Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
St000291: Binary words ⟶ ℤ
Values
[.,[.,.]] => [2,1] => [1,2] => 0 => 0
[[.,.],.] => [1,2] => [2,1] => 1 => 0
[.,[.,[.,.]]] => [3,2,1] => [1,2,3] => 00 => 0
[.,[[.,.],.]] => [2,3,1] => [1,3,2] => 01 => 0
[[.,.],[.,.]] => [3,1,2] => [2,1,3] => 10 => 1
[[.,[.,.]],.] => [2,1,3] => [3,1,2] => 01 => 0
[[[.,.],.],.] => [1,2,3] => [3,2,1] => 11 => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,2,3,4] => 000 => 0
[.,[.,[[.,.],.]]] => [3,4,2,1] => [1,2,4,3] => 001 => 0
[.,[[.,.],[.,.]]] => [4,2,3,1] => [1,3,2,4] => 010 => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => [1,4,2,3] => 001 => 0
[.,[[[.,.],.],.]] => [2,3,4,1] => [1,4,3,2] => 011 => 0
[[.,.],[.,[.,.]]] => [4,3,1,2] => [2,1,3,4] => 100 => 1
[[.,.],[[.,.],.]] => [3,4,1,2] => [2,1,4,3] => 101 => 1
[[.,[.,.]],[.,.]] => [4,2,1,3] => [3,1,2,4] => 010 => 1
[[[.,.],.],[.,.]] => [4,1,2,3] => [3,2,1,4] => 110 => 1
[[.,[.,[.,.]]],.] => [3,2,1,4] => [4,1,2,3] => 001 => 0
[[.,[[.,.],.]],.] => [2,3,1,4] => [4,1,3,2] => 011 => 0
[[[.,.],[.,.]],.] => [3,1,2,4] => [4,2,1,3] => 101 => 1
[[[.,[.,.]],.],.] => [2,1,3,4] => [4,3,1,2] => 011 => 0
[[[[.,.],.],.],.] => [1,2,3,4] => [4,3,2,1] => 111 => 0
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,2,3,4,5] => 0000 => 0
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [1,2,3,5,4] => 0001 => 0
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [1,2,4,3,5] => 0010 => 1
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [1,2,5,3,4] => 0001 => 0
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [1,2,5,4,3] => 0011 => 0
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [1,3,2,4,5] => 0100 => 1
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [1,3,2,5,4] => 0101 => 1
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [1,4,2,3,5] => 0010 => 1
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [1,4,3,2,5] => 0110 => 1
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [1,5,2,3,4] => 0001 => 0
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [1,5,2,4,3] => 0011 => 0
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [1,5,3,2,4] => 0101 => 1
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [1,5,4,2,3] => 0011 => 0
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,5,4,3,2] => 0111 => 0
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [2,1,3,4,5] => 1000 => 1
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [2,1,3,5,4] => 1001 => 1
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [2,1,4,3,5] => 1010 => 2
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [2,1,5,3,4] => 1001 => 1
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [2,1,5,4,3] => 1011 => 1
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [3,1,2,4,5] => 0100 => 1
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [3,1,2,5,4] => 0101 => 1
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [3,2,1,4,5] => 1100 => 1
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [3,2,1,5,4] => 1101 => 1
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [4,1,2,3,5] => 0010 => 1
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [4,1,3,2,5] => 0110 => 1
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [4,2,1,3,5] => 1010 => 2
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [4,3,1,2,5] => 0110 => 1
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [4,3,2,1,5] => 1110 => 1
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [5,1,2,3,4] => 0001 => 0
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [5,1,2,4,3] => 0011 => 0
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [5,1,3,2,4] => 0101 => 1
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [5,1,4,2,3] => 0011 => 0
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [5,1,4,3,2] => 0111 => 0
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [5,2,1,3,4] => 1001 => 1
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [5,2,1,4,3] => 1011 => 1
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [5,3,1,2,4] => 0101 => 1
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [5,3,2,1,4] => 1101 => 1
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [5,4,1,2,3] => 0011 => 0
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [5,4,1,3,2] => 0111 => 0
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [5,4,2,1,3] => 1011 => 1
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [5,4,3,1,2] => 0111 => 0
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [5,4,3,2,1] => 1111 => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => 00000 => 0
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [1,2,3,4,6,5] => 00001 => 0
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => 00010 => 1
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [1,2,3,6,4,5] => 00001 => 0
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => 00011 => 0
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => 00100 => 1
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [1,2,4,3,6,5] => 00101 => 1
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [1,2,5,3,4,6] => 00010 => 1
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [1,2,5,4,3,6] => 00110 => 1
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [1,2,6,3,4,5] => 00001 => 0
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [1,2,6,3,5,4] => 00011 => 0
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [1,2,6,4,3,5] => 00101 => 1
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [1,2,6,5,3,4] => 00011 => 0
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [1,2,6,5,4,3] => 00111 => 0
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [1,3,2,4,5,6] => 01000 => 1
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [1,3,2,4,6,5] => 01001 => 1
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => 01010 => 2
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [1,3,2,6,4,5] => 01001 => 1
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [1,3,2,6,5,4] => 01011 => 1
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [1,4,2,3,5,6] => 00100 => 1
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [1,4,2,3,6,5] => 00101 => 1
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [1,4,3,2,5,6] => 01100 => 1
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [1,4,3,2,6,5] => 01101 => 1
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [1,5,2,3,4,6] => 00010 => 1
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [1,5,2,4,3,6] => 00110 => 1
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [1,5,3,2,4,6] => 01010 => 2
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [1,5,4,2,3,6] => 00110 => 1
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => 01110 => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [1,6,2,3,4,5] => 00001 => 0
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [1,6,2,3,5,4] => 00011 => 0
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [1,6,2,4,3,5] => 00101 => 1
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [1,6,2,5,3,4] => 00011 => 0
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [1,6,2,5,4,3] => 00111 => 0
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [1,6,3,2,4,5] => 01001 => 1
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [1,6,3,2,5,4] => 01011 => 1
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [1,6,4,2,3,5] => 00101 => 1
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [1,6,4,3,2,5] => 01101 => 1
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [1,6,5,2,3,4] => 00011 => 0
>>> Load all 1948 entries. <<<[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [1,6,5,2,4,3] => 00111 => 0
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [1,6,5,3,2,4] => 01011 => 1
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [1,6,5,4,2,3] => 00111 => 0
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => 01111 => 0
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [2,1,3,4,5,6] => 10000 => 1
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => 10001 => 1
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [2,1,3,5,4,6] => 10010 => 2
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [2,1,3,6,4,5] => 10001 => 1
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [2,1,3,6,5,4] => 10011 => 1
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [2,1,4,3,5,6] => 10100 => 2
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => 10101 => 2
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [2,1,5,3,4,6] => 10010 => 2
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [2,1,5,4,3,6] => 10110 => 2
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [2,1,6,3,4,5] => 10001 => 1
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [2,1,6,3,5,4] => 10011 => 1
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [2,1,6,4,3,5] => 10101 => 2
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [2,1,6,5,3,4] => 10011 => 1
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [2,1,6,5,4,3] => 10111 => 1
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [3,1,2,4,5,6] => 01000 => 1
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [3,1,2,4,6,5] => 01001 => 1
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [3,1,2,5,4,6] => 01010 => 2
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [3,1,2,6,4,5] => 01001 => 1
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [3,1,2,6,5,4] => 01011 => 1
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [3,2,1,4,5,6] => 11000 => 1
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [3,2,1,4,6,5] => 11001 => 1
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => 11010 => 2
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => 11001 => 1
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => 11011 => 1
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [4,1,2,3,5,6] => 00100 => 1
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [4,1,2,3,6,5] => 00101 => 1
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [4,1,3,2,5,6] => 01100 => 1
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [4,1,3,2,6,5] => 01101 => 1
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [4,2,1,3,5,6] => 10100 => 2
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [4,2,1,3,6,5] => 10101 => 2
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [4,3,1,2,5,6] => 01100 => 1
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [4,3,1,2,6,5] => 01101 => 1
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => 11100 => 1
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => 11101 => 1
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [5,1,2,3,4,6] => 00010 => 1
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [5,1,2,4,3,6] => 00110 => 1
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [5,1,3,2,4,6] => 01010 => 2
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [5,1,4,2,3,6] => 00110 => 1
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [5,1,4,3,2,6] => 01110 => 1
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [5,2,1,3,4,6] => 10010 => 2
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => 10110 => 2
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [5,3,1,2,4,6] => 01010 => 2
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => 11010 => 2
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [5,4,1,2,3,6] => 00110 => 1
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [5,4,1,3,2,6] => 01110 => 1
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => 10110 => 2
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => 01110 => 1
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => 11110 => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => 00001 => 0
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [6,1,2,3,5,4] => 00011 => 0
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [6,1,2,4,3,5] => 00101 => 1
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [6,1,2,5,3,4] => 00011 => 0
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [6,1,2,5,4,3] => 00111 => 0
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [6,1,3,2,4,5] => 01001 => 1
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [6,1,3,2,5,4] => 01011 => 1
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [6,1,4,2,3,5] => 00101 => 1
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [6,1,4,3,2,5] => 01101 => 1
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [6,1,5,2,3,4] => 00011 => 0
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [6,1,5,2,4,3] => 00111 => 0
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [6,1,5,3,2,4] => 01011 => 1
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [6,1,5,4,2,3] => 00111 => 0
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => 01111 => 0
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [6,2,1,3,4,5] => 10001 => 1
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [6,2,1,3,5,4] => 10011 => 1
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [6,2,1,4,3,5] => 10101 => 2
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [6,2,1,5,3,4] => 10011 => 1
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [6,2,1,5,4,3] => 10111 => 1
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [6,3,1,2,4,5] => 01001 => 1
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [6,3,1,2,5,4] => 01011 => 1
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [6,3,2,1,4,5] => 11001 => 1
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [6,3,2,1,5,4] => 11011 => 1
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [6,4,1,2,3,5] => 00101 => 1
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [6,4,1,3,2,5] => 01101 => 1
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [6,4,2,1,3,5] => 10101 => 2
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [6,4,3,1,2,5] => 01101 => 1
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [6,4,3,2,1,5] => 11101 => 1
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => 00011 => 0
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [6,5,1,2,4,3] => 00111 => 0
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [6,5,1,3,2,4] => 01011 => 1
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [6,5,1,4,2,3] => 00111 => 0
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => 01111 => 0
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [6,5,2,1,3,4] => 10011 => 1
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [6,5,2,1,4,3] => 10111 => 1
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [6,5,3,1,2,4] => 01011 => 1
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [6,5,3,2,1,4] => 11011 => 1
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => 00111 => 0
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => 01111 => 0
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [6,5,4,2,1,3] => 10111 => 1
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => 01111 => 0
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 11111 => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 000000 => 0
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [1,2,3,4,5,7,6] => 000001 => 0
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [1,2,3,4,6,5,7] => 000010 => 1
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [1,2,3,4,7,5,6] => 000001 => 0
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [1,2,3,4,7,6,5] => 000011 => 0
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [1,2,3,5,4,6,7] => 000100 => 1
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [1,2,3,5,4,7,6] => 000101 => 1
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [1,2,3,6,4,5,7] => 000010 => 1
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [1,2,3,6,5,4,7] => 000110 => 1
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [1,2,3,7,4,5,6] => 000001 => 0
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [1,2,3,7,4,6,5] => 000011 => 0
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [1,2,3,7,5,4,6] => 000101 => 1
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [1,2,3,7,6,4,5] => 000011 => 0
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => 000111 => 0
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [1,2,4,3,5,6,7] => 001000 => 1
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [1,2,4,3,5,7,6] => 001001 => 1
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [1,2,4,3,6,5,7] => 001010 => 2
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [1,2,4,3,7,5,6] => 001001 => 1
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [1,2,4,3,7,6,5] => 001011 => 1
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [1,2,5,3,4,6,7] => 000100 => 1
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [1,2,5,3,4,7,6] => 000101 => 1
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => 001100 => 1
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [1,2,5,4,3,7,6] => 001101 => 1
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => [1,2,6,3,4,5,7] => 000010 => 1
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => [1,2,6,3,5,4,7] => 000110 => 1
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [1,2,6,4,3,5,7] => 001010 => 2
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => [1,2,6,5,3,4,7] => 000110 => 1
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [1,2,6,5,4,3,7] => 001110 => 1
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [1,2,7,3,4,5,6] => 000001 => 0
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [1,2,7,3,4,6,5] => 000011 => 0
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [1,2,7,3,5,4,6] => 000101 => 1
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [1,2,7,3,6,4,5] => 000011 => 0
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [1,2,7,3,6,5,4] => 000111 => 0
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [1,2,7,4,3,5,6] => 001001 => 1
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [1,2,7,4,3,6,5] => 001011 => 1
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [1,2,7,5,3,4,6] => 000101 => 1
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [1,2,7,5,4,3,6] => 001101 => 1
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [1,2,7,6,3,4,5] => 000011 => 0
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [1,2,7,6,3,5,4] => 000111 => 0
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [1,2,7,6,4,3,5] => 001011 => 1
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [1,2,7,6,5,3,4] => 000111 => 0
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [1,2,7,6,5,4,3] => 001111 => 0
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [1,3,2,4,5,6,7] => 010000 => 1
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [1,3,2,4,5,7,6] => 010001 => 1
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => 010010 => 2
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [1,3,2,4,7,5,6] => 010001 => 1
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [1,3,2,4,7,6,5] => 010011 => 1
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,3,2,5,4,6,7] => 010100 => 2
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [1,3,2,5,4,7,6] => 010101 => 2
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [1,3,2,6,4,5,7] => 010010 => 2
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [1,3,2,6,5,4,7] => 010110 => 2
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [1,3,2,7,4,5,6] => 010001 => 1
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [1,3,2,7,4,6,5] => 010011 => 1
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [1,3,2,7,5,4,6] => 010101 => 2
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => [1,3,2,7,6,4,5] => 010011 => 1
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [1,3,2,7,6,5,4] => 010111 => 1
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [1,4,2,3,5,6,7] => 001000 => 1
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [1,4,2,3,5,7,6] => 001001 => 1
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => [1,4,2,3,6,5,7] => 001010 => 2
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => [1,4,2,3,7,5,6] => 001001 => 1
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => [1,4,2,3,7,6,5] => 001011 => 1
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [1,4,3,2,5,6,7] => 011000 => 1
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [1,4,3,2,5,7,6] => 011001 => 1
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [1,4,3,2,6,5,7] => 011010 => 2
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [1,4,3,2,7,5,6] => 011001 => 1
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [1,4,3,2,7,6,5] => 011011 => 1
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [1,5,2,3,4,6,7] => 000100 => 1
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => [1,5,2,3,4,7,6] => 000101 => 1
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [1,5,2,4,3,6,7] => 001100 => 1
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => [1,5,2,4,3,7,6] => 001101 => 1
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [1,5,3,2,4,6,7] => 010100 => 2
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [1,5,3,2,4,7,6] => 010101 => 2
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [1,5,4,2,3,6,7] => 001100 => 1
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => [1,5,4,2,3,7,6] => 001101 => 1
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [1,5,4,3,2,6,7] => 011100 => 1
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [1,5,4,3,2,7,6] => 011101 => 1
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [1,6,2,3,4,5,7] => 000010 => 1
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [1,6,2,3,5,4,7] => 000110 => 1
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [1,6,2,4,3,5,7] => 001010 => 2
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [1,6,2,5,3,4,7] => 000110 => 1
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [1,6,2,5,4,3,7] => 001110 => 1
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [1,6,3,2,4,5,7] => 010010 => 2
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [1,6,3,2,5,4,7] => 010110 => 2
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [1,6,4,2,3,5,7] => 001010 => 2
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [1,6,4,3,2,5,7] => 011010 => 2
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [1,6,5,2,3,4,7] => 000110 => 1
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [1,6,5,2,4,3,7] => 001110 => 1
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [1,6,5,3,2,4,7] => 010110 => 2
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [1,6,5,4,2,3,7] => 001110 => 1
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [1,6,5,4,3,2,7] => 011110 => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [1,7,2,3,4,5,6] => 000001 => 0
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [1,7,2,3,4,6,5] => 000011 => 0
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [1,7,2,3,5,4,6] => 000101 => 1
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [1,7,2,3,6,4,5] => 000011 => 0
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [1,7,2,3,6,5,4] => 000111 => 0
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [1,7,2,4,3,5,6] => 001001 => 1
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [1,7,2,4,3,6,5] => 001011 => 1
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [1,7,2,5,3,4,6] => 000101 => 1
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [1,7,2,5,4,3,6] => 001101 => 1
