5,4] => 000101 => 1
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [1,2,6,7,3,4,5] => 000001 => 0
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => [1,3,6,7,2,4,5] => 000001 => 0
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => [1,3,6,7,2,4,5] => 000001 => 0
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [1,2,3,6,7,4,5] => 000001 => 0
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [1,2,3,6,7,4,5] => 000001 => 0
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [1,4,6,7,2,3,5] => 000001 => 0
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [1,4,6,7,2,3,5] => 000001 => 0
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [1,2,4,6,7,3,5] => 000001 => 0
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [1,3,4,6,7,2,5] => 000001 => 0
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [1,2,3,4,6,7,5] => 000001 => 0
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [1,5,6,7,2,3,4] => 000001 => 0
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [1,5,6,7,2,3,4] => 000001 => 0
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [1,5,6,7,2,3,4] => 000001 => 0
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [1,5,6,7,2,4,3] => 001001 => 1
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [1,5,6,7,2,3,4] => 000001 => 0
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [1,2,5,6,7,3,4] => 000001 => 0
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [1,2,5,6,7,3,4] => 000001 => 0
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [1,3,5,6,7,2,4] => 000001 => 0
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [1,2,3,5,6,7,4] => 000001 => 0
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [1,4,5,6,7,2,3] => 000001 => 0
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [1,4,5,6,7,2,3] => 000001 => 0
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [1,2,4,5,6,7,3] => 000001 => 0
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [1,3,4,5,6,7,2] => 000001 => 0
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [1,2,3,4,5,6,8,7] => 0000001 => 0
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [1,2,3,4,5,8,6,7] => 0000001 => 0
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => [1,2,3,4,5,6,8,7] => 0000001 => 0
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [1,2,3,4,5,7,8,6] => 0000001 => 0
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [1,2,3,4,8,5,6,7] => 0000001 => 0
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [1,2,3,4,8,5,7,6] => 0000011 => 0
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => [1,2,3,4,5,8,6,7] => 0000001 => 0
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => [1,2,3,4,6,8,5,7] => 0000001 => 0
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [1,2,3,4,5,6,8,7] => 0000001 => 0
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => [1,2,3,6,4,5,7,8] => 0000100 => 1
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [6,4,5,7,3,8,2,1] => [1,2,3,8,4,5,7,6] => 0000011 => 0
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [1,2,3,8,4,6,7,5] => 0000011 => 0
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => [1,2,3,4,8,5,6,7] => 0000001 => 0
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => [1,2,3,5,8,4,6,7] => 0000001 => 0
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [1,2,3,4,5,8,6,7] => 0000001 => 0
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [6,3,4,5,7,8,2,1] => [1,2,3,4,5,7,8,6] => 0000001 => 0
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [1,2,3,5,6,7,8,4] => 0000001 => 0
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,2,4,1] => [1,2,4,3,5,6,7,8] => 0010000 => 1
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => [1,2,4,3,5,7,6,8] => 0010010 => 2
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => [1,2,4,3,5,6,7,8] => 0010000 => 1
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => [1,2,4,5,6,3,7,8] => 0000100 => 1
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [1,2,8,3,4,5,6,7] => 0000001 => 0
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [1,2,8,3,4,5,6,7] => 0000001 => 0
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [1,2,8,3,4,5,7,6] => 0000011 => 0
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [6,4,5,7,3,2,8,1] => [1,2,8,3,4,5,7,6] => 0000011 => 0
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => [1,2,8,3,4,5,6,7] => 0000001 => 0
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [1,2,8,3,7,4,5,6] => 0000011 => 0
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [1,2,8,3,7,4,6,5] => 0000111 => 0
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [6,4,5,7,2,3,8,1] => [1,2,3,8,4,5,7,6] => 0000011 => 0
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => [1,2,4,8,3,5,6,7] => 0000001 => 0
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [1,2,3,4,8,5,6,7] => 0000001 => 0
