Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00064: Permutations —reverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Images
[.,.] => [1] => [1] => =>
[.,[.,.]] => [2,1] => [1,2] => 0 => 1
[[.,.],.] => [1,2] => [2,1] => 1 => 0
[.,[.,[.,.]]] => [3,2,1] => [1,2,3] => 00 => 11
[.,[[.,.],.]] => [2,3,1] => [1,3,2] => 01 => 10
[[.,.],[.,.]] => [3,1,2] => [2,1,3] => 10 => 01
[[.,[.,.]],.] => [2,1,3] => [3,1,2] => 01 => 10
[[[.,.],.],.] => [1,2,3] => [3,2,1] => 11 => 00
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,2,3,4] => 000 => 111
[.,[.,[[.,.],.]]] => [3,4,2,1] => [1,2,4,3] => 001 => 110
[.,[[.,.],[.,.]]] => [4,2,3,1] => [1,3,2,4] => 010 => 101
[.,[[.,[.,.]],.]] => [3,2,4,1] => [1,4,2,3] => 001 => 110
[.,[[[.,.],.],.]] => [2,3,4,1] => [1,4,3,2] => 011 => 100
[[.,.],[.,[.,.]]] => [4,3,1,2] => [2,1,3,4] => 100 => 011
[[.,.],[[.,.],.]] => [3,4,1,2] => [2,1,4,3] => 101 => 010
[[.,[.,.]],[.,.]] => [4,2,1,3] => [3,1,2,4] => 010 => 101
[[[.,.],.],[.,.]] => [4,1,2,3] => [3,2,1,4] => 110 => 001
[[.,[.,[.,.]]],.] => [3,2,1,4] => [4,1,2,3] => 001 => 110
[[.,[[.,.],.]],.] => [2,3,1,4] => [4,1,3,2] => 011 => 100
[[[.,.],[.,.]],.] => [3,1,2,4] => [4,2,1,3] => 101 => 010
[[[.,[.,.]],.],.] => [2,1,3,4] => [4,3,1,2] => 011 => 100
[[[[.,.],.],.],.] => [1,2,3,4] => [4,3,2,1] => 111 => 000
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,2,3,4,5] => 0000 => 1111
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [1,2,3,5,4] => 0001 => 1110
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [1,2,4,3,5] => 0010 => 1101
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [1,2,5,3,4] => 0001 => 1110
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [1,2,5,4,3] => 0011 => 1100
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [1,3,2,4,5] => 0100 => 1011
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [1,3,2,5,4] => 0101 => 1010
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [1,4,2,3,5] => 0010 => 1101
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [1,4,3,2,5] => 0110 => 1001
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [1,5,2,3,4] => 0001 => 1110
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [1,5,2,4,3] => 0011 => 1100
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [1,5,3,2,4] => 0101 => 1010
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [1,5,4,2,3] => 0011 => 1100
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,5,4,3,2] => 0111 => 1000
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [2,1,3,4,5] => 1000 => 0111
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [2,1,3,5,4] => 1001 => 0110
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [2,1,4,3,5] => 1010 => 0101
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [2,1,5,3,4] => 1001 => 0110
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [2,1,5,4,3] => 1011 => 0100
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [3,1,2,4,5] => 0100 => 1011
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [3,1,2,5,4] => 0101 => 1010
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [3,2,1,4,5] => 1100 => 0011
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [3,2,1,5,4] => 1101 => 0010
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [4,1,2,3,5] => 0010 => 1101
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [4,1,3,2,5] => 0110 => 1001
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [4,2,1,3,5] => 1010 => 0101
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [4,3,1,2,5] => 0110 => 1001
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [4,3,2,1,5] => 1110 => 0001
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [5,1,2,3,4] => 0001 => 1110
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [5,1,2,4,3] => 0011 => 1100
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [5,1,3,2,4] => 0101 => 1010
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [5,1,4,2,3] => 0011 => 1100
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [5,1,4,3,2] => 0111 => 1000
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [5,2,1,3,4] => 1001 => 0110
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [5,2,1,4,3] => 1011 => 0100
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [5,3,1,2,4] => 0101 => 1010
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [5,3,2,1,4] => 1101 => 0010
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [5,4,1,2,3] => 0011 => 1100
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [5,4,1,3,2] => 0111 => 1000
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [5,4,2,1,3] => 1011 => 0100
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [5,4,3,1,2] => 0111 => 1000
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [5,4,3,2,1] => 1111 => 0000
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => 00000 => 11111
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [1,2,3,4,6,5] => 00001 => 11110
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => 00010 => 11101
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [1,2,3,6,4,5] => 00001 => 11110
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => 00011 => 11100
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => 00100 => 11011
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [1,2,4,3,6,5] => 00101 => 11010
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [1,2,5,3,4,6] => 00010 => 11101
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [1,2,5,4,3,6] => 00110 => 11001
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [1,2,6,3,4,5] => 00001 => 11110
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [1,2,6,3,5,4] => 00011 => 11100
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [1,2,6,4,3,5] => 00101 => 11010
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [1,2,6,5,3,4] => 00011 => 11100
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [1,2,6,5,4,3] => 00111 => 11000
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [1,3,2,4,5,6] => 01000 => 10111
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [1,3,2,4,6,5] => 01001 => 10110
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => 01010 => 10101
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [1,3,2,6,4,5] => 01001 => 10110
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [1,3,2,6,5,4] => 01011 => 10100
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [1,4,2,3,5,6] => 00100 => 11011
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [1,4,2,3,6,5] => 00101 => 11010
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [1,4,3,2,5,6] => 01100 => 10011
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [1,4,3,2,6,5] => 01101 => 10010
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [1,5,2,3,4,6] => 00010 => 11101
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [1,5,2,4,3,6] => 00110 => 11001
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [1,5,3,2,4,6] => 01010 => 10101
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [1,5,4,2,3,6] => 00110 => 11001
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => 01110 => 10001
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [1,6,2,3,4,5] => 00001 => 11110
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [1,6,2,3,5,4] => 00011 => 11100
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [1,6,2,4,3,5] => 00101 => 11010
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [1,6,2,5,3,4] => 00011 => 11100
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [1,6,2,5,4,3] => 00111 => 11000
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [1,6,3,2,4,5] => 01001 => 10110
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [1,6,3,2,5,4] => 01011 => 10100
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [1,6,4,2,3,5] => 00101 => 11010
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [1,6,4,3,2,5] => 01101 => 10010
>>> Load all 1960 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [1,6,5,2,3,4] => 00011 => 11100
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [1,6,5,2,4,3] => 00111 => 11000
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [1,6,5,3,2,4] => 01011 => 10100
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [1,6,5,4,2,3] => 00111 => 11000
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => 01111 => 10000
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [2,1,3,4,5,6] => 10000 => 01111
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => 10001 => 01110
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [2,1,3,5,4,6] => 10010 => 01101
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [2,1,3,6,4,5] => 10001 => 01110
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [2,1,3,6,5,4] => 10011 => 01100
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [2,1,4,3,5,6] => 10100 => 01011
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => 10101 => 01010
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [2,1,5,3,4,6] => 10010 => 01101
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [2,1,5,4,3,6] => 10110 => 01001
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [2,1,6,3,4,5] => 10001 => 01110
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [2,1,6,3,5,4] => 10011 => 01100
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [2,1,6,4,3,5] => 10101 => 01010
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [2,1,6,5,3,4] => 10011 => 01100
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [2,1,6,5,4,3] => 10111 => 01000
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [3,1,2,4,5,6] => 01000 => 10111
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [3,1,2,4,6,5] => 01001 => 10110
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [3,1,2,5,4,6] => 01010 => 10101
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [3,1,2,6,4,5] => 01001 => 10110
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [3,1,2,6,5,4] => 01011 => 10100
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [3,2,1,4,5,6] => 11000 => 00111
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [3,2,1,4,6,5] => 11001 => 00110
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => 11010 => 00101
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => 11001 => 00110
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => 11011 => 00100
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [4,1,2,3,5,6] => 00100 => 11011
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [4,1,2,3,6,5] => 00101 => 11010
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [4,1,3,2,5,6] => 01100 => 10011
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [4,1,3,2,6,5] => 01101 => 10010
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [4,2,1,3,5,6] => 10100 => 01011
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [4,2,1,3,6,5] => 10101 => 01010
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [4,3,1,2,5,6] => 01100 => 10011
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [4,3,1,2,6,5] => 01101 => 10010
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => 11100 => 00011
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => 11101 => 00010
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [5,1,2,3,4,6] => 00010 => 11101
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [5,1,2,4,3,6] => 00110 => 11001
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [5,1,3,2,4,6] => 01010 => 10101
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [5,1,4,2,3,6] => 00110 => 11001
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [5,1,4,3,2,6] => 01110 => 10001
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [5,2,1,3,4,6] => 10010 => 01101
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => 10110 => 01001
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [5,3,1,2,4,6] => 01010 => 10101
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => 11010 => 00101
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [5,4,1,2,3,6] => 00110 => 11001
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [5,4,1,3,2,6] => 01110 => 10001
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => 10110 => 01001
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => 01110 => 10001