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [1,7,2,6,3,4,5] => 000011 => 0
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [1,7,2,6,3,5,4] => 000111 => 0
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => [1,7,2,6,4,3,5] => 001011 => 1
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [1,7,2,6,5,3,4] => 000111 => 0
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [1,7,2,6,5,4,3] => 001111 => 0
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [1,7,3,2,4,5,6] => 010001 => 1
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [1,7,3,2,4,6,5] => 010011 => 1
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [1,7,3,2,5,4,6] => 010101 => 2
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [1,7,3,2,6,4,5] => 010011 => 1
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [1,7,3,2,6,5,4] => 010111 => 1
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [1,7,4,2,3,5,6] => 001001 => 1
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => [1,7,4,2,3,6,5] => 001011 => 1
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [1,7,4,3,2,5,6] => 011001 => 1
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [1,7,4,3,2,6,5] => 011011 => 1
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [1,7,5,2,3,4,6] => 000101 => 1
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => [1,7,5,2,4,3,6] => 001101 => 1
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => [1,7,5,3,2,4,6] => 010101 => 2
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => [1,7,5,4,2,3,6] => 001101 => 1
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [1,7,5,4,3,2,6] => 011101 => 1
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [1,7,6,2,3,4,5] => 000011 => 0
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [1,7,6,2,3,5,4] => 000111 => 0
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [1,7,6,2,4,3,5] => 001011 => 1
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [1,7,6,2,5,3,4] => 000111 => 0
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [1,7,6,2,5,4,3] => 001111 => 0
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [1,7,6,3,2,4,5] => 010011 => 1
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [1,7,6,3,2,5,4] => 010111 => 1
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [1,7,6,4,2,3,5] => 001011 => 1
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [1,7,6,4,3,2,5] => 011011 => 1
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [1,7,6,5,2,3,4] => 000111 => 0
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [1,7,6,5,2,4,3] => 001111 => 0
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [1,7,6,5,3,2,4] => 010111 => 1
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [1,7,6,5,4,2,3] => 001111 => 0
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => 011111 => 0
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [2,1,3,4,5,6,7] => 100000 => 1
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [2,1,3,4,5,7,6] => 100001 => 1
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [2,1,3,4,6,5,7] => 100010 => 2
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [2,1,3,4,7,5,6] => 100001 => 1
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [2,1,3,4,7,6,5] => 100011 => 1
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [2,1,3,5,4,6,7] => 100100 => 2
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [2,1,3,5,4,7,6] => 100101 => 2
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [2,1,3,6,4,5,7] => 100010 => 2
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [2,1,3,6,5,4,7] => 100110 => 2
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [2,1,3,7,4,5,6] => 100001 => 1
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [2,1,3,7,4,6,5] => 100011 => 1
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [2,1,3,7,5,4,6] => 100101 => 2
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => [2,1,3,7,6,4,5] => 100011 => 1
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [2,1,3,7,6,5,4] => 100111 => 1
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [2,1,4,3,5,6,7] => 101000 => 2
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [2,1,4,3,5,7,6] => 101001 => 2
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [2,1,4,3,6,5,7] => 101010 => 3
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [2,1,4,3,7,5,6] => 101001 => 2
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [2,1,4,3,7,6,5] => 101011 => 2
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [2,1,5,3,4,6,7] => 100100 => 2
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [2,1,5,3,4,7,6] => 100101 => 2
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [2,1,5,4,3,6,7] => 101100 => 2
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [2,1,5,4,3,7,6] => 101101 => 2
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [2,1,6,3,4,5,7] => 100010 => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [2,1,6,3,5,4,7] => 100110 => 2
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [2,1,6,4,3,5,7] => 101010 => 3
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [2,1,6,5,3,4,7] => 100110 => 2
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [2,1,6,5,4,3,7] => 101110 => 2
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [2,1,7,3,4,5,6] => 100001 => 1
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [2,1,7,3,4,6,5] => 100011 => 1
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [2,1,7,3,5,4,6] => 100101 => 2
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => [2,1,7,3,6,4,5] => 100011 => 1
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [2,1,7,3,6,5,4] => 100111 => 1
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [2,1,7,4,3,5,6] => 101001 => 2
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [2,1,7,4,3,6,5] => 101011 => 2
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => [2,1,7,5,3,4,6] => 100101 => 2
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [2,1,7,5,4,3,6] => 101101 => 2
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => [2,1,7,6,3,4,5] => 100011 => 1
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [2,1,7,6,3,5,4] => 100111 => 1
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [2,1,7,6,4,3,5] => 101011 => 2
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [2,1,7,6,5,3,4] => 100111 => 1
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [2,1,7,6,5,4,3] => 101111 => 1
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [3,1,2,4,5,6,7] => 010000 => 1
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [3,1,2,4,5,7,6] => 010001 => 1
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => [3,1,2,4,6,5,7] => 010010 => 2
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => [3,1,2,4,7,5,6] => 010001 => 1
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => [3,1,2,4,7,6,5] => 010011 => 1
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [3,1,2,5,4,6,7] => 010100 => 2
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => [3,1,2,5,4,7,6] => 010101 => 2
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => [3,1,2,6,4,5,7] => 010010 => 2
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [3,1,2,6,5,4,7] => 010110 => 2
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [3,1,2,7,4,5,6] => 010001 => 1
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => [3,1,2,7,4,6,5] => 010011 => 1
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => [3,1,2,7,5,4,6] => 010101 => 2
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => [3,1,2,7,6,4,5] => 010011 => 1
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [3,1,2,7,6,5,4] => 010111 => 1
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [3,2,1,4,5,6,7] => 110000 => 1
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [3,2,1,4,5,7,6] => 110001 => 1
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [3,2,1,4,6,5,7] => 110010 => 2
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [3,2,1,4,7,5,6] => 110001 => 1
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [3,2,1,4,7,6,5] => 110011 => 1
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [3,2,1,5,4,6,7] => 110100 => 2
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [3,2,1,5,4,7,6] => 110101 => 2
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [3,2,1,6,4,5,7] => 110010 => 2
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [3,2,1,6,5,4,7] => 110110 => 2
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [3,2,1,7,4,5,6] => 110001 => 1
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [3,2,1,7,4,6,5] => 110011 => 1
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [3,2,1,7,5,4,6] => 110101 => 2
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => [3,2,1,7,6,4,5] => 110011 => 1
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [3,2,1,7,6,5,4] => 110111 => 1
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [4,1,2,3,5,6,7] => 001000 => 1
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => [4,1,2,3,5,7,6] => 001001 => 1
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => [4,1,2,3,6,5,7] => 001010 => 2
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => [4,1,2,3,7,5,6] => 001001 => 1
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => [4,1,2,3,7,6,5] => 001011 => 1
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [4,1,3,2,5,6,7] => 011000 => 1
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => [4,1,3,2,5,7,6] => 011001 => 1
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => [4,1,3,2,6,5,7] => 011010 => 2
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => [4,1,3,2,7,5,6] => 011001 => 1
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => [4,1,3,2,7,6,5] => 011011 => 1
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [4,2,1,3,5,6,7] => 101000 => 2
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [4,2,1,3,5,7,6] => 101001 => 2
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [4,2,1,3,6,5,7] => 101010 => 3
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [4,2,1,3,7,5,6] => 101001 => 2
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [4,2,1,3,7,6,5] => 101011 => 2
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [4,3,1,2,5,6,7] => 011000 => 1
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => [4,3,1,2,5,7,6] => 011001 => 1
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => [4,3,1,2,6,5,7] => 011010 => 2
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => [4,3,1,2,7,5,6] => 011001 => 1
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => [4,3,1,2,7,6,5] => 011011 => 1
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [4,3,2,1,5,6,7] => 111000 => 1
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [4,3,2,1,5,7,6] => 111001 => 1
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [4,3,2,1,6,5,7] => 111010 => 2
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [4,3,2,1,7,5,6] => 111001 => 1
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => 111011 => 1
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [5,1,2,3,4,6,7] => 000100 => 1
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [5,1,2,3,4,7,6] => 000101 => 1
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [5,1,2,4,3,6,7] => 001100 => 1
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [5,1,2,4,3,7,6] => 001101 => 1
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [5,1,3,2,4,6,7] => 010100 => 2
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [5,1,3,2,4,7,6] => 010101 => 2
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [5,1,4,2,3,6,7] => 001100 => 1
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [5,1,4,2,3,7,6] => 001101 => 1
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [5,1,4,3,2,6,7] => 011100 => 1
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [5,1,4,3,2,7,6] => 011101 => 1
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [5,2,1,3,4,6,7] => 100100 => 2
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [5,2,1,3,4,7,6] => 100101 => 2
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [5,2,1,4,3,6,7] => 101100 => 2
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [5,2,1,4,3,7,6] => 101101 => 2
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [5,3,1,2,4,6,7] => 010100 => 2
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [5,3,1,2,4,7,6] => 010101 => 2
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [5,3,2,1,4,6,7] => 110100 => 2
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [5,3,2,1,4,7,6] => 110101 => 2
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [5,4,1,2,3,6,7] => 001100 => 1
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [5,4,1,2,3,7,6] => 001101 => 1
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [5,4,1,3,2,6,7] => 011100 => 1
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [5,4,1,3,2,7,6] => 011101 => 1
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [5,4,2,1,3,6,7] => 101100 => 2
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [5,4,2,1,3,7,6] => 101101 => 2
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [5,4,3,1,2,6,7] => 011100 => 1
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => [5,4,3,1,2,7,6] => 011101 => 1
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [5,4,3,2,1,6,7] => 111100 => 1
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => 111101 => 1
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [6,1,2,3,4,5,7] => 000010 => 1
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [6,1,2,3,5,4,7] => 000110 => 1
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [6,1,2,4,3,5,7] => 001010 => 2
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [6,1,2,5,3,4,7] => 000110 => 1
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [6,1,2,5,4,3,7] => 001110 => 1
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [6,1,3,2,4,5,7] => 010010 => 2
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [6,1,3,2,5,4,7] => 010110 => 2
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [6,1,4,2,3,5,7] => 001010 => 2
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [6,1,4,3,2,5,7] => 011010 => 2
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [6,1,5,2,3,4,7] => 000110 => 1
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [6,1,5,2,4,3,7] => 001110 => 1
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [6,1,5,3,2,4,7] => 010110 => 2
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [6,1,5,4,2,3,7] => 001110 => 1
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [6,1,5,4,3,2,7] => 011110 => 1
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [6,2,1,3,4,5,7] => 100010 => 2
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [6,2,1,3,5,4,7] => 100110 => 2
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [6,2,1,4,3,5,7] => 101010 => 3
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [6,2,1,5,3,4,7] => 100110 => 2
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [6,2,1,5,4,3,7] => 101110 => 2
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [6,3,1,2,4,5,7] => 010010 => 2
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [6,3,1,2,5,4,7] => 010110 => 2
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [6,3,2,1,4,5,7] => 110010 => 2
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [6,3,2,1,5,4,7] => 110110 => 2
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [6,4,1,2,3,5,7] => 001010 => 2
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [6,4,1,3,2,5,7] => 011010 => 2
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [6,4,2,1,3,5,7] => 101010 => 3
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => [6,4,3,1,2,5,7] => 011010 => 2
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [6,4,3,2,1,5,7] => 111010 => 2
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [6,5,1,2,3,4,7] => 000110 => 1
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [6,5,1,2,4,3,7] => 001110 => 1
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [6,5,1,3,2,4,7] => 010110 => 2
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [6,5,1,4,2,3,7] => 001110 => 1
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [6,5,1,4,3,2,7] => 011110 => 1
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [6,5,2,1,3,4,7] => 100110 => 2
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [6,5,2,1,4,3,7] => 101110 => 2
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => [6,5,3,1,2,4,7] => 010110 => 2
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [6,5,3,2,1,4,7] => 110110 => 2
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => [6,5,4,1,2,3,7] => 001110 => 1
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [6,5,4,1,3,2,7] => 011110 => 1
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [6,5,4,2,1,3,7] => 101110 => 2
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [6,5,4,3,1,2,7] => 011110 => 1
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => 111110 => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [7,1,2,3,4,5,6] => 000001 => 0
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [7,1,2,3,4,6,5] => 000011 => 0
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [7,1,2,3,5,4,6] => 000101 => 1
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [7,1,2,3,6,4,5] => 000011 => 0
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [7,1,2,3,6,5,4] => 000111 => 0
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [7,1,2,4,3,5,6] => 001001 => 1
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [7,1,2,4,3,6,5] => 001011 => 1
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [7,1,2,5,3,4,6] => 000101 => 1
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [7,1,2,5,4,3,6] => 001101 => 1
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [7,1,2,6,3,4,5] => 000011 => 0
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [7,1,2,6,3,5,4] => 000111 => 0
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => [7,1,2,6,4,3,5] => 001011 => 1
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [7,1,2,6,5,3,4] => 000111 => 0
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [7,1,2,6,5,4,3] => 001111 => 0
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => [7,1,3,2,4,5,6] => 010001 => 1
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [7,1,3,2,4,6,5] => 010011 => 1
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [7,1,3,2,5,4,6] => 010101 => 2
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => [7,1,3,2,6,4,5] => 010011 => 1
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => [7,1,3,2,6,5,4] => 010111 => 1
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [7,1,4,2,3,5,6] => 001001 => 1
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => [7,1,4,2,3,6,5] => 001011 => 1
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [7,1,4,3,2,5,6] => 011001 => 1
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => [7,1,4,3,2,6,5] => 011011 => 1
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [7,1,5,2,3,4,6] => 000101 => 1
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => [7,1,5,2,4,3,6] => 001101 => 1
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [7,1,5,3,2,4,6] => 010101 => 2
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => [7,1,5,4,2,3,6] => 001101 => 1
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => [7,1,5,4,3,2,6] => 011101 => 1
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [7,1,6,2,3,4,5] => 000011 => 0
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [7,1,6,2,3,5,4] => 000111 => 0
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [7,1,6,2,4,3,5] => 001011 => 1
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [7,1,6,2,5,3,4] => 000111 => 0
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [7,1,6,2,5,4,3] => 001111 => 0
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [7,1,6,3,2,4,5] => 010011 => 1
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [7,1,6,3,2,5,4] => 010111 => 1
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [7,1,6,4,2,3,5] => 001011 => 1
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [7,1,6,4,3,2,5] => 011011 => 1
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [7,1,6,5,2,3,4] => 000111 => 0
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [7,1,6,5,2,4,3] => 001111 => 0
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [7,1,6,5,3,2,4] => 010111 => 1
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [7,1,6,5,4,2,3] => 001111 => 0
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [7,1,6,5,4,3,2] => 011111 => 0
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [7,2,1,3,4,5,6] => 100001 => 1
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [7,2,1,3,4,6,5] => 100011 => 1
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [7,2,1,3,5,4,6] => 100101 => 2
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => [7,2,1,3,6,4,5] => 100011 => 1
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [7,2,1,3,6,5,4] => 100111 => 1
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [7,2,1,4,3,5,6] => 101001 => 2
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [7,2,1,4,3,6,5] => 101011 => 2
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => [7,2,1,5,3,4,6] => 100101 => 2
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [7,2,1,5,4,3,6] => 101101 => 2
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => [7,2,1,6,3,4,5] => 100011 => 1
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [7,2,1,6,3,5,4] => 100111 => 1
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [7,2,1,6,4,3,5] => 101011 => 2
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [7,2,1,6,5,3,4] => 100111 => 1
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [7,2,1,6,5,4,3] => 101111 => 1
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [7,3,1,2,4,5,6] => 010001 => 1
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => [7,3,1,2,4,6,5] => 010011 => 1
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => [7,3,1,2,5,4,6] => 010101 => 2
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => [7,3,1,2,6,4,5] => 010011 => 1
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [7,3,1,2,6,5,4] => 010111 => 1
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [7,3,2,1,4,5,6] => 110001 => 1
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [7,3,2,1,4,6,5] => 110011 => 1
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [7,3,2,1,5,4,6] => 110101 => 2
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [7,3,2,1,6,4,5] => 110011 => 1
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [7,3,2,1,6,5,4] => 110111 => 1
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [7,4,1,2,3,5,6] => 001001 => 1
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => [7,4,1,2,3,6,5] => 001011 => 1
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => [7,4,1,3,2,5,6] => 011001 => 1
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => [7,4,1,3,2,6,5] => 011011 => 1
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [7,4,2,1,3,5,6] => 101001 => 2
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => [7,4,2,1,3,6,5] => 101011 => 2
[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => [7,4,3,1,2,5,6] => 011001 => 1
[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => [7,4,3,1,2,6,5] => 011011 => 1
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [7,4,3,2,1,5,6] => 111001 => 1