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => [1,2,3,4,5,8,6,7] => 0000001 => 0
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [1,2,6,7,8,3,4,5] => 0000001 => 0
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [1,2,6,7,8,3,4,5] => 0000001 => 0
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => [1,2,3,4,6,7,8,5] => 0000001 => 0
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [1,2,5,6,7,8,3,4] => 0000001 => 0
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [1,2,5,6,7,8,3,4] => 0000001 => 0
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => [1,2,3,5,6,7,8,4] => 0000001 => 0
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [1,2,4,5,6,7,8,3] => 0000001 => 0
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => [1,2,3,4,5,7,8,6] => 0000001 => 0
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => [1,2,3,4,5,8,6,7] => 0000001 => 0
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => [1,2,3,4,5,8,6,7] => 0000001 => 0
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [1,2,3,4,5,6,8,7] => 0000001 => 0
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => [1,2,3,4,5,7,8,6] => 0000001 => 0
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => [1,2,3,6,4,5,7,8] => 0000100 => 1
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => [1,2,3,6,4,5,7,8] => 0000100 => 1
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => [1,2,3,4,6,5,7,8] => 0000100 => 1
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => [1,2,3,5,6,4,7,8] => 0000100 => 1
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => [1,2,3,5,6,7,4,8] => 0000010 => 1
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2] => [1,2,3,8,4,5,7,6] => 0000011 => 0
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [5,6,7,4,3,8,1,2] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => [1,2,3,8,4,7,5,6] => 0000011 => 0
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [5,4,6,7,3,8,1,2] => [1,2,3,8,4,6,7,5] => 0000011 => 0
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => [1,2,3,7,8,4,6,5] => 0000101 => 1
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => [1,2,3,4,7,8,5,6] => 0000001 => 0
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => [1,2,3,5,7,8,4,6] => 0000001 => 0
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => [1,2,3,4,5,7,8,6] => 0000001 => 0
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => [1,2,3,6,7,8,4,5] => 0000001 => 0
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => [1,2,3,6,7,8,4,5] => 0000001 => 0
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => [1,2,3,5,6,7,8,4] => 0000001 => 0
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => [1,3,2,4,5,6,7,8] => 0100000 => 1
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => [1,3,2,4,5,6,8,7] => 0100001 => 1
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => [1,3,2,4,5,6,7,8] => 0100000 => 1
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => [1,3,2,4,5,6,7,8] => 0100000 => 1
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => [1,2,3,4,5,7,8,6] => 0000001 => 0
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => [1,2,3,4,5,8,6,7] => 0000001 => 0
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => [1,2,3,4,7,8,5,6] => 0000001 => 0
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => [1,4,2,3,5,6,7,8] => 0010000 => 1
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => [1,4,2,3,5,6,7,8] => 0010000 => 1
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => [1,4,2,3,5,8,6,7] => 0010001 => 1
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => [1,4,2,3,5,6,7,8] => 0010000 => 1
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,3,1,4] => [1,4,2,3,5,6,7,8] => 0010000 => 1
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [7,8,5,6,2,3,1,4] => [1,4,2,3,5,6,7,8] => 0010000 => 1
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [6,7,5,8,2,3,1,4] => [1,4,2,3,5,8,6,7] => 0010001 => 1
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => [1,4,2,3,5,6,8,7] => 0010001 => 1
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [5,6,7,8,2,3,1,4] => [1,4,2,3,5,6,7,8] => 0010000 => 1
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [1,2,4,3,5,6,7,8] => 0010000 => 1
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => [1,2,4,3,5,6,7,8] => 0010000 => 1
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => [1,2,4,3,5,8,6,7] => 0010001 => 1
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => [1,2,4,3,5,6,8,7] => 0010001 => 1
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => [1,2,4,3,5,6,7,8] => 0010000 => 1
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => 0010000 => 1
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => 0010000 => 1
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => 0010000 => 1