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => 11110 => 00001
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => 00001 => 11110
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [6,1,2,3,5,4] => 00011 => 11100
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [6,1,2,4,3,5] => 00101 => 11010
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [6,1,2,5,3,4] => 00011 => 11100
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [6,1,2,5,4,3] => 00111 => 11000
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [6,1,3,2,4,5] => 01001 => 10110
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [6,1,3,2,5,4] => 01011 => 10100
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [6,1,4,2,3,5] => 00101 => 11010
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [6,1,4,3,2,5] => 01101 => 10010
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [6,1,5,2,3,4] => 00011 => 11100
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [6,1,5,2,4,3] => 00111 => 11000
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [6,1,5,3,2,4] => 01011 => 10100
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [6,1,5,4,2,3] => 00111 => 11000
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => 01111 => 10000
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [6,2,1,3,4,5] => 10001 => 01110
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [6,2,1,3,5,4] => 10011 => 01100
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [6,2,1,4,3,5] => 10101 => 01010
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [6,2,1,5,3,4] => 10011 => 01100
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [6,2,1,5,4,3] => 10111 => 01000
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [6,3,1,2,4,5] => 01001 => 10110
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [6,3,1,2,5,4] => 01011 => 10100
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [6,3,2,1,4,5] => 11001 => 00110
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [6,3,2,1,5,4] => 11011 => 00100
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [6,4,1,2,3,5] => 00101 => 11010
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [6,4,1,3,2,5] => 01101 => 10010
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [6,4,2,1,3,5] => 10101 => 01010
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [6,4,3,1,2,5] => 01101 => 10010
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [6,4,3,2,1,5] => 11101 => 00010
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => 00011 => 11100
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [6,5,1,2,4,3] => 00111 => 11000
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [6,5,1,3,2,4] => 01011 => 10100
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [6,5,1,4,2,3] => 00111 => 11000
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => 01111 => 10000
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [6,5,2,1,3,4] => 10011 => 01100
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [6,5,2,1,4,3] => 10111 => 01000
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [6,5,3,1,2,4] => 01011 => 10100
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [6,5,3,2,1,4] => 11011 => 00100
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => 00111 => 11000
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => 01111 => 10000
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [6,5,4,2,1,3] => 10111 => 01000
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => 01111 => 10000
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 11111 => 00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 000000 => 111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [1,2,3,4,5,7,6] => 000001 => 111110
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [1,2,3,4,6,5,7] => 000010 => 111101
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [1,2,3,4,7,5,6] => 000001 => 111110
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [1,2,3,4,7,6,5] => 000011 => 111100
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [1,2,3,5,4,6,7] => 000100 => 111011
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [1,2,3,5,4,7,6] => 000101 => 111010
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [1,2,3,6,4,5,7] => 000010 => 111101
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [1,2,3,6,5,4,7] => 000110 => 111001
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [1,2,3,7,4,5,6] => 000001 => 111110
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [1,2,3,7,4,6,5] => 000011 => 111100
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [1,2,3,7,5,4,6] => 000101 => 111010
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [1,2,3,7,6,4,5] => 000011 => 111100
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => 000111 => 111000
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [1,2,4,3,5,6,7] => 001000 => 110111
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [1,2,4,3,5,7,6] => 001001 => 110110
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [1,2,4,3,6,5,7] => 001010 => 110101
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [1,2,4,3,7,5,6] => 001001 => 110110
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [1,2,4,3,7,6,5] => 001011 => 110100
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [1,2,5,3,4,6,7] => 000100 => 111011
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [1,2,5,3,4,7,6] => 000101 => 111010
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => 001100 => 110011
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [1,2,5,4,3,7,6] => 001101 => 110010
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => [1,2,6,3,4,5,7] => 000010 => 111101
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => [1,2,6,3,5,4,7] => 000110 => 111001
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [1,2,6,4,3,5,7] => 001010 => 110101
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => [1,2,6,5,3,4,7] => 000110 => 111001
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [1,2,6,5,4,3,7] => 001110 => 110001
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [1,2,7,3,4,5,6] => 000001 => 111110
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [1,2,7,3,4,6,5] => 000011 => 111100
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [1,2,7,3,5,4,6] => 000101 => 111010
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [1,2,7,3,6,4,5] => 000011 => 111100
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [1,2,7,3,6,5,4] => 000111 => 111000
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [1,2,7,4,3,5,6] => 001001 => 110110
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [1,2,7,4,3,6,5] => 001011 => 110100
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [1,2,7,5,3,4,6] => 000101 => 111010
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [1,2,7,5,4,3,6] => 001101 => 110010
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [1,2,7,6,3,4,5] => 000011 => 111100
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [1,2,7,6,3,5,4] => 000111 => 111000
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [1,2,7,6,4,3,5] => 001011 => 110100
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [1,2,7,6,5,3,4] => 000111 => 111000
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [1,2,7,6,5,4,3] => 001111 => 110000
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [1,3,2,4,5,6,7] => 010000 => 101111
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [1,3,2,4,5,7,6] => 010001 => 101110
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => 010010 => 101101
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [1,3,2,4,7,5,6] => 010001 => 101110
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [1,3,2,4,7,6,5] => 010011 => 101100
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,3,2,5,4,6,7] => 010100 => 101011
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [1,3,2,5,4,7,6] => 010101 => 101010
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [1,3,2,6,4,5,7] => 010010 => 101101
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [1,3,2,6,5,4,7] => 010110 => 101001
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [1,3,2,7,4,5,6] => 010001 => 101110
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [1,3,2,7,4,6,5] => 010011 => 101100
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [1,3,2,7,5,4,6] => 010101 => 101010
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => [1,3,2,7,6,4,5] => 010011 => 101100
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [1,3,2,7,6,5,4] => 010111 => 101000
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [1,4,2,3,5,6,7] => 001000 => 110111
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [1,4,2,3,5,7,6] => 001001 => 110110
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => [1,4,2,3,6,5,7] => 001010 => 110101
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => [1,4,2,3,7,5,6] => 001001 => 110110
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => [1,4,2,3,7,6,5] => 001011 => 110100
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [1,4,3,2,5,6,7] => 011000 => 100111
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [1,4,3,2,5,7,6] => 011001 => 100110
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [1,4,3,2,6,5,7] => 011010 => 100101
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [1,4,3,2,7,5,6] => 011001 => 100110
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [1,4,3,2,7,6,5] => 011011 => 100100
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [1,5,2,3,4,6,7] => 000100 => 111011
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => [1,5,2,3,4,7,6] => 000101 => 111010
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [1,5,2,4,3,6,7] => 001100 => 110011
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => [1,5,2,4,3,7,6] => 001101 => 110010
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [1,5,3,2,4,6,7] => 010100 => 101011
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [1,5,3,2,4,7,6] => 010101 => 101010
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [1,5,4,2,3,6,7] => 001100 => 110011
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => [1,5,4,2,3,7,6] => 001101 => 110010
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [1,5,4,3,2,6,7] => 011100 => 100011
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [1,5,4,3,2,7,6] => 011101 => 100010
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [1,6,2,3,4,5,7] => 000010 => 111101
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [1,6,2,3,5,4,7] => 000110 => 111001
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [1,6,2,4,3,5,7] => 001010 => 110101
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [1,6,2,5,3,4,7] => 000110 => 111001
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [1,6,2,5,4,3,7] => 001110 => 110001
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [1,6,3,2,4,5,7] => 010010 => 101101
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [1,6,3,2,5,4,7] => 010110 => 101001
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [1,6,4,2,3,5,7] => 001010 => 110101
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [1,6,4,3,2,5,7] => 011010 => 100101
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [1,6,5,2,3,4,7] => 000110 => 111001
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [1,6,5,2,4,3,7] => 001110 => 110001
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [1,6,5,3,2,4,7] => 010110 => 101001
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [1,6,5,4,2,3,7] => 001110 => 110001
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [1,6,5,4,3,2,7] => 011110 => 100001
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [1,7,2,3,4,5,6] => 000001 => 111110
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [1,7,2,3,4,6,5] => 000011 => 111100
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [1,7,2,3,5,4,6] => 000101 => 111010
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [1,7,2,3,6,4,5] => 000011 => 111100
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [1,7,2,3,6,5,4] => 000111 => 111000