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [7,4,3,2,1,6,5] => 111011 => 1
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [7,5,1,2,3,4,6] => 000101 => 1
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [7,5,1,2,4,3,6] => 001101 => 1
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [7,5,1,3,2,4,6] => 010101 => 2
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [7,5,1,4,2,3,6] => 001101 => 1
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [7,5,1,4,3,2,6] => 011101 => 1
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [7,5,2,1,3,4,6] => 100101 => 2
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [7,5,2,1,4,3,6] => 101101 => 2
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => [7,5,3,1,2,4,6] => 010101 => 2
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [7,5,3,2,1,4,6] => 110101 => 2
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => [7,5,4,1,2,3,6] => 001101 => 1
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => [7,5,4,1,3,2,6] => 011101 => 1
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [7,5,4,2,1,3,6] => 101101 => 2
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [7,5,4,3,1,2,6] => 011101 => 1
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [7,5,4,3,2,1,6] => 111101 => 1
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [7,6,1,2,3,4,5] => 000011 => 0
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [7,6,1,2,3,5,4] => 000111 => 0
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [7,6,1,2,4,3,5] => 001011 => 1
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [7,6,1,2,5,3,4] => 000111 => 0
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [7,6,1,2,5,4,3] => 001111 => 0
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [7,6,1,3,2,4,5] => 010011 => 1
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [7,6,1,3,2,5,4] => 010111 => 1
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [7,6,1,4,2,3,5] => 001011 => 1
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [7,6,1,4,3,2,5] => 011011 => 1
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [7,6,1,5,2,3,4] => 000111 => 0
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [7,6,1,5,2,4,3] => 001111 => 0
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [7,6,1,5,3,2,4] => 010111 => 1
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [7,6,1,5,4,2,3] => 001111 => 0
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [7,6,1,5,4,3,2] => 011111 => 0
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [7,6,2,1,3,4,5] => 100011 => 1
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [7,6,2,1,3,5,4] => 100111 => 1
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [7,6,2,1,4,3,5] => 101011 => 2
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [7,6,2,1,5,3,4] => 100111 => 1
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [7,6,2,1,5,4,3] => 101111 => 1
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => [7,6,3,1,2,4,5] => 010011 => 1
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => [7,6,3,1,2,5,4] => 010111 => 1
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [7,6,3,2,1,4,5] => 110011 => 1
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [7,6,3,2,1,5,4] => 110111 => 1
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [7,6,4,1,2,3,5] => 001011 => 1
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [7,6,4,1,3,2,5] => 011011 => 1
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [7,6,4,2,1,3,5] => 101011 => 2
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [7,6,4,3,1,2,5] => 011011 => 1
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [7,6,4,3,2,1,5] => 111011 => 1
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [7,6,5,1,2,3,4] => 000111 => 0
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [7,6,5,1,2,4,3] => 001111 => 0
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [7,6,5,1,3,2,4] => 010111 => 1
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [7,6,5,1,4,2,3] => 001111 => 0
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [7,6,5,1,4,3,2] => 011111 => 0
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [7,6,5,2,1,3,4] => 100111 => 1
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [7,6,5,2,1,4,3] => 101111 => 1
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [7,6,5,3,1,2,4] => 010111 => 1
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [7,6,5,3,2,1,4] => 110111 => 1
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [7,6,5,4,1,2,3] => 001111 => 0
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [7,6,5,4,1,3,2] => 011111 => 0
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [7,6,5,4,2,1,3] => 101111 => 1
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [7,6,5,4,3,1,2] => 011111 => 0
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => 111111 => 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] => [1,2,3,4,5,6,8,7] => 0000001 => 0
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [8,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,8] => 0000010 => 1
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [1,2,3,4,5,8,6,7] => 0000001 => 0
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [1,2,3,4,5,8,7,6] => 0000011 => 0
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [8,7,5,6,4,3,2,1] => [1,2,3,4,6,5,7,8] => 0000100 => 1
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => [1,2,3,4,6,5,8,7] => 0000101 => 1
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [8,6,5,7,4,3,2,1] => [1,2,3,4,7,5,6,8] => 0000010 => 1
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [8,5,6,7,4,3,2,1] => [1,2,3,4,7,6,5,8] => 0000110 => 1
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [1,2,3,4,8,5,6,7] => 0000001 => 0
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => [1,2,3,4,8,5,7,6] => 0000011 => 0
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => [1,2,3,4,8,6,5,7] => 0000101 => 1
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [1,2,3,4,8,7,5,6] => 0000011 => 0
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [1,2,3,4,8,7,6,5] => 0000111 => 0
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [1,2,3,5,4,6,7,8] => 0001000 => 1
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [1,2,3,5,4,6,8,7] => 0001001 => 1
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [1,2,3,5,4,7,6,8] => 0001010 => 2
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [7,6,8,4,5,3,2,1] => [1,2,3,5,4,8,6,7] => 0001001 => 1
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [6,7,8,4,5,3,2,1] => [1,2,3,5,4,8,7,6] => 0001011 => 1
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [8,7,5,4,6,3,2,1] => [1,2,3,6,4,5,7,8] => 0000100 => 1
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [7,8,5,4,6,3,2,1] => [1,2,3,6,4,5,8,7] => 0000101 => 1
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [8,7,4,5,6,3,2,1] => [1,2,3,6,5,4,7,8] => 0001100 => 1
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [7,8,4,5,6,3,2,1] => [1,2,3,6,5,4,8,7] => 0001101 => 1
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [8,6,5,4,7,3,2,1] => [1,2,3,7,4,5,6,8] => 0000010 => 1
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [8,5,6,4,7,3,2,1] => [1,2,3,7,4,6,5,8] => 0000110 => 1
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [8,6,4,5,7,3,2,1] => [1,2,3,7,5,4,6,8] => 0001010 => 2
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [8,5,4,6,7,3,2,1] => [1,2,3,7,6,4,5,8] => 0000110 => 1
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [8,4,5,6,7,3,2,1] => [1,2,3,7,6,5,4,8] => 0001110 => 1
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [1,2,3,8,4,5,6,7] => 0000001 => 0
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => [1,2,3,8,4,5,7,6] => 0000011 => 0
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [7,5,6,4,8,3,2,1] => [1,2,3,8,4,6,5,7] => 0000101 => 1
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [1,2,3,8,4,7,5,6] => 0000011 => 0
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => [1,2,3,8,4,7,6,5] => 0000111 => 0
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => [1,2,3,8,5,4,6,7] => 0001001 => 1
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [6,7,4,5,8,3,2,1] => [1,2,3,8,5,4,7,6] => 0001011 => 1
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => [1,2,3,8,6,4,5,7] => 0000101 => 1
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [1,2,3,8,6,5,4,7] => 0001101 => 1
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => [1,2,3,8,7,4,5,6] => 0000011 => 0
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => [1,2,3,8,7,4,6,5] => 0000111 => 0
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [6,4,5,7,8,3,2,1] => [1,2,3,8,7,5,4,6] => 0001011 => 1
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => [1,2,3,8,7,6,4,5] => 0000111 => 0
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [1,2,3,8,7,6,5,4] => 0001111 => 0
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [1,2,4,3,5,6,7,8] => 0010000 => 1
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [1,2,4,3,5,6,8,7] => 0010001 => 1
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [1,2,4,3,5,7,6,8] => 0010010 => 2
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [7,6,8,5,3,4,2,1] => [1,2,4,3,5,8,6,7] => 0010001 => 1
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [6,7,8,5,3,4,2,1] => [1,2,4,3,5,8,7,6] => 0010011 => 1
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [1,2,4,3,6,5,7,8] => 0010100 => 2
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [7,8,5,6,3,4,2,1] => [1,2,4,3,6,5,8,7] => 0010101 => 2
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [8,6,5,7,3,4,2,1] => [1,2,4,3,7,5,6,8] => 0010010 => 2
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [7,6,5,8,3,4,2,1] => [1,2,4,3,8,5,6,7] => 0010001 => 1
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [6,7,5,8,3,4,2,1] => [1,2,4,3,8,5,7,6] => 0010011 => 1
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [7,5,6,8,3,4,2,1] => [1,2,4,3,8,6,5,7] => 0010101 => 2
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [6,5,7,8,3,4,2,1] => [1,2,4,3,8,7,5,6] => 0010011 => 1
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => [1,2,4,3,8,7,6,5] => 0010111 => 1
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [8,7,6,4,3,5,2,1] => [1,2,5,3,4,6,7,8] => 0001000 => 1
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [7,8,6,4,3,5,2,1] => [1,2,5,3,4,6,8,7] => 0001001 => 1
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [8,6,7,4,3,5,2,1] => [1,2,5,3,4,7,6,8] => 0001010 => 2
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [7,6,8,4,3,5,2,1] => [1,2,5,3,4,8,6,7] => 0001001 => 1
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [6,7,8,4,3,5,2,1] => [1,2,5,3,4,8,7,6] => 0001011 => 1
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1] => [1,2,5,4,3,6,7,8] => 0011000 => 1
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [7,8,6,3,4,5,2,1] => [1,2,5,4,3,6,8,7] => 0011001 => 1
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [7,6,8,3,4,5,2,1] => [1,2,5,4,3,8,6,7] => 0011001 => 1
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => [1,2,5,4,3,8,7,6] => 0011011 => 1
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => [1,2,6,3,4,5,7,8] => 0000100 => 1
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [7,8,5,4,3,6,2,1] => [1,2,6,3,4,5,8,7] => 0000101 => 1
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [8,7,4,5,3,6,2,1] => [1,2,6,3,5,4,7,8] => 0001100 => 1
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [8,7,5,3,4,6,2,1] => [1,2,6,4,3,5,7,8] => 0010100 => 2
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [8,7,4,3,5,6,2,1] => [1,2,6,5,3,4,7,8] => 0001100 => 1
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [8,7,3,4,5,6,2,1] => [1,2,6,5,4,3,7,8] => 0011100 => 1
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [8,6,5,4,3,7,2,1] => [1,2,7,3,4,5,6,8] => 0000010 => 1
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [8,5,6,4,3,7,2,1] => [1,2,7,3,4,6,5,8] => 0000110 => 1
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [8,6,4,5,3,7,2,1] => [1,2,7,3,5,4,6,8] => 0001010 => 2
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [8,5,4,6,3,7,2,1] => [1,2,7,3,6,4,5,8] => 0000110 => 1
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [8,6,5,3,4,7,2,1] => [1,2,7,4,3,5,6,8] => 0010010 => 2
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [8,6,4,3,5,7,2,1] => [1,2,7,5,3,4,6,8] => 0001010 => 2
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [8,5,4,3,6,7,2,1] => [1,2,7,6,3,4,5,8] => 0000110 => 1
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [8,5,3,4,6,7,2,1] => [1,2,7,6,4,3,5,8] => 0010110 => 2
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [8,3,4,5,6,7,2,1] => [1,2,7,6,5,4,3,8] => 0011110 => 1
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [1,2,8,3,4,5,6,7] => 0000001 => 0
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => [1,2,8,3,4,5,7,6] => 0000011 => 0
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [7,5,6,4,3,8,2,1] => [1,2,8,3,4,6,5,7] => 0000101 => 1
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => [1,2,8,3,4,7,6,5] => 0000111 => 0
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [7,6,4,5,3,8,2,1] => [1,2,8,3,5,4,6,7] => 0001001 => 1
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [6,7,4,5,3,8,2,1] => [1,2,8,3,5,4,7,6] => 0001011 => 1
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [7,5,4,6,3,8,2,1] => [1,2,8,3,6,4,5,7] => 0000101 => 1
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [7,4,5,6,3,8,2,1] => [1,2,8,3,6,5,4,7] => 0001101 => 1
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => [1,2,8,3,7,4,5,6] => 0000011 => 0
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [5,6,4,7,3,8,2,1] => [1,2,8,3,7,4,6,5] => 0000111 => 0
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [6,4,5,7,3,8,2,1] => [1,2,8,3,7,5,4,6] => 0001011 => 1
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [1,2,8,3,7,6,4,5] => 0000111 => 0
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => [1,2,8,3,7,6,5,4] => 0001111 => 0
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => [1,2,8,4,3,5,6,7] => 0010001 => 1
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [6,7,5,3,4,8,2,1] => [1,2,8,4,3,5,7,6] => 0010011 => 1
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [7,5,6,3,4,8,2,1] => [1,2,8,4,3,6,5,7] => 0010101 => 2
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => [6,5,7,3,4,8,2,1] => [1,2,8,4,3,7,5,6] => 0010011 => 1
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [5,6,7,3,4,8,2,1] => [1,2,8,4,3,7,6,5] => 0010111 => 1
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => [1,2,8,5,3,4,6,7] => 0001001 => 1
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [1,2,8,5,4,3,6,7] => 0011001 => 1
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [7,5,4,3,6,8,2,1] => [1,2,8,6,3,4,5,7] => 0000101 => 1
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [7,5,3,4,6,8,2,1] => [1,2,8,6,4,3,5,7] => 0010101 => 2
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [7,3,4,5,6,8,2,1] => [1,2,8,6,5,4,3,7] => 0011101 => 1
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => [1,2,8,7,3,4,5,6] => 0000011 => 0
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => [5,6,4,3,7,8,2,1] => [1,2,8,7,3,4,6,5] => 0000111 => 0
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => [6,4,5,3,7,8,2,1] => [1,2,8,7,3,5,4,6] => 0001011 => 1
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => [1,2,8,7,3,6,5,4] => 0001111 => 0
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [5,6,3,4,7,8,2,1] => [1,2,8,7,4,3,6,5] => 0010111 => 1
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [6,3,4,5,7,8,2,1] => [1,2,8,7,5,4,3,6] => 0011011 => 1
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => [1,2,8,7,6,3,4,5] => 0000111 => 0
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [4,5,3,6,7,8,2,1] => [1,2,8,7,6,3,5,4] => 0001111 => 0
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [5,3,4,6,7,8,2,1] => [1,2,8,7,6,4,3,5] => 0010111 => 1
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [1,2,8,7,6,5,3,4] => 0001111 => 0
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [1,2,8,7,6,5,4,3] => 0011111 => 0
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,8] => 0100000 => 1
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [1,3,2,4,5,6,8,7] => 0100001 => 1
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,3,2,4,5,7,6,8] => 0100010 => 2
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,2,3,1] => [1,3,2,4,5,8,6,7] => 0100001 => 1
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,2,3,1] => [1,3,2,4,5,8,7,6] => 0100011 => 1
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [1,3,2,4,6,5,7,8] => 0100100 => 2
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,2,3,1] => [1,3,2,4,6,5,8,7] => 0100101 => 2
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,2,3,1] => [1,3,2,4,7,6,5,8] => 0100110 => 2
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,2,3,1] => [1,3,2,4,8,5,6,7] => 0100001 => 1
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,2,3,1] => [1,3,2,4,8,5,7,6] => 0100011 => 1
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,2,3,1] => [1,3,2,4,8,6,5,7] => 0100101 => 2
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => [1,3,2,4,8,7,6,5] => 0100111 => 1
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [1,3,2,5,4,6,7,8] => 0101000 => 2
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,8] => 0101010 => 3
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [7,6,8,4,5,2,3,1] => [1,3,2,5,4,8,6,7] => 0101001 => 2
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,2,3,1] => [1,3,2,5,4,8,7,6] => 0101011 => 2
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,2,3,1] => [1,3,2,6,4,5,7,8] => 0100100 => 2
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,2,3,1] => [1,3,2,6,5,4,7,8] => 0101100 => 2
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => [1,3,2,6,5,4,8,7] => 0101101 => 2
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [8,6,5,4,7,2,3,1] => [1,3,2,7,4,5,6,8] => 0100010 => 2
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,2,3,1] => [1,3,2,7,4,6,5,8] => 0100110 => 2
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,2,3,1] => [1,3,2,7,5,4,6,8] => 0101010 => 3
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [8,5,4,6,7,2,3,1] => [1,3,2,7,6,4,5,8] => 0100110 => 2
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [8,4,5,6,7,2,3,1] => [1,3,2,7,6,5,4,8] => 0101110 => 2
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,2,3,1] => [1,3,2,8,4,5,6,7] => 0100001 => 1
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [6,7,5,4,8,2,3,1] => [1,3,2,8,4,5,7,6] => 0100011 => 1
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,2,3,1] => [1,3,2,8,4,6,5,7] => 0100101 => 2
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,2,3,1] => [1,3,2,8,4,7,5,6] => 0100011 => 1
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,2,3,1] => [1,3,2,8,5,4,6,7] => 0101001 => 2
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,2,3,1] => [1,3,2,8,5,4,7,6] => 0101011 => 2
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [7,5,4,6,8,2,3,1] => [1,3,2,8,6,4,5,7] => 0100101 => 2
[.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [7,4,5,6,8,2,3,1] => [1,3,2,8,6,5,4,7] => 0101101 => 2
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,2,3,1] => [1,3,2,8,7,4,5,6] => 0100011 => 1
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [5,6,4,7,8,2,3,1] => [1,3,2,8,7,4,6,5] => 0100111 => 1
[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [6,4,5,7,8,2,3,1] => [1,3,2,8,7,5,4,6] => 0101011 => 2
[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [5,4,6,7,8,2,3,1] => [1,3,2,8,7,6,4,5] => 0100111 => 1
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => [1,3,2,8,7,6,5,4] => 0101111 => 1
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,2,4,1] => [1,4,2,3,5,6,7,8] => 0010000 => 1
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,2,4,1] => [1,4,2,3,5,6,8,7] => 0010001 => 1
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [8,6,7,5,3,2,4,1] => [1,4,2,3,5,7,6,8] => 0010010 => 2
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,2,4,1] => [1,4,2,3,5,8,6,7] => 0010001 => 1
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,2,4,1] => [1,4,2,3,5,8,7,6] => 0010011 => 1
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,2,4,1] => [1,4,2,3,6,5,7,8] => 0010100 => 2
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,2,4,1] => [1,4,2,3,6,5,8,7] => 0010101 => 2
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => [1,4,2,3,7,5,6,8] => 0010010 => 2
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,2,4,1] => [1,4,2,3,8,5,6,7] => 0010001 => 1
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,2,4,1] => [1,4,2,3,8,5,7,6] => 0010011 => 1
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,2,4,1] => [1,4,2,3,8,6,5,7] => 0010101 => 2
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,2,4,1] => [1,4,2,3,8,7,5,6] => 0010011 => 1
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => [1,4,2,3,8,7,6,5] => 0010111 => 1
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [1,4,3,2,5,6,7,8] => 0110000 => 1
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,2,3,4,1] => [1,4,3,2,5,7,6,8] => 0110010 => 2
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,2,3,4,1] => [1,4,3,2,5,8,6,7] => 0110001 => 1
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => [1,4,3,2,5,8,7,6] => 0110011 => 1
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => [1,4,3,2,7,6,5,8] => 0110110 => 2
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,2,3,4,1] => [1,4,3,2,8,5,6,7] => 0110001 => 1
[.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [7,5,6,8,2,3,4,1] => [1,4,3,2,8,6,5,7] => 0110101 => 2
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => [1,4,3,2,8,7,6,5] => 0110111 => 1
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [8,7,6,4,3,2,5,1] => [1,5,2,3,4,6,7,8] => 0001000 => 1
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [7,8,6,4,3,2,5,1] => [1,5,2,3,4,6,8,7] => 0001001 => 1
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [8,6,7,4,3,2,5,1] => [1,5,2,3,4,7,6,8] => 0001010 => 2
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [7,6,8,4,3,2,5,1] => [1,5,2,3,4,8,6,7] => 0001001 => 1
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [6,7,8,4,3,2,5,1] => [1,5,2,3,4,8,7,6] => 0001011 => 1
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [8,7,6,3,4,2,5,1] => [1,5,2,4,3,6,7,8] => 0011000 => 1
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [7,8,6,3,4,2,5,1] => [1,5,2,4,3,6,8,7] => 0011001 => 1
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [8,6,7,3,4,2,5,1] => [1,5,2,4,3,7,6,8] => 0011010 => 2
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [7,6,8,3,4,2,5,1] => [1,5,2,4,3,8,6,7] => 0011001 => 1
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [6,7,8,3,4,2,5,1] => [1,5,2,4,3,8,7,6] => 0011011 => 1
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,2,3,5,1] => [1,5,3,2,4,6,7,8] => 0101000 => 2
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [7,8,6,4,2,3,5,1] => [1,5,3,2,4,6,8,7] => 0101001 => 2
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [8,6,7,4,2,3,5,1] => [1,5,3,2,4,7,6,8] => 0101010 => 3