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => [1,3,4,2,5,6,7,8] => 0010000 => 1
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => [1,3,4,2,5,7,8,6] => 0010001 => 1
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => [1,3,4,2,5,6,7,8] => 0010000 => 1
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => [1,2,3,4,5,6,8,7] => 0000001 => 0
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => [1,2,3,4,5,7,6,8] => 0000010 => 1
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => [1,2,3,4,5,8,6,7] => 0000001 => 0
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => [1,2,3,4,5,8,6,7] => 0000001 => 0
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => [1,2,3,4,5,6,8,7] => 0000001 => 0
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => [1,2,3,4,5,7,8,6] => 0000001 => 0
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => [1,5,2,3,4,6,7,8] => 0001000 => 1
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [6,7,8,4,3,2,1,5] => [1,5,2,3,4,6,7,8] => 0001000 => 1
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => [1,5,2,3,4,6,7,8] => 0001000 => 1
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [6,7,8,3,4,2,1,5] => [1,5,2,3,4,6,7,8] => 0001000 => 1
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,2,3,1,5] => [1,5,2,3,4,6,7,8] => 0001000 => 1
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [6,7,8,4,2,3,1,5] => [1,5,2,3,4,6,7,8] => 0001000 => 1
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => [1,5,2,4,3,6,7,8] => 0011000 => 1
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [6,7,8,3,2,4,1,5] => [1,5,2,4,3,6,7,8] => 0011000 => 1
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [8,7,6,2,3,4,1,5] => [1,5,2,3,4,6,7,8] => 0001000 => 1
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [6,7,8,2,3,4,1,5] => [1,5,2,3,4,6,7,8] => 0001000 => 1
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => [1,2,5,3,4,6,7,8] => 0001000 => 1
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => [1,2,5,3,4,6,7,8] => 0001000 => 1
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => [1,2,5,3,4,6,7,8] => 0001000 => 1
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => [1,2,5,3,4,6,7,8] => 0001000 => 1
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => [1,3,5,2,4,6,7,8] => 0001000 => 1
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => [1,3,5,2,4,6,7,8] => 0001000 => 1
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [1,2,3,5,4,6,7,8] => 0001000 => 1
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => [1,2,3,5,4,6,7,8] => 0001000 => 1
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => [1,4,5,2,3,6,7,8] => 0001000 => 1
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [6,7,8,3,2,1,4,5] => [1,4,5,2,3,6,7,8] => 0001000 => 1
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [8,7,6,2,3,1,4,5] => [1,4,5,2,3,6,7,8] => 0001000 => 1
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [6,7,8,2,3,1,4,5] => [1,4,5,2,3,6,7,8] => 0001000 => 1
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => [1,3,4,5,2,6,7,8] => 0001000 => 1
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => [1,3,4,5,2,6,7,8] => 0001000 => 1
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => [1,2,3,4,5,6,8,7] => 0000001 => 0
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => [1,6,2,3,4,5,7,8] => 0000100 => 1
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [7,8,4,5,2,3,1,6] => [1,6,2,3,4,5,7,8] => 0000100 => 1
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [7,8,3,4,2,5,1,6] => [1,6,2,5,3,4,7,8] => 0001100 => 1
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => [1,3,6,2,4,5,7,8] => 0000100 => 1
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => [1,2,3,6,4,5,7,8] => 0000100 => 1
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => [1,2,3,6,4,5,7,8] => 0000100 => 1
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => [1,3,4,6,2,5,7,8] => 0000100 => 1
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => [1,3,4,6,2,5,7,8] => 0000100 => 1
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => [1,2,3,4,6,5,7,8] => 0000100 => 1
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [1,2,3,4,6,5,7,8] => 0000100 => 1
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [8,7,4,3,2,1,5,6] => [1,5,6,2,3,4,7,8] => 0000100 => 1
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => [1,5,6,2,3,4,7,8] => 0000100 => 1
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [7,8,2,3,4,1,5,6] => [1,5,6,2,3,4,7,8] => 0000100 => 1
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => [1,2,5,6,3,4,7,8] => 0000100 => 1
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => [1,3,5,6,2,4,7,8] => 0000100 => 1
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => [1,2,3,5,6,4,7,8] => 0000100 => 1