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [1,7,2,4,3,5,6] => 001001 => 110110
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [1,7,2,4,3,6,5] => 001011 => 110100
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [1,7,2,5,3,4,6] => 000101 => 111010
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [1,7,2,5,4,3,6] => 001101 => 110010
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [1,7,2,6,3,4,5] => 000011 => 111100
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [1,7,2,6,3,5,4] => 000111 => 111000
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => [1,7,2,6,4,3,5] => 001011 => 110100
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [1,7,2,6,5,3,4] => 000111 => 111000
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [1,7,2,6,5,4,3] => 001111 => 110000
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [1,7,3,2,4,5,6] => 010001 => 101110
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [1,7,3,2,4,6,5] => 010011 => 101100
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [1,7,3,2,5,4,6] => 010101 => 101010
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [1,7,3,2,6,4,5] => 010011 => 101100
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [1,7,3,2,6,5,4] => 010111 => 101000
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [1,7,4,2,3,5,6] => 001001 => 110110
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => [1,7,4,2,3,6,5] => 001011 => 110100
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [1,7,4,3,2,5,6] => 011001 => 100110
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [1,7,4,3,2,6,5] => 011011 => 100100
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [1,7,5,2,3,4,6] => 000101 => 111010
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => [1,7,5,2,4,3,6] => 001101 => 110010
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => [1,7,5,3,2,4,6] => 010101 => 101010
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => [1,7,5,4,2,3,6] => 001101 => 110010
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [1,7,5,4,3,2,6] => 011101 => 100010
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [1,7,6,2,3,4,5] => 000011 => 111100
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [1,7,6,2,3,5,4] => 000111 => 111000
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [1,7,6,2,4,3,5] => 001011 => 110100
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [1,7,6,2,5,3,4] => 000111 => 111000
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [1,7,6,2,5,4,3] => 001111 => 110000
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [1,7,6,3,2,4,5] => 010011 => 101100
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [1,7,6,3,2,5,4] => 010111 => 101000
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [1,7,6,4,2,3,5] => 001011 => 110100
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [1,7,6,4,3,2,5] => 011011 => 100100
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [1,7,6,5,2,3,4] => 000111 => 111000
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [1,7,6,5,2,4,3] => 001111 => 110000
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [1,7,6,5,3,2,4] => 010111 => 101000
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [1,7,6,5,4,2,3] => 001111 => 110000
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => 011111 => 100000
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [2,1,3,4,5,6,7] => 100000 => 011111
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [2,1,3,4,5,7,6] => 100001 => 011110
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [2,1,3,4,6,5,7] => 100010 => 011101
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [2,1,3,4,7,5,6] => 100001 => 011110
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [2,1,3,4,7,6,5] => 100011 => 011100
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [2,1,3,5,4,6,7] => 100100 => 011011
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [2,1,3,5,4,7,6] => 100101 => 011010
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [2,1,3,6,4,5,7] => 100010 => 011101
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [2,1,3,6,5,4,7] => 100110 => 011001
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [2,1,3,7,4,5,6] => 100001 => 011110
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [2,1,3,7,4,6,5] => 100011 => 011100
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [2,1,3,7,5,4,6] => 100101 => 011010
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => [2,1,3,7,6,4,5] => 100011 => 011100
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [2,1,3,7,6,5,4] => 100111 => 011000
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [2,1,4,3,5,6,7] => 101000 => 010111
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [2,1,4,3,5,7,6] => 101001 => 010110
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [2,1,4,3,6,5,7] => 101010 => 010101
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [2,1,4,3,7,5,6] => 101001 => 010110
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [2,1,4,3,7,6,5] => 101011 => 010100
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [2,1,5,3,4,6,7] => 100100 => 011011
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [2,1,5,3,4,7,6] => 100101 => 011010
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [2,1,5,4,3,6,7] => 101100 => 010011
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [2,1,5,4,3,7,6] => 101101 => 010010
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [2,1,6,3,4,5,7] => 100010 => 011101
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [2,1,6,3,5,4,7] => 100110 => 011001
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [2,1,6,4,3,5,7] => 101010 => 010101
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [2,1,6,5,3,4,7] => 100110 => 011001
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [2,1,6,5,4,3,7] => 101110 => 010001
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [2,1,7,3,4,5,6] => 100001 => 011110
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [2,1,7,3,4,6,5] => 100011 => 011100
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [2,1,7,3,5,4,6] => 100101 => 011010
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => [2,1,7,3,6,4,5] => 100011 => 011100
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [2,1,7,3,6,5,4] => 100111 => 011000
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [2,1,7,4,3,5,6] => 101001 => 010110
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [2,1,7,4,3,6,5] => 101011 => 010100
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => [2,1,7,5,3,4,6] => 100101 => 011010
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [2,1,7,5,4,3,6] => 101101 => 010010
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => [2,1,7,6,3,4,5] => 100011 => 011100
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [2,1,7,6,3,5,4] => 100111 => 011000
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [2,1,7,6,4,3,5] => 101011 => 010100
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [2,1,7,6,5,3,4] => 100111 => 011000
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [2,1,7,6,5,4,3] => 101111 => 010000
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [3,1,2,4,5,6,7] => 010000 => 101111
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [3,1,2,4,5,7,6] => 010001 => 101110
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => [3,1,2,4,6,5,7] => 010010 => 101101
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => [3,1,2,4,7,5,6] => 010001 => 101110
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => [3,1,2,4,7,6,5] => 010011 => 101100
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [3,1,2,5,4,6,7] => 010100 => 101011
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => [3,1,2,5,4,7,6] => 010101 => 101010
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => [3,1,2,6,4,5,7] => 010010 => 101101
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [3,1,2,6,5,4,7] => 010110 => 101001
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [3,1,2,7,4,5,6] => 010001 => 101110
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => [3,1,2,7,4,6,5] => 010011 => 101100
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => [3,1,2,7,5,4,6] => 010101 => 101010
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => [3,1,2,7,6,4,5] => 010011 => 101100
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [3,1,2,7,6,5,4] => 010111 => 101000
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [3,2,1,4,5,6,7] => 110000 => 001111
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [3,2,1,4,5,7,6] => 110001 => 001110
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [3,2,1,4,6,5,7] => 110010 => 001101
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [3,2,1,4,7,5,6] => 110001 => 001110
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [3,2,1,4,7,6,5] => 110011 => 001100
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [3,2,1,5,4,6,7] => 110100 => 001011
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [3,2,1,5,4,7,6] => 110101 => 001010
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [3,2,1,6,4,5,7] => 110010 => 001101
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [3,2,1,6,5,4,7] => 110110 => 001001
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [3,2,1,7,4,5,6] => 110001 => 001110
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [3,2,1,7,4,6,5] => 110011 => 001100
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [3,2,1,7,5,4,6] => 110101 => 001010
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => [3,2,1,7,6,4,5] => 110011 => 001100
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [3,2,1,7,6,5,4] => 110111 => 001000
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [4,1,2,3,5,6,7] => 001000 => 110111
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => [4,1,2,3,5,7,6] => 001001 => 110110
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => [4,1,2,3,6,5,7] => 001010 => 110101
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => [4,1,2,3,7,5,6] => 001001 => 110110
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => [4,1,2,3,7,6,5] => 001011 => 110100
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [4,1,3,2,5,6,7] => 011000 => 100111
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => [4,1,3,2,5,7,6] => 011001 => 100110
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => [4,1,3,2,6,5,7] => 011010 => 100101
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => [4,1,3,2,7,5,6] => 011001 => 100110
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => [4,1,3,2,7,6,5] => 011011 => 100100
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [4,2,1,3,5,6,7] => 101000 => 010111
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [4,2,1,3,5,7,6] => 101001 => 010110
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [4,2,1,3,6,5,7] => 101010 => 010101
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [4,2,1,3,7,5,6] => 101001 => 010110
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [4,2,1,3,7,6,5] => 101011 => 010100
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [4,3,1,2,5,6,7] => 011000 => 100111
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => [4,3,1,2,5,7,6] => 011001 => 100110
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => [4,3,1,2,6,5,7] => 011010 => 100101
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => [4,3,1,2,7,5,6] => 011001 => 100110
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => [4,3,1,2,7,6,5] => 011011 => 100100
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [4,3,2,1,5,6,7] => 111000 => 000111
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [4,3,2,1,5,7,6] => 111001 => 000110
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [4,3,2,1,6,5,7] => 111010 => 000101
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [4,3,2,1,7,5,6] => 111001 => 000110
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => 111011 => 000100
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [5,1,2,3,4,6,7] => 000100 => 111011
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [5,1,2,3,4,7,6] => 000101 => 111010
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [5,1,2,4,3,6,7] => 001100 => 110011