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [7,6,8,4,2,3,5,1] => [1,5,3,2,4,8,6,7] => 0101001 => 2
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [6,7,8,4,2,3,5,1] => [1,5,3,2,4,8,7,6] => 0101011 => 2
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [8,7,6,3,2,4,5,1] => [1,5,4,2,3,6,7,8] => 0011000 => 1
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [7,8,6,3,2,4,5,1] => [1,5,4,2,3,6,8,7] => 0011001 => 1
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [8,6,7,3,2,4,5,1] => [1,5,4,2,3,7,6,8] => 0011010 => 2
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [7,6,8,3,2,4,5,1] => [1,5,4,2,3,8,6,7] => 0011001 => 1
[.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [6,7,8,3,2,4,5,1] => [1,5,4,2,3,8,7,6] => 0011011 => 1
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => [1,5,4,3,2,6,7,8] => 0111000 => 1
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [8,6,7,2,3,4,5,1] => [1,5,4,3,2,7,6,8] => 0111010 => 2
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [6,7,8,2,3,4,5,1] => [1,5,4,3,2,8,7,6] => 0111011 => 1
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [8,7,5,4,3,2,6,1] => [1,6,2,3,4,5,7,8] => 0000100 => 1
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [7,8,5,4,3,2,6,1] => [1,6,2,3,4,5,8,7] => 0000101 => 1
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [8,7,5,3,4,2,6,1] => [1,6,2,4,3,5,7,8] => 0010100 => 2
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [7,8,5,3,4,2,6,1] => [1,6,2,4,3,5,8,7] => 0010101 => 2
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [8,7,4,3,5,2,6,1] => [1,6,2,5,3,4,7,8] => 0001100 => 1
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [7,8,4,3,5,2,6,1] => [1,6,2,5,3,4,8,7] => 0001101 => 1
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,2,3,6,1] => [1,6,3,2,4,5,7,8] => 0100100 => 2
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [8,7,4,5,2,3,6,1] => [1,6,3,2,5,4,7,8] => 0101100 => 2
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [8,7,5,3,2,4,6,1] => [1,6,4,2,3,5,7,8] => 0010100 => 2
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [7,8,5,3,2,4,6,1] => [1,6,4,2,3,5,8,7] => 0010101 => 2
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [8,7,5,2,3,4,6,1] => [1,6,4,3,2,5,7,8] => 0110100 => 2
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [7,8,4,3,2,5,6,1] => [1,6,5,2,3,4,8,7] => 0001101 => 1
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [8,7,4,2,3,5,6,1] => [1,6,5,3,2,4,7,8] => 0101100 => 2
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [7,8,4,2,3,5,6,1] => [1,6,5,3,2,4,8,7] => 0101101 => 2
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => [1,6,5,4,2,3,8,7] => 0011101 => 1
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [8,7,2,3,4,5,6,1] => [1,6,5,4,3,2,7,8] => 0111100 => 1
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [7,8,2,3,4,5,6,1] => [1,6,5,4,3,2,8,7] => 0111101 => 1
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [8,6,5,4,3,2,7,1] => [1,7,2,3,4,5,6,8] => 0000010 => 1
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [8,5,6,4,3,2,7,1] => [1,7,2,3,4,6,5,8] => 0000110 => 1
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [8,6,4,5,3,2,7,1] => [1,7,2,3,5,4,6,8] => 0001010 => 2
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [8,5,4,6,3,2,7,1] => [1,7,2,3,6,4,5,8] => 0000110 => 1
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [8,6,5,3,4,2,7,1] => [1,7,2,4,3,5,6,8] => 0010010 => 2
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [8,5,6,3,4,2,7,1] => [1,7,2,4,3,6,5,8] => 0010110 => 2
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [8,6,4,3,5,2,7,1] => [1,7,2,5,3,4,6,8] => 0001010 => 2
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [8,6,3,4,5,2,7,1] => [1,7,2,5,4,3,6,8] => 0011010 => 2
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [8,5,4,3,6,2,7,1] => [1,7,2,6,3,4,5,8] => 0000110 => 1
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [8,4,5,3,6,2,7,1] => [1,7,2,6,3,5,4,8] => 0001110 => 1
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [8,5,3,4,6,2,7,1] => [1,7,2,6,4,3,5,8] => 0010110 => 2
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [8,3,4,5,6,2,7,1] => [1,7,2,6,5,4,3,8] => 0011110 => 1
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,2,3,7,1] => [1,7,3,2,4,5,6,8] => 0100010 => 2
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [8,5,6,4,2,3,7,1] => [1,7,3,2,4,6,5,8] => 0100110 => 2
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [8,6,4,5,2,3,7,1] => [1,7,3,2,5,4,6,8] => 0101010 => 3
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [8,6,5,3,2,4,7,1] => [1,7,4,2,3,5,6,8] => 0010010 => 2
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [8,6,5,2,3,4,7,1] => [1,7,4,3,2,5,6,8] => 0110010 => 2
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [8,6,4,3,2,5,7,1] => [1,7,5,2,3,4,6,8] => 0001010 => 2
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [8,6,4,2,3,5,7,1] => [1,7,5,3,2,4,6,8] => 0101010 => 3
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [8,6,2,3,4,5,7,1] => [1,7,5,4,3,2,6,8] => 0111010 => 2
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [8,5,4,3,2,6,7,1] => [1,7,6,2,3,4,5,8] => 0000110 => 1
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [8,5,3,4,2,6,7,1] => [1,7,6,2,4,3,5,8] => 0010110 => 2
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [8,5,4,2,3,6,7,1] => [1,7,6,3,2,4,5,8] => 0100110 => 2
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [8,4,5,2,3,6,7,1] => [1,7,6,3,2,5,4,8] => 0101110 => 2
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [8,5,3,2,4,6,7,1] => [1,7,6,4,2,3,5,8] => 0010110 => 2
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [8,3,4,2,5,6,7,1] => [1,7,6,5,2,4,3,8] => 0011110 => 1
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [8,4,2,3,5,6,7,1] => [1,7,6,5,3,2,4,8] => 0101110 => 2
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [8,3,2,4,5,6,7,1] => [1,7,6,5,4,2,3,8] => 0011110 => 1
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [8,2,3,4,5,6,7,1] => [1,7,6,5,4,3,2,8] => 0111110 => 1
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [1,8,2,3,4,5,6,7] => 0000001 => 0
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [1,8,2,3,4,5,7,6] => 0000011 => 0
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [7,5,6,4,3,2,8,1] => [1,8,2,3,4,6,5,7] => 0000101 => 1
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [1,8,2,3,4,7,5,6] => 0000011 => 0
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => [1,8,2,3,4,7,6,5] => 0000111 => 0
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [7,6,4,5,3,2,8,1] => [1,8,2,3,5,4,6,7] => 0001001 => 1
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [7,5,4,6,3,2,8,1] => [1,8,2,3,6,4,5,7] => 0000101 => 1
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [7,4,5,6,3,2,8,1] => [1,8,2,3,6,5,4,7] => 0001101 => 1
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [6,4,5,7,3,2,8,1] => [1,8,2,3,7,5,4,6] => 0001011 => 1
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => [5,4,6,7,3,2,8,1] => [1,8,2,3,7,6,4,5] => 0000111 => 0
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => [1,8,2,3,7,6,5,4] => 0001111 => 0
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [7,6,5,3,4,2,8,1] => [1,8,2,4,3,5,6,7] => 0010001 => 1
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [7,5,6,3,4,2,8,1] => [1,8,2,4,3,6,5,7] => 0010101 => 2
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [6,5,7,3,4,2,8,1] => [1,8,2,4,3,7,5,6] => 0010011 => 1
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [5,6,7,3,4,2,8,1] => [1,8,2,4,3,7,6,5] => 0010111 => 1
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [7,6,4,3,5,2,8,1] => [1,8,2,5,3,4,6,7] => 0001001 => 1
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [6,7,4,3,5,2,8,1] => [1,8,2,5,3,4,7,6] => 0001011 => 1
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [7,5,4,3,6,2,8,1] => [1,8,2,6,3,4,5,7] => 0000101 => 1
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [7,4,5,3,6,2,8,1] => [1,8,2,6,3,5,4,7] => 0001101 => 1
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [7,5,3,4,6,2,8,1] => [1,8,2,6,4,3,5,7] => 0010101 => 2
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [7,4,3,5,6,2,8,1] => [1,8,2,6,5,3,4,7] => 0001101 => 1
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [1,8,2,7,3,4,5,6] => 0000011 => 0
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [5,6,4,3,7,2,8,1] => [1,8,2,7,3,4,6,5] => 0000111 => 0
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [6,4,5,3,7,2,8,1] => [1,8,2,7,3,5,4,6] => 0001011 => 1
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [1,8,2,7,3,6,4,5] => 0000111 => 0
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => [1,8,2,7,3,6,5,4] => 0001111 => 0
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [6,5,3,4,7,2,8,1] => [1,8,2,7,4,3,5,6] => 0010011 => 1
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [5,6,3,4,7,2,8,1] => [1,8,2,7,4,3,6,5] => 0010111 => 1
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [6,4,3,5,7,2,8,1] => [1,8,2,7,5,3,4,6] => 0001011 => 1
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [6,3,4,5,7,2,8,1] => [1,8,2,7,5,4,3,6] => 0011011 => 1
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => [1,8,2,7,6,3,4,5] => 0000111 => 0
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => [1,8,2,7,6,3,5,4] => 0001111 => 0
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [5,3,4,6,7,2,8,1] => [1,8,2,7,6,4,3,5] => 0010111 => 1
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => [1,8,2,7,6,5,4,3] => 0011111 => 0
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [1,8,3,2,4,5,6,7] => 0100001 => 1
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [6,7,5,4,2,3,8,1] => [1,8,3,2,4,5,7,6] => 0100011 => 1
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,2,3,8,1] => [1,8,3,2,4,7,5,6] => 0100011 => 1
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,2,3,8,1] => [1,8,3,2,5,4,6,7] => 0101001 => 2
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => [1,8,3,2,5,4,7,6] => 0101011 => 2
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,2,3,8,1] => [1,8,3,2,6,4,5,7] => 0100101 => 2
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [6,4,5,7,2,3,8,1] => [1,8,3,2,7,5,4,6] => 0101011 => 2
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [5,4,6,7,2,3,8,1] => [1,8,3,2,7,6,4,5] => 0100111 => 1
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => [1,8,3,2,7,6,5,4] => 0101111 => 1
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => [1,8,4,2,3,5,6,7] => 0010001 => 1
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [6,7,5,3,2,4,8,1] => [1,8,4,2,3,5,7,6] => 0010011 => 1
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [7,5,6,3,2,4,8,1] => [1,8,4,2,3,6,5,7] => 0010101 => 2
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [6,5,7,3,2,4,8,1] => [1,8,4,2,3,7,5,6] => 0010011 => 1
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [5,6,7,3,2,4,8,1] => [1,8,4,2,3,7,6,5] => 0010111 => 1
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [1,8,4,3,2,5,6,7] => 0110001 => 1
[.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [6,7,5,2,3,4,8,1] => [1,8,4,3,2,5,7,6] => 0110011 => 1
[.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [6,5,7,2,3,4,8,1] => [1,8,4,3,2,7,5,6] => 0110011 => 1
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [5,6,7,2,3,4,8,1] => [1,8,4,3,2,7,6,5] => 0110111 => 1
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [6,7,4,3,2,5,8,1] => [1,8,5,2,3,4,7,6] => 0001011 => 1
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [7,6,4,2,3,5,8,1] => [1,8,5,3,2,4,6,7] => 0101001 => 2
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [6,7,4,2,3,5,8,1] => [1,8,5,3,2,4,7,6] => 0101011 => 2
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [7,6,3,2,4,5,8,1] => [1,8,5,4,2,3,6,7] => 0011001 => 1
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [6,7,3,2,4,5,8,1] => [1,8,5,4,2,3,7,6] => 0011011 => 1
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [7,6,2,3,4,5,8,1] => [1,8,5,4,3,2,6,7] => 0111001 => 1
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => [1,8,5,4,3,2,7,6] => 0111011 => 1
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [7,5,4,3,2,6,8,1] => [1,8,6,2,3,4,5,7] => 0000101 => 1
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [7,5,3,4,2,6,8,1] => [1,8,6,2,4,3,5,7] => 0010101 => 2
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [7,4,3,5,2,6,8,1] => [1,8,6,2,5,3,4,7] => 0001101 => 1
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [7,5,4,2,3,6,8,1] => [1,8,6,3,2,4,5,7] => 0100101 => 2
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [7,4,5,2,3,6,8,1] => [1,8,6,3,2,5,4,7] => 0101101 => 2
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [7,5,3,2,4,6,8,1] => [1,8,6,4,2,3,5,7] => 0010101 => 2
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [7,4,2,3,5,6,8,1] => [1,8,6,5,3,2,4,7] => 0101101 => 2
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [7,3,2,4,5,6,8,1] => [1,8,6,5,4,2,3,7] => 0011101 => 1
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [7,2,3,4,5,6,8,1] => [1,8,6,5,4,3,2,7] => 0111101 => 1
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => [1,8,7,2,3,4,5,6] => 0000011 => 0
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [5,6,4,3,2,7,8,1] => [1,8,7,2,3,4,6,5] => 0000111 => 0
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => [6,4,5,3,2,7,8,1] => [1,8,7,2,3,5,4,6] => 0001011 => 1
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => [1,8,7,2,3,6,4,5] => 0000111 => 0
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => [1,8,7,2,3,6,5,4] => 0001111 => 0
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [6,4,3,5,2,7,8,1] => [1,8,7,2,5,3,4,6] => 0001011 => 1
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [6,3,4,5,2,7,8,1] => [1,8,7,2,5,4,3,6] => 0011011 => 1
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => [1,8,7,2,6,3,4,5] => 0000111 => 0
[.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [4,5,3,6,2,7,8,1] => [1,8,7,2,6,3,5,4] => 0001111 => 0
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => [1,8,7,2,6,5,3,4] => 0001111 => 0
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => [1,8,7,2,6,5,4,3] => 0011111 => 0
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [6,5,4,2,3,7,8,1] => [1,8,7,3,2,4,5,6] => 0100011 => 1
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [5,6,4,2,3,7,8,1] => [1,8,7,3,2,4,6,5] => 0100111 => 1
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [6,4,5,2,3,7,8,1] => [1,8,7,3,2,5,4,6] => 0101011 => 2
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [5,4,6,2,3,7,8,1] => [1,8,7,3,2,6,4,5] => 0100111 => 1
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [6,5,3,2,4,7,8,1] => [1,8,7,4,2,3,5,6] => 0010011 => 1
[.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [5,6,3,2,4,7,8,1] => [1,8,7,4,2,3,6,5] => 0010111 => 1
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [6,5,2,3,4,7,8,1] => [1,8,7,4,3,2,5,6] => 0110011 => 1
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [5,6,2,3,4,7,8,1] => [1,8,7,4,3,2,6,5] => 0110111 => 1
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [6,4,3,2,5,7,8,1] => [1,8,7,5,2,3,4,6] => 0001011 => 1
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [6,4,2,3,5,7,8,1] => [1,8,7,5,3,2,4,6] => 0101011 => 2
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [6,2,3,4,5,7,8,1] => [1,8,7,5,4,3,2,6] => 0111011 => 1
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [1,8,7,6,2,3,4,5] => 0000111 => 0
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [5,3,4,2,6,7,8,1] => [1,8,7,6,2,4,3,5] => 0010111 => 1
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [1,8,7,6,2,5,4,3] => 0011111 => 0
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [5,4,2,3,6,7,8,1] => [1,8,7,6,3,2,4,5] => 0100111 => 1
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [4,5,2,3,6,7,8,1] => [1,8,7,6,3,2,5,4] => 0101111 => 1
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [5,3,2,4,6,7,8,1] => [1,8,7,6,4,2,3,5] => 0010111 => 1
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => [1,8,7,6,4,3,2,5] => 0110111 => 1
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [1,8,7,6,5,2,3,4] => 0001111 => 0
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [1,8,7,6,5,2,4,3] => 0011111 => 0
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => [1,8,7,6,5,3,2,4] => 0101111 => 1
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [1,8,7,6,5,4,2,3] => 0011111 => 0
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2] => 0111111 => 0
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8] => 1000000 => 1
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [2,1,3,4,5,6,8,7] => 1000001 => 1
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [2,1,3,4,5,7,6,8] => 1000010 => 2
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,3,1,2] => [2,1,3,4,5,8,6,7] => 1000001 => 1
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => [2,1,3,4,5,8,7,6] => 1000011 => 1
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [2,1,3,4,6,5,7,8] => 1000100 => 2
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,3,1,2] => [2,1,3,4,6,5,8,7] => 1000101 => 2
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,3,1,2] => [2,1,3,4,7,5,6,8] => 1000010 => 2
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,3,1,2] => [2,1,3,4,8,5,6,7] => 1000001 => 1
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,3,1,2] => [2,1,3,4,8,5,7,6] => 1000011 => 1
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => [2,1,3,4,8,6,5,7] => 1000101 => 2
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => [2,1,3,4,8,7,5,6] => 1000011 => 1
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [2,1,3,4,8,7,6,5] => 1000111 => 1
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [2,1,3,5,4,6,7,8] => 1001000 => 2
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [2,1,3,5,4,6,8,7] => 1001001 => 2
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => [2,1,3,5,4,8,7,6] => 1001011 => 2
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,3,1,2] => [2,1,3,6,4,5,7,8] => 1000100 => 2
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [7,8,5,4,6,3,1,2] => [2,1,3,6,4,5,8,7] => 1000101 => 2
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => [2,1,3,6,5,4,8,7] => 1001101 => 2
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,3,1,2] => [2,1,3,8,4,5,6,7] => 1000001 => 1
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [6,7,5,4,8,3,1,2] => [2,1,3,8,4,5,7,6] => 1000011 => 1
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,3,1,2] => [2,1,3,8,4,6,5,7] => 1000101 => 2
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,3,1,2] => [2,1,3,8,4,7,5,6] => 1000011 => 1
[[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [5,6,7,4,8,3,1,2] => [2,1,3,8,4,7,6,5] => 1000111 => 1
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => [2,1,3,8,5,4,6,7] => 1001001 => 2
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,3,1,2] => [2,1,3,8,5,4,7,6] => 1001011 => 2
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [7,5,4,6,8,3,1,2] => [2,1,3,8,6,4,5,7] => 1000101 => 2
[[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [7,4,5,6,8,3,1,2] => [2,1,3,8,6,5,4,7] => 1001101 => 2
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,3,1,2] => [2,1,3,8,7,4,5,6] => 1000011 => 1
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [5,6,4,7,8,3,1,2] => [2,1,3,8,7,4,6,5] => 1000111 => 1
[[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [6,4,5,7,8,3,1,2] => [2,1,3,8,7,5,4,6] => 1001011 => 2
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [5,4,6,7,8,3,1,2] => [2,1,3,8,7,6,4,5] => 1000111 => 1
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => [2,1,3,8,7,6,5,4] => 1001111 => 1
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [2,1,4,3,5,6,7,8] => 1010000 => 2
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [2,1,4,3,5,6,8,7] => 1010001 => 2
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,4,1,2] => [2,1,4,3,5,8,6,7] => 1010001 => 2
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => [2,1,4,3,5,8,7,6] => 1010011 => 2
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [2,1,4,3,6,5,7,8] => 1010100 => 3
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7] => 1010101 => 3
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => [2,1,4,3,8,5,6,7] => 1010001 => 2
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => [2,1,4,3,8,5,7,6] => 1010011 => 2
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [2,1,4,3,8,6,5,7] => 1010101 => 3
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => [2,1,4,3,8,7,5,6] => 1010011 => 2
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [2,1,4,3,8,7,6,5] => 1010111 => 2
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,3,5,1,2] => [2,1,5,3,4,6,7,8] => 1001000 => 2
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [7,8,6,4,3,5,1,2] => [2,1,5,3,4,6,8,7] => 1001001 => 2
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => [2,1,5,4,3,6,7,8] => 1011000 => 2
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => [2,1,5,4,3,6,8,7] => 1011001 => 2
[[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => [2,1,5,4,3,7,6,8] => 1011010 => 3
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [6,7,8,3,4,5,1,2] => [2,1,5,4,3,8,7,6] => 1011011 => 2
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => [2,1,6,3,4,5,8,7] => 1000101 => 2
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => [2,1,6,3,5,4,8,7] => 1001101 => 2
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [8,7,5,3,4,6,1,2] => [2,1,6,4,3,5,7,8] => 1010100 => 3
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => [2,1,6,4,3,5,8,7] => 1010101 => 3
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => [2,1,6,5,3,4,8,7] => 1001101 => 2
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [2,1,6,5,4,3,8,7] => 1011101 => 2
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,3,7,1,2] => [2,1,7,3,4,5,6,8] => 1000010 => 2
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [8,5,4,6,3,7,1,2] => [2,1,7,3,6,4,5,8] => 1000110 => 2
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [8,5,4,3,6,7,1,2] => [2,1,7,6,3,4,5,8] => 1000110 => 2
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => [2,1,7,6,5,3,4,8] => 1001110 => 2
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [2,1,7,6,5,4,3,8] => 1011110 => 2
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [2,1,8,3,4,5,6,7] => 1000001 => 1
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2] => [2,1,8,3,4,7,5,6] => 1000011 => 1
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [5,6,7,4,3,8,1,2] => [2,1,8,3,4,7,6,5] => 1000111 => 1
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => [2,1,8,3,5,4,7,6] => 1001011 => 2
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,3,8,1,2] => [2,1,8,3,6,4,5,7] => 1000101 => 2
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [6,5,4,7,3,8,1,2] => [2,1,8,3,7,4,5,6] => 1000011 => 1
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => [2,1,8,3,7,4,6,5] => 1000111 => 1
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [6,4,5,7,3,8,1,2] => [2,1,8,3,7,5,4,6] => 1001011 => 2
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [5,4,6,7,3,8,1,2] => [2,1,8,3,7,6,4,5] => 1000111 => 1