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => [1,4,5,6,2,3,7,8] => 0000100 => 1
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => [1,4,5,6,2,3,7,8] => 0000100 => 1
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => [1,3,4,5,6,2,7,8] => 0000100 => 1
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => [1,7,2,3,4,5,6,8] => 0000010 => 1
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => [1,7,2,3,4,5,6,8] => 0000010 => 1
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => [1,2,7,3,4,5,6,8] => 0000010 => 1
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [1,2,7,3,4,5,6,8] => 0000010 => 1
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => [1,2,7,3,4,5,6,8] => 0000010 => 1
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => [1,3,7,2,4,5,6,8] => 0000010 => 1
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [1,2,3,7,4,5,6,8] => 0000010 => 1
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => [1,4,7,2,3,5,6,8] => 0000010 => 1
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [8,5,6,2,3,1,4,7] => [1,4,7,2,3,5,6,8] => 0000010 => 1
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => [1,3,4,7,2,5,6,8] => 0000010 => 1
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => [1,2,3,4,7,5,6,8] => 0000010 => 1
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => [1,2,3,4,7,5,6,8] => 0000010 => 1
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => [1,5,7,2,3,4,6,8] => 0000010 => 1
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [8,6,3,4,2,1,5,7] => [1,5,7,2,3,4,6,8] => 0000010 => 1
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => [1,3,5,7,2,4,6,8] => 0000010 => 1
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => [1,5,6,7,2,3,4,8] => 0000010 => 1
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => [1,5,6,7,2,3,4,8] => 0000010 => 1
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => [1,2,3,5,6,7,4,8] => 0000010 => 1
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => [1,4,5,6,7,2,3,8] => 0000010 => 1
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => [1,4,5,6,7,2,3,8] => 0000010 => 1
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => [1,2,4,5,6,7,3,8] => 0000010 => 1
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => [1,3,4,5,6,7,2,8] => 0000010 => 1
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [1,8,2,3,4,5,7,6] => 0000011 => 0
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [1,8,2,3,4,7,5,6] => 0000011 => 0
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [5,6,7,3,4,2,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => [1,8,2,3,5,4,6,7] => 0001001 => 1
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => [1,8,2,3,6,4,5,7] => 0000101 => 1
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [5,6,7,4,2,3,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [6,7,4,5,2,3,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [7,4,5,6,2,3,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [5,6,4,7,2,3,1,8] => [1,8,2,3,4,7,5,6] => 0000011 => 0
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [4,5,6,7,2,3,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => [1,8,2,4,3,5,6,7] => 0010001 => 1
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [6,7,5,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [7,5,6,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => [1,8,2,3,4,5,7,6] => 0000011 => 0
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [6,7,3,4,2,5,1,8] => [1,8,2,5,3,4,6,7] => 0001001 => 1
[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [7,4,5,2,3,6,1,8] => [1,8,2,3,6,4,5,7] => 0000101 => 1
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [5,6,3,4,2,7,1,8] => [1,8,2,7,3,4,5,6] => 0000011 => 0
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [1,8,2,7,3,6,4,5] => 0000111 => 0
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [1,8,2,6,7,3,4,5] => 0000011 => 0
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [1,8,2,4,5,6,7,3] => 0000011 => 0
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [1,2,8,3,4,5,6,7] => 0000001 => 0
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => [1,2,8,3,4,5,6,7] => 0000001 => 0
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [7,4,5,6,3,1,2,8] => [1,2,8,3,4,5,6,7] => 0000001 => 0
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [4,5,6,7,3,1,2,8] => [1,2,8,3,4,5,6,7] => 0000001 => 0
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => [1,3,8,2,4,5,6,7] => 0000001 => 0
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => [1,3,8,2,4,5,7,6] => 0000011 => 0
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => [1,3,8,2,4,6,5,7] => 0000101 => 1
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [7,4,5,6,2,1,3,8] => [1,3,8,2,4,5,6,7] => 0000001 => 0