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [5,1,2,4,3,7,6] => 001101 => 110010
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [5,1,3,2,4,6,7] => 010100 => 101011
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [5,1,3,2,4,7,6] => 010101 => 101010
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [5,1,4,2,3,6,7] => 001100 => 110011
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [5,1,4,2,3,7,6] => 001101 => 110010
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [5,1,4,3,2,6,7] => 011100 => 100011
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [5,1,4,3,2,7,6] => 011101 => 100010
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [5,2,1,3,4,6,7] => 100100 => 011011
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [5,2,1,3,4,7,6] => 100101 => 011010
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [5,2,1,4,3,6,7] => 101100 => 010011
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [5,2,1,4,3,7,6] => 101101 => 010010
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [5,3,1,2,4,6,7] => 010100 => 101011
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [5,3,1,2,4,7,6] => 010101 => 101010
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [5,3,2,1,4,6,7] => 110100 => 001011
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [5,3,2,1,4,7,6] => 110101 => 001010
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [5,4,1,2,3,6,7] => 001100 => 110011
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [5,4,1,2,3,7,6] => 001101 => 110010
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [5,4,1,3,2,6,7] => 011100 => 100011
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [5,4,1,3,2,7,6] => 011101 => 100010
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [5,4,2,1,3,6,7] => 101100 => 010011
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [5,4,2,1,3,7,6] => 101101 => 010010
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [5,4,3,1,2,6,7] => 011100 => 100011
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => [5,4,3,1,2,7,6] => 011101 => 100010
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [5,4,3,2,1,6,7] => 111100 => 000011
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => 111101 => 000010
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [6,1,2,3,4,5,7] => 000010 => 111101
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [6,1,2,3,5,4,7] => 000110 => 111001
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [6,1,2,4,3,5,7] => 001010 => 110101
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [6,1,2,5,3,4,7] => 000110 => 111001
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [6,1,2,5,4,3,7] => 001110 => 110001
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [6,1,3,2,4,5,7] => 010010 => 101101
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [6,1,3,2,5,4,7] => 010110 => 101001
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [6,1,4,2,3,5,7] => 001010 => 110101
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [6,1,4,3,2,5,7] => 011010 => 100101
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [6,1,5,2,3,4,7] => 000110 => 111001
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [6,1,5,2,4,3,7] => 001110 => 110001
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [6,1,5,3,2,4,7] => 010110 => 101001
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [6,1,5,4,2,3,7] => 001110 => 110001
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [6,1,5,4,3,2,7] => 011110 => 100001
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [6,2,1,3,4,5,7] => 100010 => 011101
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [6,2,1,3,5,4,7] => 100110 => 011001
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [6,2,1,4,3,5,7] => 101010 => 010101
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [6,2,1,5,3,4,7] => 100110 => 011001
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [6,2,1,5,4,3,7] => 101110 => 010001
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [6,3,1,2,4,5,7] => 010010 => 101101
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [6,3,1,2,5,4,7] => 010110 => 101001
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [6,3,2,1,4,5,7] => 110010 => 001101
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [6,3,2,1,5,4,7] => 110110 => 001001
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [6,4,1,2,3,5,7] => 001010 => 110101
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [6,4,1,3,2,5,7] => 011010 => 100101
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [6,4,2,1,3,5,7] => 101010 => 010101
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => [6,4,3,1,2,5,7] => 011010 => 100101
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [6,4,3,2,1,5,7] => 111010 => 000101
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [6,5,1,2,3,4,7] => 000110 => 111001
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [6,5,1,2,4,3,7] => 001110 => 110001
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [6,5,1,3,2,4,7] => 010110 => 101001
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [6,5,1,4,2,3,7] => 001110 => 110001
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [6,5,1,4,3,2,7] => 011110 => 100001
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [6,5,2,1,3,4,7] => 100110 => 011001
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [6,5,2,1,4,3,7] => 101110 => 010001
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => [6,5,3,1,2,4,7] => 010110 => 101001
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [6,5,3,2,1,4,7] => 110110 => 001001
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => [6,5,4,1,2,3,7] => 001110 => 110001
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [6,5,4,1,3,2,7] => 011110 => 100001
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [6,5,4,2,1,3,7] => 101110 => 010001
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [6,5,4,3,1,2,7] => 011110 => 100001
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => 111110 => 000001
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [7,1,2,3,4,5,6] => 000001 => 111110
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [7,1,2,3,4,6,5] => 000011 => 111100
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [7,1,2,3,5,4,6] => 000101 => 111010
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [7,1,2,3,6,4,5] => 000011 => 111100
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [7,1,2,3,6,5,4] => 000111 => 111000
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [7,1,2,4,3,5,6] => 001001 => 110110
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [7,1,2,4,3,6,5] => 001011 => 110100
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [7,1,2,5,3,4,6] => 000101 => 111010
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [7,1,2,5,4,3,6] => 001101 => 110010
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [7,1,2,6,3,4,5] => 000011 => 111100
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [7,1,2,6,3,5,4] => 000111 => 111000
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => [7,1,2,6,4,3,5] => 001011 => 110100
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [7,1,2,6,5,3,4] => 000111 => 111000
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [7,1,2,6,5,4,3] => 001111 => 110000
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => [7,1,3,2,4,5,6] => 010001 => 101110
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [7,1,3,2,4,6,5] => 010011 => 101100
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [7,1,3,2,5,4,6] => 010101 => 101010
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => [7,1,3,2,6,4,5] => 010011 => 101100
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => [7,1,3,2,6,5,4] => 010111 => 101000
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [7,1,4,2,3,5,6] => 001001 => 110110
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => [7,1,4,2,3,6,5] => 001011 => 110100
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [7,1,4,3,2,5,6] => 011001 => 100110
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => [7,1,4,3,2,6,5] => 011011 => 100100
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [7,1,5,2,3,4,6] => 000101 => 111010
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => [7,1,5,2,4,3,6] => 001101 => 110010
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [7,1,5,3,2,4,6] => 010101 => 101010
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => [7,1,5,4,2,3,6] => 001101 => 110010
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => [7,1,5,4,3,2,6] => 011101 => 100010
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [7,1,6,2,3,4,5] => 000011 => 111100
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [7,1,6,2,3,5,4] => 000111 => 111000
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [7,1,6,2,4,3,5] => 001011 => 110100
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [7,1,6,2,5,3,4] => 000111 => 111000
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [7,1,6,2,5,4,3] => 001111 => 110000
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [7,1,6,3,2,4,5] => 010011 => 101100
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [7,1,6,3,2,5,4] => 010111 => 101000
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [7,1,6,4,2,3,5] => 001011 => 110100
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [7,1,6,4,3,2,5] => 011011 => 100100
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [7,1,6,5,2,3,4] => 000111 => 111000
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [7,1,6,5,2,4,3] => 001111 => 110000
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [7,1,6,5,3,2,4] => 010111 => 101000
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [7,1,6,5,4,2,3] => 001111 => 110000
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [7,1,6,5,4,3,2] => 011111 => 100000
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [7,2,1,3,4,5,6] => 100001 => 011110
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [7,2,1,3,4,6,5] => 100011 => 011100
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [7,2,1,3,5,4,6] => 100101 => 011010
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => [7,2,1,3,6,4,5] => 100011 => 011100
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [7,2,1,3,6,5,4] => 100111 => 011000
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [7,2,1,4,3,5,6] => 101001 => 010110
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [7,2,1,4,3,6,5] => 101011 => 010100
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => [7,2,1,5,3,4,6] => 100101 => 011010
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [7,2,1,5,4,3,6] => 101101 => 010010
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => [7,2,1,6,3,4,5] => 100011 => 011100
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [7,2,1,6,3,5,4] => 100111 => 011000
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [7,2,1,6,4,3,5] => 101011 => 010100
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [7,2,1,6,5,3,4] => 100111 => 011000
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [7,2,1,6,5,4,3] => 101111 => 010000
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [7,3,1,2,4,5,6] => 010001 => 101110
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => [7,3,1,2,4,6,5] => 010011 => 101100
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => [7,3,1,2,5,4,6] => 010101 => 101010
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => [7,3,1,2,6,4,5] => 010011 => 101100
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [7,3,1,2,6,5,4] => 010111 => 101000
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [7,3,2,1,4,5,6] => 110001 => 001110
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [7,3,2,1,4,6,5] => 110011 => 001100
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [7,3,2,1,5,4,6] => 110101 => 001010
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [7,3,2,1,6,4,5] => 110011 => 001100
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [7,3,2,1,6,5,4] => 110111 => 001000
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [7,4,1,2,3,5,6] => 001001 => 110110