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => [2,1,8,3,7,6,5,4] => 1001111 => 1
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [6,7,5,3,4,8,1,2] => [2,1,8,4,3,5,7,6] => 1010011 => 2
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => [2,1,8,4,3,6,5,7] => 1010101 => 3
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [6,5,7,3,4,8,1,2] => [2,1,8,4,3,7,5,6] => 1010011 => 2
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [5,6,7,3,4,8,1,2] => [2,1,8,4,3,7,6,5] => 1010111 => 2
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [7,6,4,3,5,8,1,2] => [2,1,8,5,3,4,6,7] => 1001001 => 2
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [6,7,4,3,5,8,1,2] => [2,1,8,5,3,4,7,6] => 1001011 => 2
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => [2,1,8,5,4,3,6,7] => 1011001 => 2
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [6,7,3,4,5,8,1,2] => [2,1,8,5,4,3,7,6] => 1011011 => 2
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [7,4,5,3,6,8,1,2] => [2,1,8,6,3,5,4,7] => 1001101 => 2
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [7,5,3,4,6,8,1,2] => [2,1,8,6,4,3,5,7] => 1010101 => 3
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [7,3,4,5,6,8,1,2] => [2,1,8,6,5,4,3,7] => 1011101 => 2
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [6,5,4,3,7,8,1,2] => [2,1,8,7,3,4,5,6] => 1000011 => 1
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [5,6,4,3,7,8,1,2] => [2,1,8,7,3,4,6,5] => 1000111 => 1
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [6,4,5,3,7,8,1,2] => [2,1,8,7,3,5,4,6] => 1001011 => 2
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => [2,1,8,7,3,6,4,5] => 1000111 => 1
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [4,5,6,3,7,8,1,2] => [2,1,8,7,3,6,5,4] => 1001111 => 1
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [6,5,3,4,7,8,1,2] => [2,1,8,7,4,3,5,6] => 1010011 => 2
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => [2,1,8,7,4,3,6,5] => 1010111 => 2
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => [2,1,8,7,5,3,4,6] => 1001011 => 2
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => [2,1,8,7,5,4,3,6] => 1011011 => 2
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => [2,1,8,7,6,3,4,5] => 1000111 => 1
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => [2,1,8,7,6,3,5,4] => 1001111 => 1
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [5,3,4,6,7,8,1,2] => [2,1,8,7,6,4,3,5] => 1010111 => 2
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => [2,1,8,7,6,5,3,4] => 1001111 => 1
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,8] => 0100000 => 1
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,2,1,3] => [3,1,2,4,5,6,8,7] => 0100001 => 1
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [8,6,7,5,4,2,1,3] => [3,1,2,4,5,7,6,8] => 0100010 => 2
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => [3,1,2,4,5,8,6,7] => 0100001 => 1
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,2,1,3] => [3,1,2,4,6,5,8,7] => 0100101 => 2
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,2,1,3] => [3,1,2,4,7,5,6,8] => 0100010 => 2
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,2,1,3] => [3,1,2,4,8,5,6,7] => 0100001 => 1
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,2,1,3] => [3,1,2,4,8,5,7,6] => 0100011 => 1
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,2,1,3] => [3,1,2,4,8,6,5,7] => 0100101 => 2
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,2,1,3] => [3,1,2,4,8,7,5,6] => 0100011 => 1
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => [3,1,2,4,8,7,6,5] => 0100111 => 1
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [7,8,6,4,5,2,1,3] => [3,1,2,5,4,6,8,7] => 0101001 => 2
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,2,1,3] => [3,1,2,5,4,7,6,8] => 0101010 => 3
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [7,8,5,4,6,2,1,3] => [3,1,2,6,4,5,8,7] => 0100101 => 2
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,2,1,3] => [3,1,2,7,4,5,6,8] => 0100010 => 2
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,2,1,3] => [3,1,2,7,5,4,6,8] => 0101010 => 3
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [8,5,4,6,7,2,1,3] => [3,1,2,7,6,4,5,8] => 0100110 => 2
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,2,1,3] => [3,1,2,8,4,5,6,7] => 0100001 => 1
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,2,1,3] => [3,1,2,8,4,5,7,6] => 0100011 => 1
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,2,1,3] => [3,1,2,8,4,7,5,6] => 0100011 => 1
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,2,1,3] => [3,1,2,8,5,4,7,6] => 0101011 => 2
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,2,1,3] => [3,1,2,8,6,4,5,7] => 0100101 => 2
[[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,2,1,3] => [3,1,2,8,6,5,4,7] => 0101101 => 2
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,2,1,3] => [3,1,2,8,7,4,5,6] => 0100011 => 1
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [5,6,4,7,8,2,1,3] => [3,1,2,8,7,4,6,5] => 0100111 => 1
[[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [6,4,5,7,8,2,1,3] => [3,1,2,8,7,5,4,6] => 0101011 => 2
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,2,1,3] => [3,1,2,8,7,6,4,5] => 0100111 => 1
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => [3,1,2,8,7,6,5,4] => 0101111 => 1
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [3,2,1,4,5,6,7,8] => 1100000 => 1
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => [3,2,1,4,5,6,8,7] => 1100001 => 1
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [8,6,7,5,4,1,2,3] => [3,2,1,4,5,7,6,8] => 1100010 => 2
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,1,2,3] => [3,2,1,4,5,8,6,7] => 1100001 => 1
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => [3,2,1,4,5,8,7,6] => 1100011 => 1
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [3,2,1,4,7,6,5,8] => 1100110 => 2
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,1,2,3] => [3,2,1,4,8,5,6,7] => 1100001 => 1
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,1,2,3] => [3,2,1,4,8,5,7,6] => 1100011 => 1
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,1,2,3] => [3,2,1,4,8,6,5,7] => 1100101 => 2
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => [3,2,1,4,8,7,5,6] => 1100011 => 1
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => [3,2,1,4,8,7,6,5] => 1100111 => 1
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [3,2,1,5,4,6,7,8] => 1101000 => 2
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [3,2,1,5,4,7,6,8] => 1101010 => 3
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [8,7,5,4,6,1,2,3] => [3,2,1,6,4,5,7,8] => 1100100 => 2
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [3,2,1,6,5,4,7,8] => 1101100 => 2
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [3,2,1,6,5,4,8,7] => 1101101 => 2
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,1,2,3] => [3,2,1,7,4,5,6,8] => 1100010 => 2
[[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [8,5,6,4,7,1,2,3] => [3,2,1,7,4,6,5,8] => 1100110 => 2
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => [3,2,1,7,5,4,6,8] => 1101010 => 3
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [8,5,4,6,7,1,2,3] => [3,2,1,7,6,4,5,8] => 1100110 => 2
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => [3,2,1,7,6,5,4,8] => 1101110 => 2
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,1,2,3] => [3,2,1,8,4,5,6,7] => 1100001 => 1
[[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,1,2,3] => [3,2,1,8,4,5,7,6] => 1100011 => 1
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [7,5,6,4,8,1,2,3] => [3,2,1,8,4,6,5,7] => 1100101 => 2
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,1,2,3] => [3,2,1,8,4,7,5,6] => 1100011 => 1
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,1,2,3] => [3,2,1,8,4,7,6,5] => 1100111 => 1
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,1,2,3] => [3,2,1,8,5,4,6,7] => 1101001 => 2
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => [3,2,1,8,5,4,7,6] => 1101011 => 2
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,1,2,3] => [3,2,1,8,6,4,5,7] => 1100101 => 2
[[[.,.],.],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,1,2,3] => [3,2,1,8,6,5,4,7] => 1101101 => 2
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => [3,2,1,8,7,4,5,6] => 1100011 => 1
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [5,6,4,7,8,1,2,3] => [3,2,1,8,7,4,6,5] => 1100111 => 1
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [6,4,5,7,8,1,2,3] => [3,2,1,8,7,5,4,6] => 1101011 => 2
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,1,2,3] => [3,2,1,8,7,6,4,5] => 1100111 => 1
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => [3,2,1,8,7,6,5,4] => 1101111 => 1
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => [4,1,2,3,5,6,7,8] => 0010000 => 1
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,2,1,4] => [4,1,2,3,5,6,8,7] => 0010001 => 1
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,2,1,4] => [4,1,2,3,5,7,6,8] => 0010010 => 2
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,2,1,4] => [4,1,2,3,5,8,6,7] => 0010001 => 1
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,2,1,4] => [4,1,2,3,5,8,7,6] => 0010011 => 1
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,2,1,4] => [4,1,2,3,6,5,7,8] => 0010100 => 2
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => [4,1,2,3,6,5,8,7] => 0010101 => 2
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,2,1,4] => [4,1,2,3,7,5,6,8] => 0010010 => 2
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,2,1,4] => [4,1,2,3,7,6,5,8] => 0010110 => 2
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => [4,1,2,3,8,5,6,7] => 0010001 => 1
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,2,1,4] => [4,1,2,3,8,5,7,6] => 0010011 => 1
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,2,1,4] => [4,1,2,3,8,6,5,7] => 0010101 => 2
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,2,1,4] => [4,1,2,3,8,7,5,6] => 0010011 => 1
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => [4,1,2,3,8,7,6,5] => 0010111 => 1
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,3,1,4] => [4,1,3,2,5,6,7,8] => 0110000 => 1
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,3,1,4] => [4,1,3,2,5,7,6,8] => 0110010 => 2
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [7,8,5,6,2,3,1,4] => [4,1,3,2,6,5,8,7] => 0110101 => 2
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,3,1,4] => [4,1,3,2,8,5,6,7] => 0110001 => 1
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [6,7,5,8,2,3,1,4] => [4,1,3,2,8,5,7,6] => 0110011 => 1
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => [4,1,3,2,8,6,5,7] => 0110101 => 2
[[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [6,5,7,8,2,3,1,4] => [4,1,3,2,8,7,5,6] => 0110011 => 1
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [5,6,7,8,2,3,1,4] => [4,1,3,2,8,7,6,5] => 0110111 => 1
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [4,2,1,3,5,6,7,8] => 1010000 => 2
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,1,2,4] => [4,2,1,3,5,6,8,7] => 1010001 => 2
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,1,2,4] => [4,2,1,3,5,7,6,8] => 1010010 => 3
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,1,2,4] => [4,2,1,3,5,8,6,7] => 1010001 => 2
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,1,2,4] => [4,2,1,3,5,8,7,6] => 1010011 => 2
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,1,2,4] => [4,2,1,3,6,5,7,8] => 1010100 => 3
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => [4,2,1,3,6,5,8,7] => 1010101 => 3
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,1,2,4] => [4,2,1,3,7,5,6,8] => 1010010 => 3
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,1,2,4] => [4,2,1,3,7,6,5,8] => 1010110 => 3
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,1,2,4] => [4,2,1,3,8,5,6,7] => 1010001 => 2
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => [4,2,1,3,8,5,7,6] => 1010011 => 2
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => [4,2,1,3,8,6,5,7] => 1010101 => 3
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,1,2,4] => [4,2,1,3,8,7,5,6] => 1010011 => 2
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => [4,2,1,3,8,7,6,5] => 1010111 => 2
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => [4,3,1,2,5,6,7,8] => 0110000 => 1
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => [4,3,1,2,5,6,8,7] => 0110001 => 1
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,1,3,4] => [4,3,1,2,5,7,6,8] => 0110010 => 2
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => [4,3,1,2,5,8,7,6] => 0110011 => 1
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,1,3,4] => [4,3,1,2,6,5,7,8] => 0110100 => 2
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => [4,3,1,2,6,5,8,7] => 0110101 => 2
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,1,3,4] => [4,3,1,2,8,5,6,7] => 0110001 => 1
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [6,7,5,8,2,1,3,4] => [4,3,1,2,8,5,7,6] => 0110011 => 1
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [7,5,6,8,2,1,3,4] => [4,3,1,2,8,6,5,7] => 0110101 => 2
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => [4,3,1,2,8,7,5,6] => 0110011 => 1
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => [4,3,1,2,8,7,6,5] => 0110111 => 1
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [4,3,2,1,5,6,7,8] => 1110000 => 1
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [4,3,2,1,5,6,8,7] => 1110001 => 1
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [4,3,2,1,5,7,6,8] => 1110010 => 2
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => [4,3,2,1,5,8,6,7] => 1110001 => 1
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => [4,3,2,1,5,8,7,6] => 1110011 => 1
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [4,3,2,1,6,5,7,8] => 1110100 => 2
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [4,3,2,1,6,5,8,7] => 1110101 => 2
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => [4,3,2,1,7,5,6,8] => 1110010 => 2
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [4,3,2,1,7,6,5,8] => 1110110 => 2
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => [4,3,2,1,8,5,6,7] => 1110001 => 1
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => [4,3,2,1,8,5,7,6] => 1110011 => 1
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => [4,3,2,1,8,6,5,7] => 1110101 => 2
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => [4,3,2,1,8,7,5,6] => 1110011 => 1
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => 1110111 => 1
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => [5,1,2,3,4,6,7,8] => 0001000 => 1
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [7,8,6,4,3,2,1,5] => [5,1,2,3,4,6,8,7] => 0001001 => 1
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [7,6,8,4,3,2,1,5] => [5,1,2,3,4,8,6,7] => 0001001 => 1
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [6,7,8,4,3,2,1,5] => [5,1,2,3,4,8,7,6] => 0001011 => 1
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => [5,1,2,4,3,6,7,8] => 0011000 => 1
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [7,8,6,3,4,2,1,5] => [5,1,2,4,3,6,8,7] => 0011001 => 1
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [8,6,7,3,4,2,1,5] => [5,1,2,4,3,7,6,8] => 0011010 => 2
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [6,7,8,3,4,2,1,5] => [5,1,2,4,3,8,7,6] => 0011011 => 1
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,2,3,1,5] => [5,1,3,2,4,6,7,8] => 0101000 => 2
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [7,8,6,4,2,3,1,5] => [5,1,3,2,4,6,8,7] => 0101001 => 2
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [8,6,7,4,2,3,1,5] => [5,1,3,2,4,7,6,8] => 0101010 => 3
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [7,6,8,4,2,3,1,5] => [5,1,3,2,4,8,6,7] => 0101001 => 2
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [6,7,8,4,2,3,1,5] => [5,1,3,2,4,8,7,6] => 0101011 => 2
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => [5,1,4,2,3,6,7,8] => 0011000 => 1
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [7,6,8,3,2,4,1,5] => [5,1,4,2,3,8,6,7] => 0011001 => 1
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [6,7,8,3,2,4,1,5] => [5,1,4,2,3,8,7,6] => 0011011 => 1
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [8,7,6,2,3,4,1,5] => [5,1,4,3,2,6,7,8] => 0111000 => 1
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [7,8,6,2,3,4,1,5] => [5,1,4,3,2,6,8,7] => 0111001 => 1
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [6,7,8,2,3,4,1,5] => [5,1,4,3,2,8,7,6] => 0111011 => 1
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => [5,2,1,3,4,6,7,8] => 1001000 => 2
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => [5,2,1,3,4,8,7,6] => 1001011 => 2
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => [5,2,1,4,3,6,7,8] => 1011000 => 2
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [7,8,6,3,4,1,2,5] => [5,2,1,4,3,6,8,7] => 1011001 => 2
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [8,6,7,3,4,1,2,5] => [5,2,1,4,3,7,6,8] => 1011010 => 3
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [7,6,8,3,4,1,2,5] => [5,2,1,4,3,8,6,7] => 1011001 => 2
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => [5,2,1,4,3,8,7,6] => 1011011 => 2
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => [5,3,1,2,4,6,7,8] => 0101000 => 2
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,2,1,3,5] => [5,3,1,2,4,6,8,7] => 0101001 => 2
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,2,1,3,5] => [5,3,1,2,4,7,6,8] => 0101010 => 3
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [7,6,8,4,2,1,3,5] => [5,3,1,2,4,8,6,7] => 0101001 => 2
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => [5,3,1,2,4,8,7,6] => 0101011 => 2
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [5,3,2,1,4,6,7,8] => 1101000 => 2
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => [5,3,2,1,4,6,8,7] => 1101001 => 2
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,1,2,3,5] => [5,3,2,1,4,7,6,8] => 1101010 => 3
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [7,6,8,4,1,2,3,5] => [5,3,2,1,4,8,6,7] => 1101001 => 2
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => [5,3,2,1,4,8,7,6] => 1101011 => 2
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => [5,4,1,2,3,6,7,8] => 0011000 => 1
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [7,6,8,3,2,1,4,5] => [5,4,1,2,3,8,6,7] => 0011001 => 1
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [6,7,8,3,2,1,4,5] => [5,4,1,2,3,8,7,6] => 0011011 => 1
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [8,7,6,2,3,1,4,5] => [5,4,1,3,2,6,7,8] => 0111000 => 1
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [7,6,8,2,3,1,4,5] => [5,4,1,3,2,8,6,7] => 0111001 => 1
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [6,7,8,2,3,1,4,5] => [5,4,1,3,2,8,7,6] => 0111011 => 1
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [8,7,6,3,1,2,4,5] => [5,4,2,1,3,6,7,8] => 1011000 => 2
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [6,7,8,3,1,2,4,5] => [5,4,2,1,3,8,7,6] => 1011011 => 2
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => [5,4,3,1,2,6,7,8] => 0111000 => 1
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [8,6,7,2,1,3,4,5] => [5,4,3,1,2,7,6,8] => 0111010 => 2
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [7,6,8,2,1,3,4,5] => [5,4,3,1,2,8,6,7] => 0111001 => 1
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => [5,4,3,1,2,8,7,6] => 0111011 => 1
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [5,4,3,2,1,6,7,8] => 1111000 => 1
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [5,4,3,2,1,6,8,7] => 1111001 => 1
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [5,4,3,2,1,7,6,8] => 1111010 => 2
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => [5,4,3,2,1,8,6,7] => 1111001 => 1
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => [5,4,3,2,1,8,7,6] => 1111011 => 1
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [8,7,5,4,3,2,1,6] => [6,1,2,3,4,5,7,8] => 0000100 => 1
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => [6,1,2,3,4,5,8,7] => 0000101 => 1
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [8,7,4,5,3,2,1,6] => [6,1,2,3,5,4,7,8] => 0001100 => 1
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [8,7,5,3,4,2,1,6] => [6,1,2,4,3,5,7,8] => 0010100 => 2
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [7,8,5,3,4,2,1,6] => [6,1,2,4,3,5,8,7] => 0010101 => 2
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [8,7,4,3,5,2,1,6] => [6,1,2,5,3,4,7,8] => 0001100 => 1
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [7,8,3,4,5,2,1,6] => [6,1,2,5,4,3,8,7] => 0011101 => 1
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [7,8,5,4,2,3,1,6] => [6,1,3,2,4,5,8,7] => 0100101 => 2
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [7,8,4,5,2,3,1,6] => [6,1,3,2,5,4,8,7] => 0101101 => 2
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [8,7,5,3,2,4,1,6] => [6,1,4,2,3,5,7,8] => 0010100 => 2
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [7,8,5,3,2,4,1,6] => [6,1,4,2,3,5,8,7] => 0010101 => 2
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [8,7,4,3,2,5,1,6] => [6,1,5,2,3,4,7,8] => 0001100 => 1
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [7,8,4,3,2,5,1,6] => [6,1,5,2,3,4,8,7] => 0001101 => 1
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [7,8,3,4,2,5,1,6] => [6,1,5,2,4,3,8,7] => 0011101 => 1
[[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [7,8,3,2,4,5,1,6] => [6,1,5,4,2,3,8,7] => 0011101 => 1
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [7,8,2,3,4,5,1,6] => [6,1,5,4,3,2,8,7] => 0111101 => 1
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => [6,2,1,3,4,5,7,8] => 1000100 => 2
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [8,7,5,3,4,1,2,6] => [6,2,1,4,3,5,7,8] => 1010100 => 3
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [7,8,5,3,4,1,2,6] => [6,2,1,4,3,5,8,7] => 1010101 => 3
[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [7,8,4,3,5,1,2,6] => [6,2,1,5,3,4,8,7] => 1001101 => 2
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [8,7,3,4,5,1,2,6] => [6,2,1,5,4,3,7,8] => 1011100 => 2
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [7,8,3,4,5,1,2,6] => [6,2,1,5,4,3,8,7] => 1011101 => 2
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,2,1,3,6] => [6,3,1,2,4,5,7,8] => 0100100 => 2
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => [6,3,1,2,4,5,8,7] => 0100101 => 2
[[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [7,8,4,5,2,1,3,6] => [6,3,1,2,5,4,8,7] => 0101101 => 2
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => [6,3,2,1,4,5,7,8] => 1100100 => 2
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => [6,3,2,1,4,5,8,7] => 1100101 => 2
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => [6,3,2,1,5,4,7,8] => 1101100 => 2
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => [6,3,2,1,5,4,8,7] => 1101101 => 2
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [8,7,5,3,2,1,4,6] => [6,4,1,2,3,5,7,8] => 0010100 => 2
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]] => [8,7,5,2,3,1,4,6] => [6,4,1,3,2,5,7,8] => 0110100 => 2
[[[.,[[.,.],.]],[.,.]],[[.,.],.]] => [7,8,5,2,3,1,4,6] => [6,4,1,3,2,5,8,7] => 0110101 => 2