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [4,5,6,7,2,1,3,8] => [1,3,8,2,4,5,6,7] => 0000001 => 0
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => [1,2,3,8,4,7,5,6] => 0000011 => 0
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => [1,2,3,8,4,6,7,5] => 0000011 => 0
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => [1,2,4,8,3,5,6,7] => 0000001 => 0
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => [1,3,4,8,2,5,6,7] => 0000001 => 0
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => 0000001 => 0
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => 0000001 => 0
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => 0000001 => 0
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => [1,2,3,4,8,5,7,6] => 0000011 => 0
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => 0000001 => 0
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => [1,5,8,2,3,4,6,7] => 0000001 => 0
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => [1,2,5,8,3,4,6,7] => 0000001 => 0
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => [1,2,3,4,5,8,6,7] => 0000001 => 0
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8] => [1,2,4,6,8,3,5,7] => 0000001 => 0
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [1,2,3,4,6,8,5,7] => 0000001 => 0
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8] => [1,5,6,8,2,3,4,7] => 0000001 => 0
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => [1,2,4,5,6,8,3,7] => 0000001 => 0
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => [1,3,4,5,6,8,2,7] => 0000001 => 0
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,6,8,7] => 0000001 => 0
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [1,7,8,2,3,4,5,6] => 0000001 => 0
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [4,2,3,5,6,1,7,8] => [1,7,8,2,3,5,6,4] => 0000101 => 1
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [1,7,8,2,3,4,5,6] => 0000001 => 0
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => [1,2,7,8,3,4,5,6] => 0000001 => 0
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => [1,2,7,8,3,4,6,5] => 0000101 => 1
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => [1,2,7,8,3,4,5,6] => 0000001 => 0
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => [1,2,7,8,3,6,4,5] => 0000101 => 1
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => [1,3,7,8,2,4,5,6] => 0000001 => 0
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => [1,2,3,7,8,4,5,6] => 0000001 => 0
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => [1,4,7,8,2,3,5,6] => 0000001 => 0
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8] => [1,5,7,8,2,3,4,6] => 0000001 => 0
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [6,4,3,1,2,5,7,8] => [1,2,5,7,8,3,4,6] => 0000001 => 0
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => [1,2,3,5,7,8,4,6] => 0000001 => 0
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [6,2,3,1,4,5,7,8] => [1,4,5,7,8,2,3,6] => 0000001 => 0
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => [1,2,3,4,5,7,8,6] => 0000001 => 0
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [1,6,7,8,2,3,4,5] => 0000001 => 0
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [4,5,2,3,1,6,7,8] => [1,6,7,8,2,3,4,5] => 0000001 => 0
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [5,2,3,4,1,6,7,8] => [1,6,7,8,2,3,4,5] => 0000001 => 0
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [1,6,7,8,2,3,4,5] => 0000001 => 0
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => [1,2,4,6,7,8,3,5] => 0000001 => 0
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => [1,2,3,4,6,7,8,5] => 0000001 => 0
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [1,5,6,7,8,2,3,4] => 0000001 => 0
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [1,5,6,7,8,2,4,3] => 0010001 => 1
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [1,5,6,7,8,2,3,4] => 0000001 => 0
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => [1,2,5,6,7,8,3,4] => 0000001 => 0
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => [1,2,3,5,6,7,8,4] => 0000001 => 0
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [1,4,5,6,7,8,2,3] => 0000001 => 0
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => [1,2,4,5,6,7,8,3] => 0000001 => 0
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,2] => 0000001 => 0
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => 00000001 => 0
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [1,2,3,4,5,6,9,7,8] => 00000001 => 0
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [1,2,3,4,5,9,6,7,8] => 00000001 => 0
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [1,2,3,4,9,5,6,7,8] => 00000001 => 0
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [1,2,3,9,4,5,6,7,8] => 00000001 => 0
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [1,2,9,3,4,5,6,7,8] => 00000001 => 0