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => [7,4,1,2,3,6,5] => 001011 => 110100
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => [7,4,1,3,2,5,6] => 011001 => 100110
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => [7,4,1,3,2,6,5] => 011011 => 100100
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [7,4,2,1,3,5,6] => 101001 => 010110
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => [7,4,2,1,3,6,5] => 101011 => 010100
[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => [7,4,3,1,2,5,6] => 011001 => 100110
[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => [7,4,3,1,2,6,5] => 011011 => 100100
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [7,4,3,2,1,5,6] => 111001 => 000110
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [7,4,3,2,1,6,5] => 111011 => 000100
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [7,5,1,2,3,4,6] => 000101 => 111010
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [7,5,1,2,4,3,6] => 001101 => 110010
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [7,5,1,3,2,4,6] => 010101 => 101010
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [7,5,1,4,2,3,6] => 001101 => 110010
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [7,5,1,4,3,2,6] => 011101 => 100010
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [7,5,2,1,3,4,6] => 100101 => 011010
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [7,5,2,1,4,3,6] => 101101 => 010010
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => [7,5,3,1,2,4,6] => 010101 => 101010
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [7,5,3,2,1,4,6] => 110101 => 001010
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => [7,5,4,1,2,3,6] => 001101 => 110010
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => [7,5,4,1,3,2,6] => 011101 => 100010
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [7,5,4,2,1,3,6] => 101101 => 010010
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [7,5,4,3,1,2,6] => 011101 => 100010
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [7,5,4,3,2,1,6] => 111101 => 000010
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [7,6,1,2,3,4,5] => 000011 => 111100
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [7,6,1,2,3,5,4] => 000111 => 111000
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [7,6,1,2,4,3,5] => 001011 => 110100
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [7,6,1,2,5,3,4] => 000111 => 111000
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [7,6,1,2,5,4,3] => 001111 => 110000
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [7,6,1,3,2,4,5] => 010011 => 101100
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [7,6,1,3,2,5,4] => 010111 => 101000
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [7,6,1,4,2,3,5] => 001011 => 110100
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [7,6,1,4,3,2,5] => 011011 => 100100
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [7,6,1,5,2,3,4] => 000111 => 111000
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [7,6,1,5,2,4,3] => 001111 => 110000
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [7,6,1,5,3,2,4] => 010111 => 101000
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [7,6,1,5,4,2,3] => 001111 => 110000
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [7,6,1,5,4,3,2] => 011111 => 100000
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [7,6,2,1,3,4,5] => 100011 => 011100
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [7,6,2,1,3,5,4] => 100111 => 011000
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [7,6,2,1,4,3,5] => 101011 => 010100
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [7,6,2,1,5,3,4] => 100111 => 011000
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [7,6,2,1,5,4,3] => 101111 => 010000
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => [7,6,3,1,2,4,5] => 010011 => 101100
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => [7,6,3,1,2,5,4] => 010111 => 101000
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [7,6,3,2,1,4,5] => 110011 => 001100
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [7,6,3,2,1,5,4] => 110111 => 001000
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [7,6,4,1,2,3,5] => 001011 => 110100
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [7,6,4,1,3,2,5] => 011011 => 100100
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [7,6,4,2,1,3,5] => 101011 => 010100
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [7,6,4,3,1,2,5] => 011011 => 100100
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [7,6,4,3,2,1,5] => 111011 => 000100
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [7,6,5,1,2,3,4] => 000111 => 111000
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [7,6,5,1,2,4,3] => 001111 => 110000
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [7,6,5,1,3,2,4] => 010111 => 101000
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [7,6,5,1,4,2,3] => 001111 => 110000
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [7,6,5,1,4,3,2] => 011111 => 100000
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [7,6,5,2,1,3,4] => 100111 => 011000
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [7,6,5,2,1,4,3] => 101111 => 010000
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [7,6,5,3,1,2,4] => 010111 => 101000
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [7,6,5,3,2,1,4] => 110111 => 001000
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [7,6,5,4,1,2,3] => 001111 => 110000
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [7,6,5,4,1,3,2] => 011111 => 100000
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [7,6,5,4,2,1,3] => 101111 => 010000
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [7,6,5,4,3,1,2] => 011111 => 100000
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => 111111 => 000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 0000000 => 1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,7] => 0000001 => 1111110
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [8,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,8] => 0000010 => 1111101
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [1,2,3,4,5,8,6,7] => 0000001 => 1111110
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [1,2,3,4,5,8,7,6] => 0000011 => 1111100
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [8,7,5,6,4,3,2,1] => [1,2,3,4,6,5,7,8] => 0000100 => 1111011
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => [1,2,3,4,6,5,8,7] => 0000101 => 1111010
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [8,6,5,7,4,3,2,1] => [1,2,3,4,7,5,6,8] => 0000010 => 1111101
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [8,5,6,7,4,3,2,1] => [1,2,3,4,7,6,5,8] => 0000110 => 1111001
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [1,2,3,4,8,5,6,7] => 0000001 => 1111110
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => [1,2,3,4,8,5,7,6] => 0000011 => 1111100
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => [1,2,3,4,8,6,5,7] => 0000101 => 1111010
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [1,2,3,4,8,7,5,6] => 0000011 => 1111100
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [1,2,3,4,8,7,6,5] => 0000111 => 1111000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [1,2,3,5,4,6,7,8] => 0001000 => 1110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [1,2,3,5,4,6,8,7] => 0001001 => 1110110
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [1,2,3,5,4,7,6,8] => 0001010 => 1110101
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [7,6,8,4,5,3,2,1] => [1,2,3,5,4,8,6,7] => 0001001 => 1110110
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [6,7,8,4,5,3,2,1] => [1,2,3,5,4,8,7,6] => 0001011 => 1110100
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [8,7,5,4,6,3,2,1] => [1,2,3,6,4,5,7,8] => 0000100 => 1111011
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [7,8,5,4,6,3,2,1] => [1,2,3,6,4,5,8,7] => 0000101 => 1111010
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [8,7,4,5,6,3,2,1] => [1,2,3,6,5,4,7,8] => 0001100 => 1110011
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [7,8,4,5,6,3,2,1] => [1,2,3,6,5,4,8,7] => 0001101 => 1110010
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [8,6,5,4,7,3,2,1] => [1,2,3,7,4,5,6,8] => 0000010 => 1111101
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [8,5,6,4,7,3,2,1] => [1,2,3,7,4,6,5,8] => 0000110 => 1111001
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [8,6,4,5,7,3,2,1] => [1,2,3,7,5,4,6,8] => 0001010 => 1110101
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [8,5,4,6,7,3,2,1] => [1,2,3,7,6,4,5,8] => 0000110 => 1111001
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [8,4,5,6,7,3,2,1] => [1,2,3,7,6,5,4,8] => 0001110 => 1110001
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [1,2,3,8,4,5,6,7] => 0000001 => 1111110
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => [1,2,3,8,4,5,7,6] => 0000011 => 1111100
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [7,5,6,4,8,3,2,1] => [1,2,3,8,4,6,5,7] => 0000101 => 1111010
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [1,2,3,8,4,7,5,6] => 0000011 => 1111100
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => [1,2,3,8,4,7,6,5] => 0000111 => 1111000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => [1,2,3,8,5,4,6,7] => 0001001 => 1110110
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [6,7,4,5,8,3,2,1] => [1,2,3,8,5,4,7,6] => 0001011 => 1110100
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => [1,2,3,8,6,4,5,7] => 0000101 => 1111010
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [1,2,3,8,6,5,4,7] => 0001101 => 1110010
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => [1,2,3,8,7,4,5,6] => 0000011 => 1111100
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => [1,2,3,8,7,4,6,5] => 0000111 => 1111000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [6,4,5,7,8,3,2,1] => [1,2,3,8,7,5,4,6] => 0001011 => 1110100
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => [1,2,3,8,7,6,4,5] => 0000111 => 1111000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [1,2,3,8,7,6,5,4] => 0001111 => 1110000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [1,2,4,3,5,6,7,8] => 0010000 => 1101111
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [1,2,4,3,5,6,8,7] => 0010001 => 1101110
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [1,2,4,3,5,7,6,8] => 0010010 => 1101101
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [7,6,8,5,3,4,2,1] => [1,2,4,3,5,8,6,7] => 0010001 => 1101110
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [6,7,8,5,3,4,2,1] => [1,2,4,3,5,8,7,6] => 0010011 => 1101100
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [1,2,4,3,6,5,7,8] => 0010100 => 1101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [7,8,5,6,3,4,2,1] => [1,2,4,3,6,5,8,7] => 0010101 => 1101010
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [8,6,5,7,3,4,2,1] => [1,2,4,3,7,5,6,8] => 0010010 => 1101101
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [7,6,5,8,3,4,2,1] => [1,2,4,3,8,5,6,7] => 0010001 => 1101110
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [6,7,5,8,3,4,2,1] => [1,2,4,3,8,5,7,6] => 0010011 => 1101100
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [7,5,6,8,3,4,2,1] => [1,2,4,3,8,6,5,7] => 0010101 => 1101010
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [6,5,7,8,3,4,2,1] => [1,2,4,3,8,7,5,6] => 0010011 => 1101100
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => [1,2,4,3,8,7,6,5] => 0010111 => 1101000
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [8,7,6,4,3,5,2,1] => [1,2,5,3,4,6,7,8] => 0001000 => 1110111
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [7,8,6,4,3,5,2,1] => [1,2,5,3,4,6,8,7] => 0001001 => 1110110
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [8,6,7,4,3,5,2,1] => [1,2,5,3,4,7,6,8] => 0001010 => 1110101
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [7,6,8,4,3,5,2,1] => [1,2,5,3,4,8,6,7] => 0001001 => 1110110
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [6,7,8,4,3,5,2,1] => [1,2,5,3,4,8,7,6] => 0001011 => 1110100