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [8,7,5,3,1,2,4,6] => [6,4,2,1,3,5,7,8] => 1010100 => 3
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [7,8,5,3,1,2,4,6] => [6,4,2,1,3,5,8,7] => 1010101 => 3
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => [6,4,3,1,2,5,7,8] => 0110100 => 2
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => [6,4,3,1,2,5,8,7] => 0110101 => 2
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => [6,4,3,2,1,5,7,8] => 1110100 => 2
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [6,4,3,2,1,5,8,7] => 1110101 => 2
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => [6,5,1,2,3,4,8,7] => 0001101 => 1
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [7,8,3,4,2,1,5,6] => [6,5,1,2,4,3,8,7] => 0011101 => 1
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [7,8,3,2,4,1,5,6] => [6,5,1,4,2,3,8,7] => 0011101 => 1
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [8,7,2,3,4,1,5,6] => [6,5,1,4,3,2,7,8] => 0111100 => 1
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [7,8,2,3,4,1,5,6] => [6,5,1,4,3,2,8,7] => 0111101 => 1
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [7,8,4,3,1,2,5,6] => [6,5,2,1,3,4,8,7] => 1001101 => 2
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => [6,5,2,1,4,3,8,7] => 1011101 => 2
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => [6,5,3,1,2,4,8,7] => 0101101 => 2
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => [6,5,3,2,1,4,7,8] => 1101100 => 2
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [7,8,4,1,2,3,5,6] => [6,5,3,2,1,4,8,7] => 1101101 => 2
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => [6,5,4,1,2,3,7,8] => 0011100 => 1
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => [6,5,4,1,2,3,8,7] => 0011101 => 1
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [7,8,2,3,1,4,5,6] => [6,5,4,1,3,2,8,7] => 0111101 => 1
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [8,7,3,1,2,4,5,6] => [6,5,4,2,1,3,7,8] => 1011100 => 2
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [7,8,3,1,2,4,5,6] => [6,5,4,2,1,3,8,7] => 1011101 => 2
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [8,7,2,1,3,4,5,6] => [6,5,4,3,1,2,7,8] => 0111100 => 1
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => [6,5,4,3,1,2,8,7] => 0111101 => 1
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [6,5,4,3,2,1,7,8] => 1111100 => 1
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [6,5,4,3,2,1,8,7] => 1111101 => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,8] => 0000010 => 1
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [8,5,6,4,3,2,1,7] => [7,1,2,3,4,6,5,8] => 0000110 => 1
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [8,6,4,5,3,2,1,7] => [7,1,2,3,5,4,6,8] => 0001010 => 2
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [8,5,4,6,3,2,1,7] => [7,1,2,3,6,4,5,8] => 0000110 => 1
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => [7,1,2,3,6,5,4,8] => 0001110 => 1
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [8,6,5,3,4,2,1,7] => [7,1,2,4,3,5,6,8] => 0010010 => 2
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [8,6,4,3,5,2,1,7] => [7,1,2,5,3,4,6,8] => 0001010 => 2
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [8,5,4,3,6,2,1,7] => [7,1,2,6,3,4,5,8] => 0000110 => 1
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [8,4,5,3,6,2,1,7] => [7,1,2,6,3,5,4,8] => 0001110 => 1
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [8,5,3,4,6,2,1,7] => [7,1,2,6,4,3,5,8] => 0010110 => 2
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [8,4,3,5,6,2,1,7] => [7,1,2,6,5,3,4,8] => 0001110 => 1
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [8,3,4,5,6,2,1,7] => [7,1,2,6,5,4,3,8] => 0011110 => 1
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,2,3,1,7] => [7,1,3,2,4,5,6,8] => 0100010 => 2
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,2,3,1,7] => [7,1,3,2,5,4,6,8] => 0101010 => 3
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [8,6,5,3,2,4,1,7] => [7,1,4,2,3,5,6,8] => 0010010 => 2
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [8,6,5,2,3,4,1,7] => [7,1,4,3,2,5,6,8] => 0110010 => 2
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [8,6,3,4,2,5,1,7] => [7,1,5,2,4,3,6,8] => 0011010 => 2
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [8,6,4,2,3,5,1,7] => [7,1,5,3,2,4,6,8] => 0101010 => 3
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [8,6,3,2,4,5,1,7] => [7,1,5,4,2,3,6,8] => 0011010 => 2
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [8,5,4,3,2,6,1,7] => [7,1,6,2,3,4,5,8] => 0000110 => 1
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [8,4,3,5,2,6,1,7] => [7,1,6,2,5,3,4,8] => 0001110 => 1
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [8,3,4,5,2,6,1,7] => [7,1,6,2,5,4,3,8] => 0011110 => 1
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [8,4,5,2,3,6,1,7] => [7,1,6,3,2,5,4,8] => 0101110 => 2
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [8,5,3,2,4,6,1,7] => [7,1,6,4,2,3,5,8] => 0010110 => 2
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [8,3,4,2,5,6,1,7] => [7,1,6,5,2,4,3,8] => 0011110 => 1
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [8,4,2,3,5,6,1,7] => [7,1,6,5,3,2,4,8] => 0101110 => 2
[[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [8,3,2,4,5,6,1,7] => [7,1,6,5,4,2,3,8] => 0011110 => 1
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [8,2,3,4,5,6,1,7] => [7,1,6,5,4,3,2,8] => 0111110 => 1
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => [7,2,1,3,4,5,6,8] => 1000010 => 2
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,3,1,2,7] => [7,2,1,3,5,4,6,8] => 1001010 => 3
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [8,6,5,3,4,1,2,7] => [7,2,1,4,3,5,6,8] => 1010010 => 3
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [7,2,1,4,3,6,5,8] => 1010110 => 3
[[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [8,6,3,4,5,1,2,7] => [7,2,1,5,4,3,6,8] => 1011010 => 3
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [8,4,5,3,6,1,2,7] => [7,2,1,6,3,5,4,8] => 1001110 => 2
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [8,4,3,5,6,1,2,7] => [7,2,1,6,5,3,4,8] => 1001110 => 2
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => [7,2,1,6,5,4,3,8] => 1011110 => 2
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => [7,3,1,2,4,5,6,8] => 0100010 => 2
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,2,1,3,7] => [7,3,1,2,4,6,5,8] => 0100110 => 2
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,2,1,3,7] => [7,3,1,2,5,4,6,8] => 0101010 => 3
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [8,5,4,6,2,1,3,7] => [7,3,1,2,6,4,5,8] => 0100110 => 2
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => [7,3,2,1,4,5,6,8] => 1100010 => 2
[[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,1,2,3,7] => [7,3,2,1,4,6,5,8] => 1100110 => 2
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [7,3,2,1,5,4,6,8] => 1101010 => 3
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [8,5,4,6,1,2,3,7] => [7,3,2,1,6,4,5,8] => 1100110 => 2
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [8,6,5,3,2,1,4,7] => [7,4,1,2,3,5,6,8] => 0010010 => 2
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => [7,4,1,3,2,5,6,8] => 0110010 => 2
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [8,5,6,2,3,1,4,7] => [7,4,1,3,2,6,5,8] => 0110110 => 2
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [8,6,5,2,1,3,4,7] => [7,4,3,1,2,5,6,8] => 0110010 => 2
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => [7,4,3,1,2,6,5,8] => 0110110 => 2
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => [7,4,3,2,1,5,6,8] => 1110010 => 2
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => [7,4,3,2,1,6,5,8] => 1110110 => 2
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => [7,5,1,2,3,4,6,8] => 0001010 => 2
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [8,6,3,4,2,1,5,7] => [7,5,1,2,4,3,6,8] => 0011010 => 2
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [8,6,4,2,3,1,5,7] => [7,5,1,3,2,4,6,8] => 0101010 => 3
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [8,6,3,2,4,1,5,7] => [7,5,1,4,2,3,6,8] => 0011010 => 2
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => [7,5,3,1,2,4,6,8] => 0101010 => 3
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [8,6,4,1,2,3,5,7] => [7,5,3,2,1,4,6,8] => 1101010 => 3
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [8,6,2,3,1,4,5,7] => [7,5,4,1,3,2,6,8] => 0111010 => 2
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [8,6,2,1,3,4,5,7] => [7,5,4,3,1,2,6,8] => 0111010 => 2
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => [7,5,4,3,2,1,6,8] => 1111010 => 2
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [8,5,4,3,2,1,6,7] => [7,6,1,2,3,4,5,8] => 0000110 => 1
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [8,4,5,3,2,1,6,7] => [7,6,1,2,3,5,4,8] => 0001110 => 1
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [8,3,4,5,2,1,6,7] => [7,6,1,2,5,4,3,8] => 0011110 => 1
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [8,5,3,2,4,1,6,7] => [7,6,1,4,2,3,5,8] => 0010110 => 2
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [8,5,2,3,4,1,6,7] => [7,6,1,4,3,2,5,8] => 0110110 => 2
[[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [8,3,4,2,5,1,6,7] => [7,6,1,5,2,4,3,8] => 0011110 => 1
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [8,3,4,5,1,2,6,7] => [7,6,2,1,5,4,3,8] => 1011110 => 2
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [8,4,5,2,1,3,6,7] => [7,6,3,1,2,5,4,8] => 0101110 => 2
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [8,5,4,1,2,3,6,7] => [7,6,3,2,1,4,5,8] => 1100110 => 2
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [8,4,5,1,2,3,6,7] => [7,6,3,2,1,5,4,8] => 1101110 => 2
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [8,5,3,1,2,4,6,7] => [7,6,4,2,1,3,5,8] => 1010110 => 3
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [8,5,2,1,3,4,6,7] => [7,6,4,3,1,2,5,8] => 0110110 => 2
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => [7,6,4,3,2,1,5,8] => 1110110 => 2
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => [7,6,5,1,2,3,4,8] => 0001110 => 1
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [8,3,4,2,1,5,6,7] => [7,6,5,1,2,4,3,8] => 0011110 => 1
[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [8,4,2,3,1,5,6,7] => [7,6,5,1,3,2,4,8] => 0101110 => 2
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [8,3,2,4,1,5,6,7] => [7,6,5,1,4,2,3,8] => 0011110 => 1
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => [7,6,5,1,4,3,2,8] => 0111110 => 1
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [8,4,3,1,2,5,6,7] => [7,6,5,2,1,3,4,8] => 1001110 => 2
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [8,3,4,1,2,5,6,7] => [7,6,5,2,1,4,3,8] => 1011110 => 2
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => [7,6,5,3,2,1,4,8] => 1101110 => 2
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => [7,6,5,4,1,2,3,8] => 0011110 => 1
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => [7,6,5,4,1,3,2,8] => 0111110 => 1
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => [7,6,5,4,2,1,3,8] => 1011110 => 2
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => [7,6,5,4,3,1,2,8] => 0111110 => 1
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,8] => 1111110 => 1
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7] => 0000001 => 0
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [8,1,2,3,4,5,7,6] => 0000011 => 0
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [7,5,6,4,3,2,1,8] => [8,1,2,3,4,6,5,7] => 0000101 => 1
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [8,1,2,3,4,7,5,6] => 0000011 => 0
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [8,1,2,3,4,7,6,5] => 0000111 => 0
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => [8,1,2,3,5,4,6,7] => 0001001 => 1
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [6,7,4,5,3,2,1,8] => [8,1,2,3,5,4,7,6] => 0001011 => 1
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [7,5,4,6,3,2,1,8] => [8,1,2,3,6,4,5,7] => 0000101 => 1
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => [8,1,2,3,6,5,4,7] => 0001101 => 1
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [8,1,2,3,7,4,5,6] => 0000011 => 0
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [6,4,5,7,3,2,1,8] => [8,1,2,3,7,5,4,6] => 0001011 => 1
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => [8,1,2,3,7,6,5,4] => 0001111 => 0
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [7,6,5,3,4,2,1,8] => [8,1,2,4,3,5,6,7] => 0010001 => 1
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [6,7,5,3,4,2,1,8] => [8,1,2,4,3,5,7,6] => 0010011 => 1
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => [8,1,2,4,3,6,5,7] => 0010101 => 2
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [5,6,7,3,4,2,1,8] => [8,1,2,4,3,7,6,5] => 0010111 => 1
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => [8,1,2,5,3,4,6,7] => 0001001 => 1
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [6,7,4,3,5,2,1,8] => [8,1,2,5,3,4,7,6] => 0001011 => 1
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => [8,1,2,5,4,3,6,7] => 0011001 => 1
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => [8,1,2,6,3,4,5,7] => 0000101 => 1
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [7,4,3,5,6,2,1,8] => [8,1,2,6,5,3,4,7] => 0001101 => 1
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [7,3,4,5,6,2,1,8] => [8,1,2,6,5,4,3,7] => 0011101 => 1
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => [8,1,2,7,3,4,5,6] => 0000011 => 0
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => [8,1,2,7,3,4,6,5] => 0000111 => 0
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [6,4,5,3,7,2,1,8] => [8,1,2,7,3,5,4,6] => 0001011 => 1
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => [8,1,2,7,3,6,4,5] => 0000111 => 0
[[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [4,5,6,3,7,2,1,8] => [8,1,2,7,3,6,5,4] => 0001111 => 0
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [5,6,3,4,7,2,1,8] => [8,1,2,7,4,3,6,5] => 0010111 => 1
[[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [6,3,4,5,7,2,1,8] => [8,1,2,7,5,4,3,6] => 0011011 => 1
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => [8,1,2,7,6,3,4,5] => 0000111 => 0
[[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [4,5,3,6,7,2,1,8] => [8,1,2,7,6,3,5,4] => 0001111 => 0
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => [8,1,2,7,6,5,4,3] => 0011111 => 0
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,2,3,1,8] => [8,1,3,2,4,5,6,7] => 0100001 => 1
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => [8,1,3,2,4,5,7,6] => 0100011 => 1
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,2,3,1,8] => [8,1,3,2,4,6,5,7] => 0100101 => 2
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [5,6,7,4,2,3,1,8] => [8,1,3,2,4,7,6,5] => 0100111 => 1
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => [8,1,3,2,5,4,6,7] => 0101001 => 2
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [6,7,4,5,2,3,1,8] => [8,1,3,2,5,4,7,6] => 0101011 => 2
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [7,4,5,6,2,3,1,8] => [8,1,3,2,6,5,4,7] => 0101101 => 2
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [5,6,4,7,2,3,1,8] => [8,1,3,2,7,4,6,5] => 0100111 => 1
[[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [6,4,5,7,2,3,1,8] => [8,1,3,2,7,5,4,6] => 0101011 => 2
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [5,4,6,7,2,3,1,8] => [8,1,3,2,7,6,4,5] => 0100111 => 1
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [4,5,6,7,2,3,1,8] => [8,1,3,2,7,6,5,4] => 0101111 => 1
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [7,6,5,3,2,4,1,8] => [8,1,4,2,3,5,6,7] => 0010001 => 1
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [6,7,5,3,2,4,1,8] => [8,1,4,2,3,5,7,6] => 0010011 => 1
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [7,5,6,3,2,4,1,8] => [8,1,4,2,3,6,5,7] => 0010101 => 2
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => [8,1,4,2,3,7,5,6] => 0010011 => 1
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => [8,1,4,2,3,7,6,5] => 0010111 => 1
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => [8,1,4,3,2,5,6,7] => 0110001 => 1
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [6,7,5,2,3,4,1,8] => [8,1,4,3,2,5,7,6] => 0110011 => 1
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [7,5,6,2,3,4,1,8] => [8,1,4,3,2,6,5,7] => 0110101 => 2
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => [8,1,4,3,2,7,5,6] => 0110011 => 1
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => [8,1,4,3,2,7,6,5] => 0110111 => 1
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [7,6,4,3,2,5,1,8] => [8,1,5,2,3,4,6,7] => 0001001 => 1
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [6,7,3,4,2,5,1,8] => [8,1,5,2,4,3,7,6] => 0011011 => 1
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [7,6,4,2,3,5,1,8] => [8,1,5,3,2,4,6,7] => 0101001 => 2
[[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [6,7,4,2,3,5,1,8] => [8,1,5,3,2,4,7,6] => 0101011 => 2
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [7,6,3,2,4,5,1,8] => [8,1,5,4,2,3,6,7] => 0011001 => 1
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [7,6,2,3,4,5,1,8] => [8,1,5,4,3,2,6,7] => 0111001 => 1
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [6,7,2,3,4,5,1,8] => [8,1,5,4,3,2,7,6] => 0111011 => 1
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [7,5,4,3,2,6,1,8] => [8,1,6,2,3,4,5,7] => 0000101 => 1
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [7,4,5,3,2,6,1,8] => [8,1,6,2,3,5,4,7] => 0001101 => 1
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [7,5,3,4,2,6,1,8] => [8,1,6,2,4,3,5,7] => 0010101 => 2
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [7,4,3,5,2,6,1,8] => [8,1,6,2,5,3,4,7] => 0001101 => 1
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [7,5,4,2,3,6,1,8] => [8,1,6,3,2,4,5,7] => 0100101 => 2
[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [7,4,5,2,3,6,1,8] => [8,1,6,3,2,5,4,7] => 0101101 => 2
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [7,5,3,2,4,6,1,8] => [8,1,6,4,2,3,5,7] => 0010101 => 2
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [7,4,3,2,5,6,1,8] => [8,1,6,5,2,3,4,7] => 0001101 => 1
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [7,2,3,4,5,6,1,8] => [8,1,6,5,4,3,2,7] => 0111101 => 1
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => [8,1,7,2,3,4,5,6] => 0000011 => 0
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => [8,1,7,2,3,6,4,5] => 0000111 => 0
[[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [4,5,6,3,2,7,1,8] => [8,1,7,2,3,6,5,4] => 0001111 => 0
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [6,5,3,4,2,7,1,8] => [8,1,7,2,4,3,5,6] => 0010011 => 1
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [5,6,3,4,2,7,1,8] => [8,1,7,2,4,3,6,5] => 0010111 => 1
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [6,4,3,5,2,7,1,8] => [8,1,7,2,5,3,4,6] => 0001011 => 1
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [6,3,4,5,2,7,1,8] => [8,1,7,2,5,4,3,6] => 0011011 => 1
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [8,1,7,2,6,3,4,5] => 0000111 => 0
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [8,1,7,2,6,3,5,4] => 0001111 => 0
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [5,3,4,6,2,7,1,8] => [8,1,7,2,6,4,3,5] => 0010111 => 1
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [8,1,7,2,6,5,4,3] => 0011111 => 0
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [6,5,4,2,3,7,1,8] => [8,1,7,3,2,4,5,6] => 0100011 => 1
[[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [6,4,5,2,3,7,1,8] => [8,1,7,3,2,5,4,6] => 0101011 => 2
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [5,4,6,2,3,7,1,8] => [8,1,7,3,2,6,4,5] => 0100111 => 1
[[.,[[[.,.],[[[.,.],.],.]],.]],.] => [4,5,6,2,3,7,1,8] => [8,1,7,3,2,6,5,4] => 0101111 => 1
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [6,5,3,2,4,7,1,8] => [8,1,7,4,2,3,5,6] => 0010011 => 1
[[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [5,6,3,2,4,7,1,8] => [8,1,7,4,2,3,6,5] => 0010111 => 1
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [5,6,2,3,4,7,1,8] => [8,1,7,4,3,2,6,5] => 0110111 => 1
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [6,3,4,2,5,7,1,8] => [8,1,7,5,2,4,3,6] => 0011011 => 1
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [6,4,2,3,5,7,1,8] => [8,1,7,5,3,2,4,6] => 0101011 => 2
[[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [6,3,2,4,5,7,1,8] => [8,1,7,5,4,2,3,6] => 0011011 => 1
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [6,2,3,4,5,7,1,8] => [8,1,7,5,4,3,2,6] => 0111011 => 1
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [8,1,7,6,2,3,4,5] => 0000111 => 0
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [5,3,4,2,6,7,1,8] => [8,1,7,6,2,4,3,5] => 0010111 => 1
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => [8,1,7,6,2,5,4,3] => 0011111 => 0
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [5,4,2,3,6,7,1,8] => [8,1,7,6,3,2,4,5] => 0100111 => 1
[[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [5,3,2,4,6,7,1,8] => [8,1,7,6,4,2,3,5] => 0010111 => 1
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [5,2,3,4,6,7,1,8] => [8,1,7,6,4,3,2,5] => 0110111 => 1
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => [8,1,7,6,5,2,3,4] => 0001111 => 0
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => [8,1,7,6,5,2,4,3] => 0011111 => 0
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [4,2,3,5,6,7,1,8] => [8,1,7,6,5,3,2,4] => 0101111 => 1
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [8,1,7,6,5,4,2,3] => 0011111 => 0
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [8,1,7,6,5,4,3,2] => 0111111 => 0
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [8,2,1,3,4,5,6,7] => 1000001 => 1
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,3,1,2,8] => [8,2,1,3,4,5,7,6] => 1000011 => 1
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => [8,2,1,3,4,6,5,7] => 1000101 => 2
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [6,5,7,4,3,1,2,8] => [8,2,1,3,4,7,5,6] => 1000011 => 1
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [7,5,4,6,3,1,2,8] => [8,2,1,3,6,4,5,7] => 1000101 => 2
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [7,4,5,6,3,1,2,8] => [8,2,1,3,6,5,4,7] => 1001101 => 2
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [5,6,4,7,3,1,2,8] => [8,2,1,3,7,4,6,5] => 1000111 => 1
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [5,4,6,7,3,1,2,8] => [8,2,1,3,7,6,4,5] => 1000111 => 1
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [4,5,6,7,3,1,2,8] => [8,2,1,3,7,6,5,4] => 1001111 => 1
[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [6,7,5,3,4,1,2,8] => [8,2,1,4,3,5,7,6] => 1010011 => 2
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [7,5,6,3,4,1,2,8] => [8,2,1,4,3,6,5,7] => 1010101 => 3
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [6,5,7,3,4,1,2,8] => [8,2,1,4,3,7,5,6] => 1010011 => 2
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [5,6,7,3,4,1,2,8] => [8,2,1,4,3,7,6,5] => 1010111 => 2
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [6,7,3,4,5,1,2,8] => [8,2,1,5,4,3,7,6] => 1011011 => 2
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [7,5,4,3,6,1,2,8] => [8,2,1,6,3,4,5,7] => 1000101 => 2