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [1,9,2,3,4,5,6,7,8] => 00000001 => 0
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,10,9] => 000000001 => 0
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [8,6,7,9,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => 00000001 => 0
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [1,2,3,4,5,6,7,10,8,9] => 000000001 => 0
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [8,7,5,6,9,4,3,2,1] => [1,2,3,4,5,6,9,7,8] => 00000001 => 0
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [1,2,3,4,5,6,10,7,8,9] => 000000001 => 0
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [8,7,6,4,5,9,3,2,1] => [1,2,3,4,5,9,6,7,8] => 00000001 => 0
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [1,2,3,4,5,10,6,7,8,9] => 000000001 => 0
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [8,7,6,5,3,4,9,2,1] => [1,2,3,4,9,5,6,7,8] => 00000001 => 0
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [1,2,3,4,10,5,6,7,8,9] => 000000001 => 0
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,2,3,9,1] => [1,2,3,9,4,5,6,7,8] => 00000001 => 0
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [1,2,3,10,4,5,6,7,8,9] => 000000001 => 0
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9] => [1,2,9,3,4,5,6,7,8] => 00000001 => 0
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [1,2,10,3,4,5,6,7,8,9] => 000000001 => 0
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [1,10,2,3,4,5,6,7,8,9] => 000000001 => 0
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,2,9] => 00000010 => 1
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [1,2,4,5,6,7,8,9,3] => 00000001 => 0
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000 => 0
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,2,10] => 000000010 => 1
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => [1,2,3,5,6,7,8,9,4] => 00000001 => 0
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => [1,2,4,5,6,7,8,9,10,3] => 000000001 => 0
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000 => 0
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => [1,9,2,3,4,5,6,7,8] => 00000001 => 0
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => [1,11,2,3,4,5,6,7,8,9,10] => 0000000001 => 0
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => [1,10,2,3,4,5,6,7,8,9] => 000000001 => 0
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [1,9,2,3,4,5,6,8,7] => 00000011 => 0
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [1,8,9,2,3,4,5,6,7] => 00000001 => 0
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => [1,7,8,9,2,3,4,5,6] => 00000001 => 0
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => [1,6,7,8,9,2,3,4,5] => 00000001 => 0
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => [1,5,6,7,8,9,2,3,4] => 00000001 => 0
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [1,4,5,6,7,8,9,2,3] => 00000001 => 0
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,2] => 00000001 => 0
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => [1,9,10,2,3,4,5,6,7,8] => 000000001 => 0
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => [1,8,9,10,2,3,4,5,6,7] => 000000001 => 0
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => [1,7,8,9,10,2,3,4,5,6] => 000000001 => 0
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => [1,6,7,8,9,10,2,3,4,5] => 000000001 => 0
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => [1,5,6,7,8,9,10,2,3,4] => 000000001 => 0
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [1,4,5,6,7,8,9,10,2,3] => 000000001 => 0
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [1,3,4,5,6,7,8,9,10,2] => 000000001 => 0
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [1,3,4,5,6,7,8,9,10,11,2] => 0000000001 => 0
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [1,9,2,3,4,5,6,7,8] => 00000001 => 0
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [1,8,9,2,3,4,5,6,7] => 00000001 => 0
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [1,10,2,3,4,5,6,7,8,9] => 000000001 => 0
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => [1,2,3,4,5,6,8,9,7] => 00000001 => 0
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => [1,2,3,4,5,6,7,9,8] => 00000001 => 0
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => [1,2,3,4,5,6,7,8,10,9] => 000000001 => 0
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
13,1 35,7 96,36 267,159,3
F2=2
F3=5
F4=13+q
F5=35+7 q
F6=96+36 q
F7=267+159 q+3 q2
Description
The number of descents of a binary word.
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
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.
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.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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