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1] => [1,2,5,4,3,6,7,8] => 0011000 => 1100111
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [7,8,6,3,4,5,2,1] => [1,2,5,4,3,6,8,7] => 0011001 => 1100110
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [7,6,8,3,4,5,2,1] => [1,2,5,4,3,8,6,7] => 0011001 => 1100110
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => [1,2,5,4,3,8,7,6] => 0011011 => 1100100
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => [1,2,6,3,4,5,7,8] => 0000100 => 1111011
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [7,8,5,4,3,6,2,1] => [1,2,6,3,4,5,8,7] => 0000101 => 1111010
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [8,7,4,5,3,6,2,1] => [1,2,6,3,5,4,7,8] => 0001100 => 1110011
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [8,7,5,3,4,6,2,1] => [1,2,6,4,3,5,7,8] => 0010100 => 1101011
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [8,7,4,3,5,6,2,1] => [1,2,6,5,3,4,7,8] => 0001100 => 1110011
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [8,7,3,4,5,6,2,1] => [1,2,6,5,4,3,7,8] => 0011100 => 1100011
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [8,6,5,4,3,7,2,1] => [1,2,7,3,4,5,6,8] => 0000010 => 1111101
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [8,5,6,4,3,7,2,1] => [1,2,7,3,4,6,5,8] => 0000110 => 1111001
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [8,6,4,5,3,7,2,1] => [1,2,7,3,5,4,6,8] => 0001010 => 1110101
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [8,5,4,6,3,7,2,1] => [1,2,7,3,6,4,5,8] => 0000110 => 1111001
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [8,6,5,3,4,7,2,1] => [1,2,7,4,3,5,6,8] => 0010010 => 1101101
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [8,6,4,3,5,7,2,1] => [1,2,7,5,3,4,6,8] => 0001010 => 1110101
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [8,5,4,3,6,7,2,1] => [1,2,7,6,3,4,5,8] => 0000110 => 1111001
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [8,5,3,4,6,7,2,1] => [1,2,7,6,4,3,5,8] => 0010110 => 1101001
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [8,3,4,5,6,7,2,1] => [1,2,7,6,5,4,3,8] => 0011110 => 1100001
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [1,2,8,3,4,5,6,7] => 0000001 => 1111110
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => [1,2,8,3,4,5,7,6] => 0000011 => 1111100
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [7,5,6,4,3,8,2,1] => [1,2,8,3,4,6,5,7] => 0000101 => 1111010
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => [1,2,8,3,4,7,6,5] => 0000111 => 1111000
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [7,6,4,5,3,8,2,1] => [1,2,8,3,5,4,6,7] => 0001001 => 1110110
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [6,7,4,5,3,8,2,1] => [1,2,8,3,5,4,7,6] => 0001011 => 1110100
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [7,5,4,6,3,8,2,1] => [1,2,8,3,6,4,5,7] => 0000101 => 1111010
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [7,4,5,6,3,8,2,1] => [1,2,8,3,6,5,4,7] => 0001101 => 1110010
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => [1,2,8,3,7,4,5,6] => 0000011 => 1111100
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [5,6,4,7,3,8,2,1] => [1,2,8,3,7,4,6,5] => 0000111 => 1111000
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [6,4,5,7,3,8,2,1] => [1,2,8,3,7,5,4,6] => 0001011 => 1110100
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [1,2,8,3,7,6,4,5] => 0000111 => 1111000
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => [1,2,8,3,7,6,5,4] => 0001111 => 1110000
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => [1,2,8,4,3,5,6,7] => 0010001 => 1101110
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [6,7,5,3,4,8,2,1] => [1,2,8,4,3,5,7,6] => 0010011 => 1101100
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [7,5,6,3,4,8,2,1] => [1,2,8,4,3,6,5,7] => 0010101 => 1101010
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => [6,5,7,3,4,8,2,1] => [1,2,8,4,3,7,5,6] => 0010011 => 1101100
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [5,6,7,3,4,8,2,1] => [1,2,8,4,3,7,6,5] => 0010111 => 1101000
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => [1,2,8,5,3,4,6,7] => 0001001 => 1110110
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [1,2,8,5,4,3,6,7] => 0011001 => 1100110
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [7,5,4,3,6,8,2,1] => [1,2,8,6,3,4,5,7] => 0000101 => 1111010
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [7,5,3,4,6,8,2,1] => [1,2,8,6,4,3,5,7] => 0010101 => 1101010
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [7,3,4,5,6,8,2,1] => [1,2,8,6,5,4,3,7] => 0011101 => 1100010
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => [1,2,8,7,3,4,5,6] => 0000011 => 1111100
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => [5,6,4,3,7,8,2,1] => [1,2,8,7,3,4,6,5] => 0000111 => 1111000
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => [6,4,5,3,7,8,2,1] => [1,2,8,7,3,5,4,6] => 0001011 => 1110100
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => [1,2,8,7,3,6,5,4] => 0001111 => 1110000
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [5,6,3,4,7,8,2,1] => [1,2,8,7,4,3,6,5] => 0010111 => 1101000
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [6,3,4,5,7,8,2,1] => [1,2,8,7,5,4,3,6] => 0011011 => 1100100
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => [1,2,8,7,6,3,4,5] => 0000111 => 1111000
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [4,5,3,6,7,8,2,1] => [1,2,8,7,6,3,5,4] => 0001111 => 1110000
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [5,3,4,6,7,8,2,1] => [1,2,8,7,6,4,3,5] => 0010111 => 1101000
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [1,2,8,7,6,5,3,4] => 0001111 => 1110000
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [1,2,8,7,6,5,4,3] => 0011111 => 1100000
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,8] => 0100000 => 1011111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [1,3,2,4,5,6,8,7] => 0100001 => 1011110
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,3,2,4,5,7,6,8] => 0100010 => 1011101
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,2,3,1] => [1,3,2,4,5,8,6,7] => 0100001 => 1011110
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,2,3,1] => [1,3,2,4,5,8,7,6] => 0100011 => 1011100
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [1,3,2,4,6,5,7,8] => 0100100 => 1011011
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,2,3,1] => [1,3,2,4,6,5,8,7] => 0100101 => 1011010
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,2,3,1] => [1,3,2,4,7,6,5,8] => 0100110 => 1011001
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,2,3,1] => [1,3,2,4,8,5,6,7] => 0100001 => 1011110
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,2,3,1] => [1,3,2,4,8,5,7,6] => 0100011 => 1011100
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,2,3,1] => [1,3,2,4,8,6,5,7] => 0100101 => 1011010
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => [1,3,2,4,8,7,6,5] => 0100111 => 1011000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [1,3,2,5,4,6,7,8] => 0101000 => 1010111
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,8] => 0101010 => 1010101
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [7,6,8,4,5,2,3,1] => [1,3,2,5,4,8,6,7] => 0101001 => 1010110
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,2,3,1] => [1,3,2,5,4,8,7,6] => 0101011 => 1010100
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,2,3,1] => [1,3,2,6,4,5,7,8] => 0100100 => 1011011
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,2,3,1] => [1,3,2,6,5,4,7,8] => 0101100 => 1010011
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => [1,3,2,6,5,4,8,7] => 0101101 => 1010010
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [8,6,5,4,7,2,3,1] => [1,3,2,7,4,5,6,8] => 0100010 => 1011101
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,2,3,1] => [1,3,2,7,4,6,5,8] => 0100110 => 1011001
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,2,3,1] => [1,3,2,7,5,4,6,8] => 0101010 => 1010101
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [8,5,4,6,7,2,3,1] => [1,3,2,7,6,4,5,8] => 0100110 => 1011001
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [8,4,5,6,7,2,3,1] => [1,3,2,7,6,5,4,8] => 0101110 => 1010001
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,2,3,1] => [1,3,2,8,4,5,6,7] => 0100001 => 1011110
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [6,7,5,4,8,2,3,1] => [1,3,2,8,4,5,7,6] => 0100011 => 1011100
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,2,3,1] => [1,3,2,8,4,6,5,7] => 0100101 => 1011010
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,2,3,1] => [1,3,2,8,4,7,5,6] => 0100011 => 1011100
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,2,3,1] => [1,3,2,8,5,4,6,7] => 0101001 => 1010110
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,2,3,1] => [1,3,2,8,5,4,7,6] => 0101011 => 1010100
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [7,5,4,6,8,2,3,1] => [1,3,2,8,6,4,5,7] => 0100101 => 1011010
[.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [7,4,5,6,8,2,3,1] => [1,3,2,8,6,5,4,7] => 0101101 => 1010010
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,2,3,1] => [1,3,2,8,7,4,5,6] => 0100011 => 1011100
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [5,6,4,7,8,2,3,1] => [1,3,2,8,7,4,6,5] => 0100111 => 1011000
[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [6,4,5,7,8,2,3,1] => [1,3,2,8,7,5,4,6] => 0101011 => 1010100
[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [5,4,6,7,8,2,3,1] => [1,3,2,8,7,6,4,5] => 0100111 => 1011000
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => [1,3,2,8,7,6,5,4] => 0101111 => 1010000
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,2,4,1] => [1,4,2,3,5,6,7,8] => 0010000 => 1101111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,2,4,1] => [1,4,2,3,5,6,8,7] => 0010001 => 1101110
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [8,6,7,5,3,2,4,1] => [1,4,2,3,5,7,6,8] => 0010010 => 1101101
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,2,4,1] => [1,4,2,3,5,8,6,7] => 0010001 => 1101110
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,2,4,1] => [1,4,2,3,5,8,7,6] => 0010011 => 1101100
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,2,4,1] => [1,4,2,3,6,5,7,8] => 0010100 => 1101011
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,2,4,1] => [1,4,2,3,6,5,8,7] => 0010101 => 1101010
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => [1,4,2,3,7,5,6,8] => 0010010 => 1101101
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,2,4,1] => [1,4,2,3,8,5,6,7] => 0010001 => 1101110
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,2,4,1] => [1,4,2,3,8,5,7,6] => 0010011 => 1101100
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,2,4,1] => [1,4,2,3,8,6,5,7] => 0010101 => 1101010
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,2,4,1] => [1,4,2,3,8,7,5,6] => 0010011 => 1101100
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => [1,4,2,3,8,7,6,5] => 0010111 => 1101000
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [1,4,3,2,5,6,7,8] => 0110000 => 1001111
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,2,3,4,1] => [1,4,3,2,5,7,6,8] => 0110010 => 1001101
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,2,3,4,1] => [1,4,3,2,5,8,6,7] => 0110001 => 1001110
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => [1,4,3,2,5,8,7,6] => 0110011 => 1001100
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => [1,4,3,2,7,6,5,8] => 0110110 => 1001001
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,2,3,4,1] => [1,4,3,2,8,5,6,7] => 0110001 => 1001110
[.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [7,5,6,8,2,3,4,1] => [1,4,3,2,8,6,5,7] => 0110101 => 1001010
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => [1,4,3,2,8,7,6,5] => 0110111 => 1001000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [8,7,6,4,3,2,5,1] => [1,5,2,3,4,6,7,8] => 0001000 => 1110111
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [7,8,6,4,3,2,5,1] => [1,5,2,3,4,6,8,7] => 0001001 => 1110110
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [8,6,7,4,3,2,5,1] => [1,5,2,3,4,7,6,8] => 0001010 => 1110101