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [7,5,3,4,6,1,2,8] => [8,2,1,6,4,3,5,7] => 1010101 => 3
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [7,4,3,5,6,1,2,8] => [8,2,1,6,5,3,4,7] => 1001101 => 2
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [6,5,4,3,7,1,2,8] => [8,2,1,7,3,4,5,6] => 1000011 => 1
[[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [6,4,5,3,7,1,2,8] => [8,2,1,7,3,5,4,6] => 1001011 => 2
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [6,5,3,4,7,1,2,8] => [8,2,1,7,4,3,5,6] => 1010011 => 2
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [5,6,3,4,7,1,2,8] => [8,2,1,7,4,3,6,5] => 1010111 => 2
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [6,4,3,5,7,1,2,8] => [8,2,1,7,5,3,4,6] => 1001011 => 2
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [6,3,4,5,7,1,2,8] => [8,2,1,7,5,4,3,6] => 1011011 => 2
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [5,4,3,6,7,1,2,8] => [8,2,1,7,6,3,4,5] => 1000111 => 1
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [4,5,3,6,7,1,2,8] => [8,2,1,7,6,3,5,4] => 1001111 => 1
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [5,3,4,6,7,1,2,8] => [8,2,1,7,6,4,3,5] => 1010111 => 2
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [4,3,5,6,7,1,2,8] => [8,2,1,7,6,5,3,4] => 1001111 => 1
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [3,4,5,6,7,1,2,8] => [8,2,1,7,6,5,4,3] => 1011111 => 1
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => [8,3,1,2,4,5,6,7] => 0100001 => 1
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [6,7,5,4,2,1,3,8] => [8,3,1,2,4,5,7,6] => 0100011 => 1
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,2,1,3,8] => [8,3,1,2,4,6,5,7] => 0100101 => 2
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => [8,3,1,2,4,7,5,6] => 0100011 => 1
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [5,6,7,4,2,1,3,8] => [8,3,1,2,4,7,6,5] => 0100111 => 1
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,2,1,3,8] => [8,3,1,2,5,4,6,7] => 0101001 => 2
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [6,7,4,5,2,1,3,8] => [8,3,1,2,5,4,7,6] => 0101011 => 2
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => [8,3,1,2,6,4,5,7] => 0100101 => 2
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [7,4,5,6,2,1,3,8] => [8,3,1,2,6,5,4,7] => 0101101 => 2
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [6,5,4,7,2,1,3,8] => [8,3,1,2,7,4,5,6] => 0100011 => 1
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [5,4,6,7,2,1,3,8] => [8,3,1,2,7,6,4,5] => 0100111 => 1
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [4,5,6,7,2,1,3,8] => [8,3,1,2,7,6,5,4] => 0101111 => 1
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [8,3,2,1,4,5,6,7] => 1100001 => 1
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [6,7,5,4,1,2,3,8] => [8,3,2,1,4,5,7,6] => 1100011 => 1
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,1,2,3,8] => [8,3,2,1,4,6,5,7] => 1100101 => 2
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,1,2,3,8] => [8,3,2,1,4,7,5,6] => 1100011 => 1
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => [8,3,2,1,4,7,6,5] => 1100111 => 1
[[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,1,2,3,8] => [8,3,2,1,5,4,6,7] => 1101001 => 2
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [6,7,4,5,1,2,3,8] => [8,3,2,1,5,4,7,6] => 1101011 => 2
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,1,2,3,8] => [8,3,2,1,6,4,5,7] => 1100101 => 2
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => [8,3,2,1,6,5,4,7] => 1101101 => 2
[[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [6,5,4,7,1,2,3,8] => [8,3,2,1,7,4,5,6] => 1100011 => 1
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => [8,3,2,1,7,4,6,5] => 1100111 => 1
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => [8,3,2,1,7,6,4,5] => 1100111 => 1
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => [8,3,2,1,7,6,5,4] => 1101111 => 1
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [7,6,5,3,2,1,4,8] => [8,4,1,2,3,5,6,7] => 0010001 => 1
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [6,5,7,3,2,1,4,8] => [8,4,1,2,3,7,5,6] => 0010011 => 1
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [7,6,5,2,3,1,4,8] => [8,4,1,3,2,5,6,7] => 0110001 => 1
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [6,7,5,2,3,1,4,8] => [8,4,1,3,2,5,7,6] => 0110011 => 1
[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [7,5,6,2,3,1,4,8] => [8,4,1,3,2,6,5,7] => 0110101 => 2
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [5,6,7,2,3,1,4,8] => [8,4,1,3,2,7,6,5] => 0110111 => 1
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [7,6,5,3,1,2,4,8] => [8,4,2,1,3,5,6,7] => 1010001 => 2
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [6,7,5,3,1,2,4,8] => [8,4,2,1,3,5,7,6] => 1010011 => 2
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [7,5,6,3,1,2,4,8] => [8,4,2,1,3,6,5,7] => 1010101 => 3
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [6,5,7,3,1,2,4,8] => [8,4,2,1,3,7,5,6] => 1010011 => 2
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => [8,4,2,1,3,7,6,5] => 1010111 => 2
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [6,7,5,2,1,3,4,8] => [8,4,3,1,2,5,7,6] => 0110011 => 1
[[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [7,5,6,2,1,3,4,8] => [8,4,3,1,2,6,5,7] => 0110101 => 2
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => [8,4,3,1,2,7,6,5] => 0110111 => 1
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [8,4,3,2,1,5,6,7] => 1110001 => 1
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => [8,4,3,2,1,5,7,6] => 1110011 => 1
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => [8,4,3,2,1,6,5,7] => 1110101 => 2
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => [8,4,3,2,1,7,5,6] => 1110011 => 1
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => [8,4,3,2,1,7,6,5] => 1110111 => 1
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => [8,5,1,2,3,4,6,7] => 0001001 => 1
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [7,6,3,4,2,1,5,8] => [8,5,1,2,4,3,6,7] => 0011001 => 1
[[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [6,7,3,4,2,1,5,8] => [8,5,1,2,4,3,7,6] => 0011011 => 1
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [7,6,4,2,3,1,5,8] => [8,5,1,3,2,4,6,7] => 0101001 => 2
[[[.,[[.,.],[.,.]]],[[.,.],.]],.] => [6,7,4,2,3,1,5,8] => [8,5,1,3,2,4,7,6] => 0101011 => 2
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [7,6,3,2,4,1,5,8] => [8,5,1,4,2,3,6,7] => 0011001 => 1
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [6,7,3,2,4,1,5,8] => [8,5,1,4,2,3,7,6] => 0011011 => 1
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => [8,5,2,1,3,4,6,7] => 1001001 => 2
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [7,6,3,4,1,2,5,8] => [8,5,2,1,4,3,6,7] => 1011001 => 2
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [6,7,3,4,1,2,5,8] => [8,5,2,1,4,3,7,6] => 1011011 => 2
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [7,6,4,2,1,3,5,8] => [8,5,3,1,2,4,6,7] => 0101001 => 2
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [6,7,4,2,1,3,5,8] => [8,5,3,1,2,4,7,6] => 0101011 => 2
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [7,6,4,1,2,3,5,8] => [8,5,3,2,1,4,6,7] => 1101001 => 2
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [6,7,4,1,2,3,5,8] => [8,5,3,2,1,4,7,6] => 1101011 => 2
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [7,6,3,2,1,4,5,8] => [8,5,4,1,2,3,6,7] => 0011001 => 1
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [6,7,3,2,1,4,5,8] => [8,5,4,1,2,3,7,6] => 0011011 => 1
[[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [7,6,2,3,1,4,5,8] => [8,5,4,1,3,2,6,7] => 0111001 => 1
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [6,7,2,3,1,4,5,8] => [8,5,4,1,3,2,7,6] => 0111011 => 1
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [7,6,3,1,2,4,5,8] => [8,5,4,2,1,3,6,7] => 1011001 => 2
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [6,7,3,1,2,4,5,8] => [8,5,4,2,1,3,7,6] => 1011011 => 2
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => [8,5,4,3,2,1,6,7] => 1111001 => 1
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => [8,5,4,3,2,1,7,6] => 1111011 => 1
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [7,5,4,3,2,1,6,8] => [8,6,1,2,3,4,5,7] => 0000101 => 1
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [7,4,5,3,2,1,6,8] => [8,6,1,2,3,5,4,7] => 0001101 => 1
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [7,5,3,4,2,1,6,8] => [8,6,1,2,4,3,5,7] => 0010101 => 2
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [7,4,3,5,2,1,6,8] => [8,6,1,2,5,3,4,7] => 0001101 => 1
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [7,3,4,5,2,1,6,8] => [8,6,1,2,5,4,3,7] => 0011101 => 1
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [7,5,4,2,3,1,6,8] => [8,6,1,3,2,4,5,7] => 0100101 => 2
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [7,5,3,2,4,1,6,8] => [8,6,1,4,2,3,5,7] => 0010101 => 2
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [7,5,2,3,4,1,6,8] => [8,6,1,4,3,2,5,7] => 0110101 => 2
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [7,4,3,2,5,1,6,8] => [8,6,1,5,2,3,4,7] => 0001101 => 1
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [7,3,4,2,5,1,6,8] => [8,6,1,5,2,4,3,7] => 0011101 => 1
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [7,4,2,3,5,1,6,8] => [8,6,1,5,3,2,4,7] => 0101101 => 2
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [7,2,3,4,5,1,6,8] => [8,6,1,5,4,3,2,7] => 0111101 => 1
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [7,4,5,3,1,2,6,8] => [8,6,2,1,3,5,4,7] => 1001101 => 2
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [7,5,3,4,1,2,6,8] => [8,6,2,1,4,3,5,7] => 1010101 => 3
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [7,4,3,5,1,2,6,8] => [8,6,2,1,5,3,4,7] => 1001101 => 2
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [7,3,4,5,1,2,6,8] => [8,6,2,1,5,4,3,7] => 1011101 => 2
[[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [7,4,5,2,1,3,6,8] => [8,6,3,1,2,5,4,7] => 0101101 => 2
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [7,5,4,1,2,3,6,8] => [8,6,3,2,1,4,5,7] => 1100101 => 2
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [7,4,5,1,2,3,6,8] => [8,6,3,2,1,5,4,7] => 1101101 => 2
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [7,5,2,3,1,4,6,8] => [8,6,4,1,3,2,5,7] => 0110101 => 2
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8] => [8,6,4,2,1,3,5,7] => 1010101 => 3
[[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [7,5,2,1,3,4,6,8] => [8,6,4,3,1,2,5,7] => 0110101 => 2
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [8,6,4,3,2,1,5,7] => 1110101 => 2
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8] => [8,6,5,1,2,3,4,7] => 0001101 => 1
[[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [7,3,4,2,1,5,6,8] => [8,6,5,1,2,4,3,7] => 0011101 => 1
[[[[.,[[.,.],[.,.]]],.],[.,.]],.] => [7,4,2,3,1,5,6,8] => [8,6,5,1,3,2,4,7] => 0101101 => 2
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [7,2,3,4,1,5,6,8] => [8,6,5,1,4,3,2,7] => 0111101 => 1
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [7,4,3,1,2,5,6,8] => [8,6,5,2,1,3,4,7] => 1001101 => 2
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [7,3,4,1,2,5,6,8] => [8,6,5,2,1,4,3,7] => 1011101 => 2
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [7,4,1,2,3,5,6,8] => [8,6,5,3,2,1,4,7] => 1101101 => 2
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [7,3,2,1,4,5,6,8] => [8,6,5,4,1,2,3,7] => 0011101 => 1
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [7,2,3,1,4,5,6,8] => [8,6,5,4,1,3,2,7] => 0111101 => 1
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => [8,6,5,4,2,1,3,7] => 1011101 => 2
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => [8,6,5,4,3,1,2,7] => 0111101 => 1
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => [8,6,5,4,3,2,1,7] => 1111101 => 1
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [8,7,1,2,3,4,5,6] => 0000011 => 0
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => [8,7,1,2,3,4,6,5] => 0000111 => 0
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => [8,7,1,2,3,6,4,5] => 0000111 => 0
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => [8,7,1,2,3,6,5,4] => 0001111 => 0
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [6,5,3,4,2,1,7,8] => [8,7,1,2,4,3,5,6] => 0010011 => 1
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [5,6,3,4,2,1,7,8] => [8,7,1,2,4,3,6,5] => 0010111 => 1
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [6,4,3,5,2,1,7,8] => [8,7,1,2,5,3,4,6] => 0001011 => 1
[[[.,[.,[[[.,.],.],[.,.]]]],.],.] => [6,3,4,5,2,1,7,8] => [8,7,1,2,5,4,3,6] => 0011011 => 1
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => [8,7,1,2,6,3,4,5] => 0000111 => 0
[[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [4,3,5,6,2,1,7,8] => [8,7,1,2,6,5,3,4] => 0001111 => 0
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => [8,7,1,2,6,5,4,3] => 0011111 => 0
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [6,5,4,2,3,1,7,8] => [8,7,1,3,2,4,5,6] => 0100011 => 1
[[[.,[[.,.],[.,[[.,.],.]]]],.],.] => [5,6,4,2,3,1,7,8] => [8,7,1,3,2,4,6,5] => 0100111 => 1
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [6,4,5,2,3,1,7,8] => [8,7,1,3,2,5,4,6] => 0101011 => 2
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [5,4,6,2,3,1,7,8] => [8,7,1,3,2,6,4,5] => 0100111 => 1
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [6,5,3,2,4,1,7,8] => [8,7,1,4,2,3,5,6] => 0010011 => 1
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [6,5,2,3,4,1,7,8] => [8,7,1,4,3,2,5,6] => 0110011 => 1
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [5,6,2,3,4,1,7,8] => [8,7,1,4,3,2,6,5] => 0110111 => 1
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [6,4,3,2,5,1,7,8] => [8,7,1,5,2,3,4,6] => 0001011 => 1
[[[.,[[[.,[.,.]],.],[.,.]]],.],.] => [6,3,2,4,5,1,7,8] => [8,7,1,5,4,2,3,6] => 0011011 => 1
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [8,7,1,6,2,3,4,5] => 0000111 => 0
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => [8,7,1,6,2,3,5,4] => 0001111 => 0
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [8,7,1,6,2,5,3,4] => 0001111 => 0
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => [8,7,1,6,2,5,4,3] => 0011111 => 0
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [5,3,2,4,6,1,7,8] => [8,7,1,6,4,2,3,5] => 0010111 => 1
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [5,2,3,4,6,1,7,8] => [8,7,1,6,4,3,2,5] => 0110111 => 1
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => [8,7,1,6,5,2,3,4] => 0001111 => 0
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => [8,7,1,6,5,2,4,3] => 0011111 => 0
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [4,2,3,5,6,1,7,8] => [8,7,1,6,5,3,2,4] => 0101111 => 1
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [8,7,1,6,5,4,3,2] => 0111111 => 0
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [6,5,4,3,1,2,7,8] => [8,7,2,1,3,4,5,6] => 1000011 => 1
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => [8,7,2,1,3,4,6,5] => 1000111 => 1
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [6,4,5,3,1,2,7,8] => [8,7,2,1,3,5,4,6] => 1001011 => 2
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => [8,7,2,1,3,6,4,5] => 1000111 => 1
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [4,5,6,3,1,2,7,8] => [8,7,2,1,3,6,5,4] => 1001111 => 1
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [6,5,3,4,1,2,7,8] => [8,7,2,1,4,3,5,6] => 1010011 => 2
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => [8,7,2,1,4,3,6,5] => 1010111 => 2
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [6,4,3,5,1,2,7,8] => [8,7,2,1,5,3,4,6] => 1001011 => 2
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [6,3,4,5,1,2,7,8] => [8,7,2,1,5,4,3,6] => 1011011 => 2
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => [8,7,2,1,6,3,4,5] => 1000111 => 1
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [3,4,5,6,1,2,7,8] => [8,7,2,1,6,5,4,3] => 1011111 => 1
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => [8,7,3,1,2,4,6,5] => 0100111 => 1
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [5,4,6,2,1,3,7,8] => [8,7,3,1,2,6,4,5] => 0100111 => 1
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8] => [8,7,3,2,1,4,5,6] => 1100011 => 1
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [5,6,4,1,2,3,7,8] => [8,7,3,2,1,4,6,5] => 1100111 => 1
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [6,4,5,1,2,3,7,8] => [8,7,3,2,1,5,4,6] => 1101011 => 2
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [5,4,6,1,2,3,7,8] => [8,7,3,2,1,6,4,5] => 1100111 => 1
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => [8,7,3,2,1,6,5,4] => 1101111 => 1
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [6,5,3,2,1,4,7,8] => [8,7,4,1,2,3,5,6] => 0010011 => 1
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => [8,7,4,1,2,3,6,5] => 0010111 => 1
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [5,6,2,3,1,4,7,8] => [8,7,4,1,3,2,6,5] => 0110111 => 1
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [6,5,3,1,2,4,7,8] => [8,7,4,2,1,3,5,6] => 1010011 => 2
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [5,6,3,1,2,4,7,8] => [8,7,4,2,1,3,6,5] => 1010111 => 2
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [6,5,1,2,3,4,7,8] => [8,7,4,3,2,1,5,6] => 1110011 => 1
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [5,6,1,2,3,4,7,8] => [8,7,4,3,2,1,6,5] => 1110111 => 1
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8] => [8,7,5,1,2,3,4,6] => 0001011 => 1
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [6,3,4,2,1,5,7,8] => [8,7,5,1,2,4,3,6] => 0011011 => 1
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [6,3,2,4,1,5,7,8] => [8,7,5,1,4,2,3,6] => 0011011 => 1
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [6,2,3,4,1,5,7,8] => [8,7,5,1,4,3,2,6] => 0111011 => 1
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [6,4,3,1,2,5,7,8] => [8,7,5,2,1,3,4,6] => 1001011 => 2
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [6,4,2,1,3,5,7,8] => [8,7,5,3,1,2,4,6] => 0101011 => 2
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => [8,7,5,3,2,1,4,6] => 1101011 => 2
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [6,3,2,1,4,5,7,8] => [8,7,5,4,1,2,3,6] => 0011011 => 1
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [6,2,3,1,4,5,7,8] => [8,7,5,4,1,3,2,6] => 0111011 => 1
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [6,2,1,3,4,5,7,8] => [8,7,5,4,3,1,2,6] => 0111011 => 1
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => [8,7,5,4,3,2,1,6] => 1111011 => 1
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [8,7,6,1,2,3,4,5] => 0000111 => 0
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => [8,7,6,1,2,3,5,4] => 0001111 => 0
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [5,3,4,2,1,6,7,8] => [8,7,6,1,2,4,3,5] => 0010111 => 1
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => [8,7,6,1,2,5,3,4] => 0001111 => 0
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => [8,7,6,1,2,5,4,3] => 0011111 => 0
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [5,4,2,3,1,6,7,8] => [8,7,6,1,3,2,4,5] => 0100111 => 1
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [4,5,2,3,1,6,7,8] => [8,7,6,1,3,2,5,4] => 0101111 => 1
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [5,3,2,4,1,6,7,8] => [8,7,6,1,4,2,3,5] => 0010111 => 1
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [5,2,3,4,1,6,7,8] => [8,7,6,1,4,3,2,5] => 0110111 => 1
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => [8,7,6,1,5,2,3,4] => 0001111 => 0
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [8,7,6,1,5,2,4,3] => 0011111 => 0
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [4,2,3,5,1,6,7,8] => [8,7,6,1,5,3,2,4] => 0101111 => 1
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => [8,7,6,1,5,4,2,3] => 0011111 => 0
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [8,7,6,1,5,4,3,2] => 0111111 => 0
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [5,4,3,1,2,6,7,8] => [8,7,6,2,1,3,4,5] => 1000111 => 1
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [5,3,4,1,2,6,7,8] => [8,7,6,2,1,4,3,5] => 1010111 => 2
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [4,3,5,1,2,6,7,8] => [8,7,6,2,1,5,3,4] => 1001111 => 1
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [5,4,2,1,3,6,7,8] => [8,7,6,3,1,2,4,5] => 0100111 => 1
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [5,4,1,2,3,6,7,8] => [8,7,6,3,2,1,4,5] => 1100111 => 1
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [4,5,1,2,3,6,7,8] => [8,7,6,3,2,1,5,4] => 1101111 => 1
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [5,3,2,1,4,6,7,8] => [8,7,6,4,1,2,3,5] => 0010111 => 1
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [5,2,3,1,4,6,7,8] => [8,7,6,4,1,3,2,5] => 0110111 => 1
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => [8,7,6,4,2,1,3,5] => 1010111 => 2
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [5,2,1,3,4,6,7,8] => [8,7,6,4,3,1,2,5] => 0110111 => 1
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => [8,7,6,4,3,2,1,5] => 1110111 => 1
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [8,7,6,5,1,2,3,4] => 0001111 => 0
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => [8,7,6,5,1,2,4,3] => 0011111 => 0
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [4,2,3,1,5,6,7,8] => [8,7,6,5,1,3,2,4] => 0101111 => 1
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [8,7,6,5,1,4,2,3] => 0011111 => 0
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [8,7,6,5,1,4,3,2] => 0111111 => 0
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [4,3,1,2,5,6,7,8] => [8,7,6,5,2,1,3,4] => 1001111 => 1
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => [8,7,6,5,2,1,4,3] => 1011111 => 1
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [4,2,1,3,5,6,7,8] => [8,7,6,5,3,1,2,4] => 0101111 => 1
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => [8,7,6,5,3,2,1,4] => 1101111 => 1
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [8,7,6,5,4,1,2,3] => 0011111 => 0
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [8,7,6,5,4,1,3,2] => 0111111 => 0
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => [8,7,6,5,4,2,1,3] => 1011111 => 1
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [8,7,6,5,4,3,1,2] => 0111111 => 0
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => 1111111 => 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] => [1,2,3,4,5,6,7,9,8] => 00000001 => 0
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [1,2,3,4,5,6,9,8,7] => 00000011 => 0
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => [1,2,3,4,5,9,8,7,6] => 00000111 => 0
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => [1,2,3,4,9,8,7,6,5] => 00001111 => 0
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => [1,2,3,9,8,7,6,5,4] => 00011111 => 0
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => [1,2,9,8,7,6,5,4,3] => 00111111 => 0
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,3,2] => 01111111 => 0
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1] => 11111111 => 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] => [1,2,3,4,5,6,7,8,10,9] => 000000001 => 0