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [7,6,8,4,3,2,5,1] => [1,5,2,3,4,8,6,7] => 0001001 => 1110110
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [6,7,8,4,3,2,5,1] => [1,5,2,3,4,8,7,6] => 0001011 => 1110100
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [8,7,6,3,4,2,5,1] => [1,5,2,4,3,6,7,8] => 0011000 => 1100111
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [7,8,6,3,4,2,5,1] => [1,5,2,4,3,6,8,7] => 0011001 => 1100110
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [8,6,7,3,4,2,5,1] => [1,5,2,4,3,7,6,8] => 0011010 => 1100101
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [7,6,8,3,4,2,5,1] => [1,5,2,4,3,8,6,7] => 0011001 => 1100110
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [6,7,8,3,4,2,5,1] => [1,5,2,4,3,8,7,6] => 0011011 => 1100100
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,2,3,5,1] => [1,5,3,2,4,6,7,8] => 0101000 => 1010111
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [7,8,6,4,2,3,5,1] => [1,5,3,2,4,6,8,7] => 0101001 => 1010110
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [8,6,7,4,2,3,5,1] => [1,5,3,2,4,7,6,8] => 0101010 => 1010101
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [7,6,8,4,2,3,5,1] => [1,5,3,2,4,8,6,7] => 0101001 => 1010110
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [6,7,8,4,2,3,5,1] => [1,5,3,2,4,8,7,6] => 0101011 => 1010100
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [8,7,6,3,2,4,5,1] => [1,5,4,2,3,6,7,8] => 0011000 => 1100111
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [7,8,6,3,2,4,5,1] => [1,5,4,2,3,6,8,7] => 0011001 => 1100110
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [8,6,7,3,2,4,5,1] => [1,5,4,2,3,7,6,8] => 0011010 => 1100101
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [7,6,8,3,2,4,5,1] => [1,5,4,2,3,8,6,7] => 0011001 => 1100110
[.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [6,7,8,3,2,4,5,1] => [1,5,4,2,3,8,7,6] => 0011011 => 1100100
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => [1,5,4,3,2,6,7,8] => 0111000 => 1000111
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [8,6,7,2,3,4,5,1] => [1,5,4,3,2,7,6,8] => 0111010 => 1000101
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [6,7,8,2,3,4,5,1] => [1,5,4,3,2,8,7,6] => 0111011 => 1000100
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [8,7,5,4,3,2,6,1] => [1,6,2,3,4,5,7,8] => 0000100 => 1111011
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [7,8,5,4,3,2,6,1] => [1,6,2,3,4,5,8,7] => 0000101 => 1111010
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [8,7,5,3,4,2,6,1] => [1,6,2,4,3,5,7,8] => 0010100 => 1101011
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [7,8,5,3,4,2,6,1] => [1,6,2,4,3,5,8,7] => 0010101 => 1101010
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [8,7,4,3,5,2,6,1] => [1,6,2,5,3,4,7,8] => 0001100 => 1110011
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [7,8,4,3,5,2,6,1] => [1,6,2,5,3,4,8,7] => 0001101 => 1110010
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,2,3,6,1] => [1,6,3,2,4,5,7,8] => 0100100 => 1011011
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [8,7,4,5,2,3,6,1] => [1,6,3,2,5,4,7,8] => 0101100 => 1010011
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [8,7,5,3,2,4,6,1] => [1,6,4,2,3,5,7,8] => 0010100 => 1101011
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [7,8,5,3,2,4,6,1] => [1,6,4,2,3,5,8,7] => 0010101 => 1101010
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [8,7,5,2,3,4,6,1] => [1,6,4,3,2,5,7,8] => 0110100 => 1001011
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [7,8,4,3,2,5,6,1] => [1,6,5,2,3,4,8,7] => 0001101 => 1110010
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [8,7,4,2,3,5,6,1] => [1,6,5,3,2,4,7,8] => 0101100 => 1010011
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [7,8,4,2,3,5,6,1] => [1,6,5,3,2,4,8,7] => 0101101 => 1010010
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => [1,6,5,4,2,3,8,7] => 0011101 => 1100010
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [8,7,2,3,4,5,6,1] => [1,6,5,4,3,2,7,8] => 0111100 => 1000011
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [7,8,2,3,4,5,6,1] => [1,6,5,4,3,2,8,7] => 0111101 => 1000010
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [8,6,5,4,3,2,7,1] => [1,7,2,3,4,5,6,8] => 0000010 => 1111101
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [8,5,6,4,3,2,7,1] => [1,7,2,3,4,6,5,8] => 0000110 => 1111001
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [8,6,4,5,3,2,7,1] => [1,7,2,3,5,4,6,8] => 0001010 => 1110101
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [8,5,4,6,3,2,7,1] => [1,7,2,3,6,4,5,8] => 0000110 => 1111001
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [8,6,5,3,4,2,7,1] => [1,7,2,4,3,5,6,8] => 0010010 => 1101101
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [8,5,6,3,4,2,7,1] => [1,7,2,4,3,6,5,8] => 0010110 => 1101001
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [8,6,4,3,5,2,7,1] => [1,7,2,5,3,4,6,8] => 0001010 => 1110101
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [8,6,3,4,5,2,7,1] => [1,7,2,5,4,3,6,8] => 0011010 => 1100101
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [8,5,4,3,6,2,7,1] => [1,7,2,6,3,4,5,8] => 0000110 => 1111001
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [8,4,5,3,6,2,7,1] => [1,7,2,6,3,5,4,8] => 0001110 => 1110001
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [8,5,3,4,6,2,7,1] => [1,7,2,6,4,3,5,8] => 0010110 => 1101001
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [8,3,4,5,6,2,7,1] => [1,7,2,6,5,4,3,8] => 0011110 => 1100001
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,2,3,7,1] => [1,7,3,2,4,5,6,8] => 0100010 => 1011101
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [8,5,6,4,2,3,7,1] => [1,7,3,2,4,6,5,8] => 0100110 => 1011001
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [8,6,4,5,2,3,7,1] => [1,7,3,2,5,4,6,8] => 0101010 => 1010101
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [8,6,5,3,2,4,7,1] => [1,7,4,2,3,5,6,8] => 0010010 => 1101101
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [8,6,5,2,3,4,7,1] => [1,7,4,3,2,5,6,8] => 0110010 => 1001101
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [8,6,4,3,2,5,7,1] => [1,7,5,2,3,4,6,8] => 0001010 => 1110101
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [8,6,4,2,3,5,7,1] => [1,7,5,3,2,4,6,8] => 0101010 => 1010101
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [8,6,2,3,4,5,7,1] => [1,7,5,4,3,2,6,8] => 0111010 => 1000101
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [8,5,4,3,2,6,7,1] => [1,7,6,2,3,4,5,8] => 0000110 => 1111001
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [8,5,3,4,2,6,7,1] => [1,7,6,2,4,3,5,8] => 0010110 => 1101001
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [8,5,4,2,3,6,7,1] => [1,7,6,3,2,4,5,8] => 0100110 => 1011001
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [8,4,5,2,3,6,7,1] => [1,7,6,3,2,5,4,8] => 0101110 => 1010001
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [8,5,3,2,4,6,7,1] => [1,7,6,4,2,3,5,8] => 0010110 => 1101001
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [8,3,4,2,5,6,7,1] => [1,7,6,5,2,4,3,8] => 0011110 => 1100001
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [8,4,2,3,5,6,7,1] => [1,7,6,5,3,2,4,8] => 0101110 => 1010001
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [8,3,2,4,5,6,7,1] => [1,7,6,5,4,2,3,8] => 0011110 => 1100001
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [8,2,3,4,5,6,7,1] => [1,7,6,5,4,3,2,8] => 0111110 => 1000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [1,8,2,3,4,5,6,7] => 0000001 => 1111110
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [1,8,2,3,4,5,7,6] => 0000011 => 1111100
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [7,5,6,4,3,2,8,1] => [1,8,2,3,4,6,5,7] => 0000101 => 1111010
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [1,8,2,3,4,7,5,6] => 0000011 => 1111100
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => [1,8,2,3,4,7,6,5] => 0000111 => 1111000
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [7,6,4,5,3,2,8,1] => [1,8,2,3,5,4,6,7] => 0001001 => 1110110
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [7,5,4,6,3,2,8,1] => [1,8,2,3,6,4,5,7] => 0000101 => 1111010
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [7,4,5,6,3,2,8,1] => [1,8,2,3,6,5,4,7] => 0001101 => 1110010
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [6,4,5,7,3,2,8,1] => [1,8,2,3,7,5,4,6] => 0001011 => 1110100
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => [5,4,6,7,3,2,8,1] => [1,8,2,3,7,6,4,5] => 0000111 => 1111000
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => [1,8,2,3,7,6,5,4] => 0001111 => 1110000
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [7,6,5,3,4,2,8,1] => [1,8,2,4,3,5,6,7] => 0010001 => 1101110
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [7,5,6,3,4,2,8,1] => [1,8,2,4,3,6,5,7] => 0010101 => 1101010
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [6,5,7,3,4,2,8,1] => [1,8,2,4,3,7,5,6] => 0010011 => 1101100
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [5,6,7,3,4,2,8,1] => [1,8,2,4,3,7,6,5] => 0010111 => 1101000
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [7,6,4,3,5,2,8,1] => [1,8,2,5,3,4,6,7] => 0001001 => 1110110
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [6,7,4,3,5,2,8,1] => [1,8,2,5,3,4,7,6] => 0001011 => 1110100
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [7,5,4,3,6,2,8,1] => [1,8,2,6,3,4,5,7] => 0000101 => 1111010
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [7,4,5,3,6,2,8,1] => [1,8,2,6,3,5,4,7] => 0001101 => 1110010
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [7,5,3,4,6,2,8,1] => [1,8,2,6,4,3,5,7] => 0010101 => 1101010
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [7,4,3,5,6,2,8,1] => [1,8,2,6,5,3,4,7] => 0001101 => 1110010
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [1,8,2,7,3,4,5,6] => 0000011 => 1111100
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [5,6,4,3,7,2,8,1] => [1,8,2,7,3,4,6,5] => 0000111 => 1111000
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [6,4,5,3,7,2,8,1] => [1,8,2,7,3,5,4,6] => 0001011 => 1110100
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [1,8,2,7,3,6,4,5] => 0000111 => 1111000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => [1,8,2,7,3,6,5,4] => 0001111 => 1110000
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [6,5,3,4,7,2,8,1] => [1,8,2,7,4,3,5,6] => 0010011 => 1101100
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [5,6,3,4,7,2,8,1] => [1,8,2,7,4,3,6,5] => 0010111 => 1101000
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [6,4,3,5,7,2,8,1] => [1,8,2,7,5,3,4,6] => 0001011 => 1110100
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [6,3,4,5,7,2,8,1] => [1,8,2,7,5,4,3,6] => 0011011 => 1100100
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => [1,8,2,7,6,3,4,5] => 0000111 => 1111000
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => [1,8,2,7,6,3,5,4] => 0001111 => 1110000
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [5,3,4,6,7,2,8,1] => [1,8,2,7,6,4,3,5] => 0010111 => 1101000
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => [1,8,2,7,6,5,4,3] => 0011111 => 1100000
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [1,8,3,2,4,5,6,7] => 0100001 => 1011110
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [6,7,5,4,2,3,8,1] => [1,8,3,2,4,5,7,6] => 0100011 => 1011100
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,2,3,8,1] => [1,8,3,2,4,7,5,6] => 0100011 => 1011100
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,2,3,8,1] => [1,8,3,2,5,4,6,7] => 0101001 => 1010110
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => [1,8,3,2,5,4,7,6] => 0101011 => 1010100
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,2,3,8,1] => [1,8,3,2,6,4,5,7] => 0100101 => 1011010
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [6,4,5,7,2,3,8,1] => [1,8,3,2,7,5,4,6] => 0101011 => 1010100
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [5,4,6,7,2,3,8,1] => [1,8,3,2,7,6,4,5] => 0100111 => 1011000