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [9,7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,7,9] => 00000010 => 1
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,10,9,8] => 000000011 => 0
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [8,9,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,9,8] => 00000101 => 1
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => [1,2,3,4,5,6,10,9,8,7] => 000000111 => 0
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [7,8,9,5,6,4,3,2,1] => [1,2,3,4,6,5,9,8,7] => 00001011 => 1
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [1,2,3,4,5,10,9,8,7,6] => 000001111 => 0
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [6,7,8,9,4,5,3,2,1] => [1,2,3,5,4,9,8,7,6] => 00010111 => 1
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => [1,2,3,4,10,9,8,7,6,5] => 000011111 => 0
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [5,6,7,8,9,3,4,2,1] => [1,2,4,3,9,8,7,6,5] => 00101111 => 1
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => [1,2,3,10,9,8,7,6,5,4] => 000111111 => 0
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,2,3,1] => [1,3,2,9,8,7,6,5,4] => 01011111 => 1
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => [1,2,10,9,8,7,6,5,4,3] => 001111111 => 0
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 0
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 0
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [1,2,3,4,5,6,9,7,8] => 00000001 => 0
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [1,2,3,4,5,9,6,7,8] => 00000001 => 0
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [1,2,3,4,9,5,6,7,8] => 00000001 => 0
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [1,2,3,9,4,5,6,7,8] => 00000001 => 0
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [1,2,9,3,4,5,6,7,8] => 00000001 => 0
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,7,8] => 00000001 => 0
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,7,8] => 00000001 => 0
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,10,8,9] => 000000001 => 0
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [8,6,7,9,5,4,3,2,1] => [1,2,3,4,5,9,7,6,8] => 00000101 => 1
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [1,2,3,4,5,6,10,7,8,9] => 000000001 => 0
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [8,7,5,6,9,4,3,2,1] => [1,2,3,4,9,6,5,7,8] => 00001001 => 1
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [1,2,3,4,5,10,6,7,8,9] => 000000001 => 0
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [8,7,6,4,5,9,3,2,1] => [1,2,3,9,5,4,6,7,8] => 00010001 => 1
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [1,2,3,4,10,5,6,7,8,9] => 000000001 => 0
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [8,7,6,5,3,4,9,2,1] => [1,2,9,4,3,5,6,7,8] => 00100001 => 1
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [1,2,3,10,4,5,6,7,8,9] => 000000001 => 0
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,2,3,9,1] => [1,9,3,2,4,5,6,7,8] => 01000001 => 1
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [1,2,10,3,4,5,6,7,8,9] => 000000001 => 0
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9] => [9,2,1,3,4,5,6,7,8] => 10000001 => 1
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [1,10,2,3,4,5,6,7,8,9] => 000000001 => 0
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,8,9] => 000000001 => 0
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9] => 101010101 => 4
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => [8,9,7,10,5,6,3,4,1,2] => [2,1,4,3,6,5,10,7,9,8] => 101010011 => 3
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => [9,10,6,7,5,8,3,4,1,2] => [2,1,4,3,8,5,7,6,10,9] => 101001101 => 3
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => [9,10,7,8,4,5,3,6,1,2] => [2,1,6,3,5,4,8,7,10,9] => 100110101 => 3
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => [8,9,7,10,4,5,3,6,1,2] => [2,1,6,3,5,4,10,7,9,8] => 100110011 => 2
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => [9,10,7,8,5,6,2,3,1,4] => [4,1,3,2,6,5,8,7,10,9] => 011010101 => 3
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]] => [8,9,7,10,5,6,2,3,1,4] => [4,1,3,2,6,5,10,7,9,8] => 011010011 => 2
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]] => [9,10,6,7,5,8,2,3,1,4] => [4,1,3,2,8,5,7,6,10,9] => 011001101 => 2
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => [8,9,6,7,4,5,2,3,1,10] => [10,1,3,2,5,4,7,6,9,8] => 010101011 => 3
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => [10,1,9,2,8,3,7,4,6,5] => 000011111 => 0
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9,12,11] => 10101010101 => 5
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [10,8,6,4,2,1,3,5,7,9] => [9,7,5,3,1,2,4,6,8,10] => 010101010 => 4
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,9] => 11111110 => 1
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1,10] => 111111110 => 1
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => [8,7,6,5,4,3,1,2,9] => 01111110 => 1
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,2,3] => 00111111 => 0
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110 => 1
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,1,2,10] => 011111110 => 1
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => [8,7,6,5,4,2,1,3,9] => 10111110 => 2
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => [1,9,8,7,6,5,3,2,4] => 01011111 => 1
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => [1,9,8,7,6,5,2,4,3] => 00111111 => 0
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,4,2,3] => 001111111 => 0
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 0
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,9,8] => 11111101 => 1
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => [6,5,4,3,2,1,9,8,7] => 11111011 => 1
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => [5,4,3,2,1,9,8,7,6] => 11110111 => 1
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [5,6,7,8,9,1,2,3,4] => [4,3,2,1,9,8,7,6,5] => 11101111 => 1
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,1,2,3] => [3,2,1,9,8,7,6,5,4] => 11011111 => 1
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,8,9] => 11111100 => 1
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,10,9] => 111111101 => 1
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,10,9,8] => 111111011 => 1
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => [6,5,4,3,2,1,10,9,8,7] => 111110111 => 1
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => 111101111 => 1
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [5,6,7,8,9,10,1,2,3,4] => [4,3,2,1,10,9,8,7,6,5] => 111011111 => 1
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [4,3,5,6,7,8,9,1,2] => [2,1,9,8,7,6,5,3,4] => 10011111 => 1
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [4,5,6,7,8,9,10,1,2,3] => [3,2,1,10,9,8,7,6,5,4] => 110111111 => 1
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,9] => 10000000 => 1
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,8,7] => 00000011 => 0
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,9,8] => 10000001 => 1
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,9,10] => 100000000 => 1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => [11,1,2,3,4,5,6,7,8,9,10] => 0000000001 => 0
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,9,8] => 000000011 => 0
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [9,1,2,3,4,5,8,6,7] => 00000011 => 0
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => [8,6,7,5,4,3,2,1,9] => [9,1,2,3,4,5,7,6,8] => 00000101 => 1
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,3,1,2] => [2,1,3,4,5,6,9,7,8] => 10000001 => 1
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => [2,1,3,4,5,6,8,7,9] => 10000010 => 2
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [9,10,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,10,9] => 100000001 => 1
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000 => 1
[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] => [9,7,8,5,6,3,4,1,2,10] => [10,2,1,4,3,6,5,8,7,9] => 101010101 => 4
[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.] => [11,9,10,7,8,5,6,3,4,1,2,12] => [12,2,1,4,3,6,5,8,7,10,9,11] => 10101010101 => 5
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,8,9] => 01000000 => 1
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,2,1,4] => [4,1,2,3,5,6,7,8,9] => 00100000 => 1
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,3,2,1,5] => [5,1,2,3,4,6,7,8,9] => 00010000 => 1
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [9,8,7,5,4,3,2,1,6] => [6,1,2,3,4,5,7,8,9] => 00001000 => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [9,8,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,8,9] => 00000100 => 1
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [9,7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7,9] => 00000010 => 1
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => [3,2,1,4,5,6,7,8,9] => 11000000 => 1
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,8,9,10] => 010000000 => 1
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,2,3,1,4] => [4,1,3,2,5,6,7,8,9] => 01100000 => 1
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,3,2,1,4] => [4,1,2,3,5,6,7,8,9,10] => 001000000 => 1
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,4,3,2,1,5] => [5,1,2,3,4,6,7,8,9,10] => 000100000 => 1
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [10,9,8,7,5,4,3,2,1,6] => [6,1,2,3,4,5,7,8,9,10] => 000010000 => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [10,9,8,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,8,9,10] => 000001000 => 1
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [9,6,7,5,4,3,2,1,8] => [8,1,2,3,4,5,7,6,9] => 00000110 => 1
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [10,9,7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7,9,10] => 000000100 => 1
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [10,8,7,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,7,8,10] => 000000010 => 1
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [9,8,1,2,3,4,5,6,7] => 00000011 => 0
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => [9,8,7,1,2,3,4,5,6] => 00000111 => 0
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => [9,8,7,6,1,2,3,4,5] => 00001111 => 0
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => [9,8,7,6,5,1,2,3,4] => 00011111 => 0
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [9,8,7,6,5,4,1,2,3] => 00111111 => 0
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,1,2] => 01111111 => 0
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => [10,9,1,2,3,4,5,6,7,8] => 000000011 => 0
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => [10,9,8,1,2,3,4,5,6,7] => 000000111 => 0
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => [10,9,8,7,1,2,3,4,5,6] => 000001111 => 0
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => [10,9,8,7,6,1,2,3,4,5] => 000011111 => 0
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => [10,9,8,7,6,5,1,2,3,4] => 000111111 => 0
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [4,3,1,2,5,6,7,8,9] => [9,8,7,6,5,2,1,3,4] => 10011111 => 1
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,1,2,3] => 001111111 => 0
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9] => [9,8,7,6,5,4,2,1,3] => 10111111 => 1
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,1,2] => 011111111 => 0
[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => [9,8,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,8,9] => 00000100 => 1
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [9,8,7,5,6,4,3,2,1] => [1,2,3,4,6,5,7,8,9] => 00001000 => 1
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,4,5,3,2,1] => [1,2,3,5,4,6,7,8,9] => 00010000 => 1
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,3,4,2,1] => [1,2,4,3,5,6,7,8,9] => 00100000 => 1
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,8,9] => 01000000 => 1
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [10,8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8,10] => 000000010 => 1
[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] => [10,9,7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,7,9,10] => 000000100 => 1
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [10,9,8,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,8,9,10] => 000001000 => 1
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,5,6,4,3,2,1] => [1,2,3,4,6,5,7,8,9,10] => 000010000 => 1
[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,4,5,3,2,1] => [1,2,3,5,4,6,7,8,9,10] => 000100000 => 1
[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,3,4,2,1] => [1,2,4,3,5,6,7,8,9,10] => 001000000 => 1
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,8,9,10] => 010000000 => 1
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [10,8,9,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,9,8,10] => 010101010 => 4
[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [10,8,9,6,7,4,5,2,1,3] => [3,1,2,5,4,7,6,9,8,10] => 010101010 => 4
[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]] => [10,8,9,6,7,4,2,1,3,5] => [5,3,1,2,4,7,6,9,8,10] => 010101010 => 4
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [10,8,9,6,4,2,1,3,5,7] => [7,5,3,1,2,4,6,9,8,10] => 010101010 => 4
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [9,2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2,9] => 01111110 => 1
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [11,10,9,8,7,6,5,4,3,1,2] => 0111111111 => 0
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [8,2,1,3,4,5,6,7,9] => [9,7,6,5,4,3,1,2,8] => 01111101 => 1
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [8,9,2,1,3,4,5,6,7] => [7,6,5,4,3,1,2,9,8] => 01111101 => 1
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => [8,2,3,4,5,6,7,9,1] => [1,9,7,6,5,4,3,2,8] => 01111101 => 1
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [8,9,2,3,4,5,6,7,1] => [1,7,6,5,4,3,2,9,8] => 01111101 => 1
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [10,2,3,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,3,2,10] => 011111110 => 1
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [4,2,1,3,5,6,7,8,9] => [9,8,7,6,5,3,1,2,4] => 01011111 => 1
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [5,3,2,1,4,6,7,8,9] => [9,8,7,6,4,1,2,3,5] => 00101111 => 1
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.] => [6,4,3,2,1,5,7,8,9] => [9,8,7,5,1,2,3,4,6] => 00010111 => 1
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.] => [7,5,4,3,2,1,6,8,9] => [9,8,6,1,2,3,4,5,7] => 00001011 => 1
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [8,6,5,4,3,2,1,7,9] => [9,7,1,2,3,4,5,6,8] => 00000101 => 1
[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]] => [7,8,6,9,5,4,3,2,1] => [1,2,3,4,5,9,6,8,7] => 00000011 => 0
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => [1,9,2,8,7,6,5,4,3] => 00111111 => 0
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [9,1,8,7,6,5,4,3,2] => 01111111 => 0
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => [9,8,7,6,5,4,1,3,2] => 01111111 => 0
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.] => [2,3,4,5,1,6,7,8,9] => [9,8,7,6,1,5,4,3,2] => 01111111 => 0
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [9,8,1,7,6,5,4,3,2] => 01111111 => 0
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [10,1,9,8,7,6,5,4,3,2] => 011111111 => 0
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9] => [9,8,7,6,5,3,2,1,4] => 11011111 => 1
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [5,1,2,3,4,6,7,8,9] => [9,8,7,6,4,3,2,1,5] => 11101111 => 1
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [6,1,2,3,4,5,7,8,9] => [9,8,7,5,4,3,2,1,6] => 11110111 => 1
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => [9,8,6,5,4,3,2,1,7] => 11111011 => 1
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => [9,7,6,5,4,3,2,1,8] => 11111101 => 1
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,2,1,3] => 101111111 => 1
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9,10] => [10,9,8,7,6,5,3,2,1,4] => 110111111 => 1
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [5,1,2,3,4,6,7,8,9,10] => [10,9,8,7,6,4,3,2,1,5] => 111011111 => 1
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [6,1,2,3,4,5,7,8,9,10] => [10,9,8,7,5,4,3,2,1,6] => 111101111 => 1
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [7,1,2,3,4,5,6,8,9,10] => [10,9,8,6,5,4,3,2,1,7] => 111110111 => 1
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [8,1,2,3,4,5,6,7,9,10] => [10,9,7,6,5,4,3,2,1,8] => 111111011 => 1
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => [10,8,7,6,5,4,3,2,1,9] => 111111101 => 1
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [9,3,4,5,6,7,8,1,2] => [2,1,8,7,6,5,4,3,9] => 10111110 => 2
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [9,7,6,5,4,3,2,8,1] => [1,8,2,3,4,5,6,7,9] => 00000010 => 1
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [9,7,6,5,4,3,1,2,8] => [8,2,1,3,4,5,6,7,9] => 10000010 => 2
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [8,9,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,9,8] => 00000101 => 1
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => [3,2,1,4,5,6,7,8,9,10] => 110000000 => 1
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,2,1,3,9] => [9,3,1,2,4,5,6,7,8] => 01000001 => 1
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [9,8,7,6,5,4,3,1,2,10] => [10,2,1,3,4,5,6,7,8,9] => 100000001 => 1
[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,2,3,1] => [1,3,2,4,5,6,9,7,8] => 01000001 => 1
[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]] => [7,2,3,4,5,6,8,9,1] => [1,9,8,6,5,4,3,2,7] => 01111011 => 1
[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]] => [7,8,2,3,4,5,6,9,1] => [1,9,6,5,4,3,2,8,7] => 01111011 => 1
[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]] => [6,2,3,4,5,7,8,9,10,1] => [1,10,9,8,7,5,4,3,2,6] => 011101111 => 1
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [10,8,7,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,7,8,10] => 000000010 => 1
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [3,4,5,6,7,8,1,2,9] => [9,2,1,8,7,6,5,4,3] => 10111111 => 1
[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]] => [8,9,6,5,4,3,2,7,1] => [1,7,2,3,4,5,6,9,8] => 00000101 => 1
[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]] => [6,7,8,5,4,3,2,9,1] => [1,9,2,3,4,5,8,7,6] => 00000111 => 0
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] => [8,9,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,9,8] => 01000001 => 1
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,9,10] => 111111100 => 1
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => [9,1,2,3,4,5,8,7,6] => 00000111 => 0
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,9,8,7] => 000000111 => 0
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]] => [10,9,8,7,6,5,4,3,2,11,1] => [1,11,2,3,4,5,6,7,8,9,10] => 0000000001 => 0
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => [6,5,4,3,2,1,7,8,9] => 11111000 => 1
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => [5,4,3,2,1,6,7,8,9] => 11110000 => 1
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => [4,3,2,1,5,6,7,8,9] => 11100000 => 1
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [9,7,1,2,3,4,5,6,8] => [8,6,5,4,3,2,1,7,9] => 11111010 => 2
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,8,9,10] => 111111000 => 1
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => [6,5,4,3,2,1,7,8,9,10] => 111110000 => 1
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => [5,4,3,2,1,6,7,8,9,10] => 111100000 => 1
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => [4,3,2,1,5,6,7,8,9,10] => 111000000 => 1
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [10,8,1,2,3,4,5,6,7,9] => [9,7,6,5,4,3,2,1,8,10] => 111111010 => 2
[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]] => [8,9,2,3,1,4,5,6,7] => [7,6,5,4,1,3,2,9,8] => 01111101 => 1
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,11,9,10] => 0000000001 => 0
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [9,8,10,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,10,8,9] => 100000001 => 1
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,9,8] => 01000001 => 1
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001 => 0
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,8,7] => 00000011 => 0
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]] => [8,9,7,6,5,4,3,2,10,1] => [1,10,2,3,4,5,6,7,9,8] => 000000011 => 0
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => [9,1,8,2,3,4,5,6,7] => 00000011 => 0
[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.] => [6,5,4,3,2,7,1,8,9] => [9,8,1,7,2,3,4,5,6] => 00000111 => 0
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => [8,7,1,2,3,4,5,6,9] => [9,6,5,4,3,2,1,7,8] => 11111001 => 1
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [8,7,5,4,3,2,1,6,9] => [9,6,1,2,3,4,5,7,8] => 00001001 => 1
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,3,9,1,2] => [2,1,9,3,4,5,6,7,8] => 10000001 => 1
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,2,3,1,9] => [9,1,3,2,4,5,6,7,8] => 01000001 => 1
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => [9,8,7,6,5,2,1,4,3] => 10111111 => 1
[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => [4,5,6,7,8,9,10,2,3,1] => [1,3,2,10,9,8,7,6,5,4] => 010111111 => 1
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [10,11,1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1,11,10] => 1111111101 => 1
[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]] => [9,10,2,1,3,4,5,6,7,8] => [8,7,6,5,4,3,1,2,10,9] => 011111101 => 1
[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]] => [8,9,3,1,2,4,5,6,7] => [7,6,5,4,2,1,3,9,8] => 10111101 => 2
[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.] => [8,7,6,1,2,3,4,5,9] => [9,5,4,3,2,1,6,7,8] => 11110001 => 1
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => [10,3,1,2,4,5,6,7,8,9] => [9,8,7,6,5,4,2,1,3,10] => 101111110 => 2
[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => [9,10,11,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,11,10,9] => 0000000011 => 0
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [9,10,7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7,10,9] => 000000101 => 1
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => [11,9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010 => 1
[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]] => [9,7,8,5,6,4,3,2,1] => [1,2,3,4,6,5,8,7,9] => 00001010 => 2
[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]] => [8,9,6,5,7,4,3,2,1] => [1,2,3,4,7,5,6,9,8] => 00000101 => 1
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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:
4,1 8,6 16,24,2 32,80,20 64,240,120,5
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 6\ q$
$F_{5} = 16 + 24\ q + 2\ q^{2}$
$F_{6} = 32 + 80\ q + 20\ q^{2}$
$F_{7} = 64 + 240\ q + 120\ q^{2} + 5\ q^{3}$
Description
The number of descents of a binary word.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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.
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