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => [1,8,3,2,7,6,5,4] => 0101111 => 1010000
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => [1,8,4,2,3,5,6,7] => 0010001 => 1101110
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [6,7,5,3,2,4,8,1] => [1,8,4,2,3,5,7,6] => 0010011 => 1101100
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [7,5,6,3,2,4,8,1] => [1,8,4,2,3,6,5,7] => 0010101 => 1101010
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [6,5,7,3,2,4,8,1] => [1,8,4,2,3,7,5,6] => 0010011 => 1101100
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [5,6,7,3,2,4,8,1] => [1,8,4,2,3,7,6,5] => 0010111 => 1101000
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [1,8,4,3,2,5,6,7] => 0110001 => 1001110
[.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [6,7,5,2,3,4,8,1] => [1,8,4,3,2,5,7,6] => 0110011 => 1001100
[.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [6,5,7,2,3,4,8,1] => [1,8,4,3,2,7,5,6] => 0110011 => 1001100
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [5,6,7,2,3,4,8,1] => [1,8,4,3,2,7,6,5] => 0110111 => 1001000
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [6,7,4,3,2,5,8,1] => [1,8,5,2,3,4,7,6] => 0001011 => 1110100
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [7,6,4,2,3,5,8,1] => [1,8,5,3,2,4,6,7] => 0101001 => 1010110
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [6,7,4,2,3,5,8,1] => [1,8,5,3,2,4,7,6] => 0101011 => 1010100
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [7,6,3,2,4,5,8,1] => [1,8,5,4,2,3,6,7] => 0011001 => 1100110
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [6,7,3,2,4,5,8,1] => [1,8,5,4,2,3,7,6] => 0011011 => 1100100
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [7,6,2,3,4,5,8,1] => [1,8,5,4,3,2,6,7] => 0111001 => 1000110
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => [1,8,5,4,3,2,7,6] => 0111011 => 1000100
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [7,5,4,3,2,6,8,1] => [1,8,6,2,3,4,5,7] => 0000101 => 1111010
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [7,5,3,4,2,6,8,1] => [1,8,6,2,4,3,5,7] => 0010101 => 1101010
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [7,4,3,5,2,6,8,1] => [1,8,6,2,5,3,4,7] => 0001101 => 1110010
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [7,5,4,2,3,6,8,1] => [1,8,6,3,2,4,5,7] => 0100101 => 1011010
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [7,4,5,2,3,6,8,1] => [1,8,6,3,2,5,4,7] => 0101101 => 1010010
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [7,5,3,2,4,6,8,1] => [1,8,6,4,2,3,5,7] => 0010101 => 1101010
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [7,4,2,3,5,6,8,1] => [1,8,6,5,3,2,4,7] => 0101101 => 1010010
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [7,3,2,4,5,6,8,1] => [1,8,6,5,4,2,3,7] => 0011101 => 1100010
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [7,2,3,4,5,6,8,1] => [1,8,6,5,4,3,2,7] => 0111101 => 1000010
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => [1,8,7,2,3,4,5,6] => 0000011 => 1111100
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [5,6,4,3,2,7,8,1] => [1,8,7,2,3,4,6,5] => 0000111 => 1111000
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => [6,4,5,3,2,7,8,1] => [1,8,7,2,3,5,4,6] => 0001011 => 1110100
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => [1,8,7,2,3,6,4,5] => 0000111 => 1111000
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => [1,8,7,2,3,6,5,4] => 0001111 => 1110000
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [6,4,3,5,2,7,8,1] => [1,8,7,2,5,3,4,6] => 0001011 => 1110100
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [6,3,4,5,2,7,8,1] => [1,8,7,2,5,4,3,6] => 0011011 => 1100100
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => [1,8,7,2,6,3,4,5] => 0000111 => 1111000
[.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [4,5,3,6,2,7,8,1] => [1,8,7,2,6,3,5,4] => 0001111 => 1110000
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => [1,8,7,2,6,5,3,4] => 0001111 => 1110000
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => [1,8,7,2,6,5,4,3] => 0011111 => 1100000
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [6,5,4,2,3,7,8,1] => [1,8,7,3,2,4,5,6] => 0100011 => 1011100
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [5,6,4,2,3,7,8,1] => [1,8,7,3,2,4,6,5] => 0100111 => 1011000
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [6,4,5,2,3,7,8,1] => [1,8,7,3,2,5,4,6] => 0101011 => 1010100
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [5,4,6,2,3,7,8,1] => [1,8,7,3,2,6,4,5] => 0100111 => 1011000
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [6,5,3,2,4,7,8,1] => [1,8,7,4,2,3,5,6] => 0010011 => 1101100
[.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [5,6,3,2,4,7,8,1] => [1,8,7,4,2,3,6,5] => 0010111 => 1101000
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [6,5,2,3,4,7,8,1] => [1,8,7,4,3,2,5,6] => 0110011 => 1001100
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [5,6,2,3,4,7,8,1] => [1,8,7,4,3,2,6,5] => 0110111 => 1001000
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [6,4,3,2,5,7,8,1] => [1,8,7,5,2,3,4,6] => 0001011 => 1110100
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [6,4,2,3,5,7,8,1] => [1,8,7,5,3,2,4,6] => 0101011 => 1010100
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [6,2,3,4,5,7,8,1] => [1,8,7,5,4,3,2,6] => 0111011 => 1000100
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [1,8,7,6,2,3,4,5] => 0000111 => 1111000
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [5,3,4,2,6,7,8,1] => [1,8,7,6,2,4,3,5] => 0010111 => 1101000
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [1,8,7,6,2,5,4,3] => 0011111 => 1100000
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [5,4,2,3,6,7,8,1] => [1,8,7,6,3,2,4,5] => 0100111 => 1011000
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [4,5,2,3,6,7,8,1] => [1,8,7,6,3,2,5,4] => 0101111 => 1010000
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [5,3,2,4,6,7,8,1] => [1,8,7,6,4,2,3,5] => 0010111 => 1101000
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => [1,8,7,6,4,3,2,5] => 0110111 => 1001000
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [1,8,7,6,5,2,3,4] => 0001111 => 1110000
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [1,8,7,6,5,2,4,3] => 0011111 => 1100000
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => [1,8,7,6,5,3,2,4] => 0101111 => 1010000
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [1,8,7,6,5,4,2,3] => 0011111 => 1100000
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2] => 0111111 => 1000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8] => 1000000 => 0111111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [2,1,3,4,5,6,8,7] => 1000001 => 0111110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [2,1,3,4,5,7,6,8] => 1000010 => 0111101
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,3,1,2] => [2,1,3,4,5,8,6,7] => 1000001 => 0111110
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => [2,1,3,4,5,8,7,6] => 1000011 => 0111100
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [2,1,3,4,6,5,7,8] => 1000100 => 0111011
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,3,1,2] => [2,1,3,4,6,5,8,7] => 1000101 => 0111010
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,3,1,2] => [2,1,3,4,7,5,6,8] => 1000010 => 0111101
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,3,1,2] => [2,1,3,4,8,5,6,7] => 1000001 => 0111110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,3,1,2] => [2,1,3,4,8,5,7,6] => 1000011 => 0111100
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => [2,1,3,4,8,6,5,7] => 1000101 => 0111010
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => [2,1,3,4,8,7,5,6] => 1000011 => 0111100
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [2,1,3,4,8,7,6,5] => 1000111 => 0111000
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [2,1,3,5,4,6,7,8] => 1001000 => 0110111
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [2,1,3,5,4,6,8,7] => 1001001 => 0110110
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => [2,1,3,5,4,8,7,6] => 1001011 => 0110100
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,3,1,2] => [2,1,3,6,4,5,7,8] => 1000100 => 0111011
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [7,8,5,4,6,3,1,2] => [2,1,3,6,4,5,8,7] => 1000101 => 0111010
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => [2,1,3,6,5,4,8,7] => 1001101 => 0110010
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,3,1,2] => [2,1,3,8,4,5,6,7] => 1000001 => 0111110
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [6,7,5,4,8,3,1,2] => [2,1,3,8,4,5,7,6] => 1000011 => 0111100
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,3,1,2] => [2,1,3,8,4,6,5,7] => 1000101 => 0111010
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,3,1,2] => [2,1,3,8,4,7,5,6] => 1000011 => 0111100
[[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [5,6,7,4,8,3,1,2] => [2,1,3,8,4,7,6,5] => 1000111 => 0111000
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => [2,1,3,8,5,4,6,7] => 1001001 => 0110110
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,3,1,2] => [2,1,3,8,5,4,7,6] => 1001011 => 0110100
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [7,5,4,6,8,3,1,2] => [2,1,3,8,6,4,5,7] => 1000101 => 0111010
[[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [7,4,5,6,8,3,1,2] => [2,1,3,8,6,5,4,7] => 1001101 => 0110010
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,3,1,2] => [2,1,3,8,7,4,5,6] => 1000011 => 0111100
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [5,6,4,7,8,3,1,2] => [2,1,3,8,7,4,6,5] => 1000111 => 0111000
[[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [6,4,5,7,8,3,1,2] => [2,1,3,8,7,5,4,6] => 1001011 => 0110100
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [5,4,6,7,8,3,1,2] => [2,1,3,8,7,6,4,5] => 1000111 => 0111000
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => [2,1,3,8,7,6,5,4] => 1001111 => 0110000
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [2,1,4,3,5,6,7,8] => 1010000 => 0101111
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [2,1,4,3,5,6,8,7] => 1010001 => 0101110
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,4,1,2] => [2,1,4,3,5,8,6,7] => 1010001 => 0101110
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => [2,1,4,3,5,8,7,6] => 1010011 => 0101100
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [2,1,4,3,6,5,7,8] => 1010100 => 0101011
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7] => 1010101 => 0101010
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => [2,1,4,3,8,5,6,7] => 1010001 => 0101110
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => [2,1,4,3,8,5,7,6] => 1010011 => 0101100
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [2,1,4,3,8,6,5,7] => 1010101 => 0101010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => [2,1,4,3,8,7,5,6] => 1010011 => 0101100
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [2,1,4,3,8,7,6,5] => 1010111 => 0101000
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,3,5,1,2] => [2,1,5,3,4,6,7,8] => 1001000 => 0110111
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [7,8,6,4,3,5,1,2] => [2,1,5,3,4,6,8,7] => 1001001 => 0110110
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => [2,1,5,4,3,6,7,8] => 1011000 => 0100111
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => [2,1,5,4,3,6,8,7] => 1011001 => 0100110
[[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => [2,1,5,4,3,7,6,8] => 1011010 => 0100101
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [6,7,8,3,4,5,1,2] => [2,1,5,4,3,8,7,6] => 1011011 => 0100100
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => [2,1,6,3,4,5,8,7] => 1000101 => 0111010
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => [2,1,6,3,5,4,8,7] => 1001101 => 0110010
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [8,7,5,3,4,6,1,2] => [2,1,6,4,3,5,7,8] => 1010100 => 0101011
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => [2,1,6,4,3,5,8,7] => 1010101 => 0101010
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => [2,1,6,5,3,4,8,7] => 1001101 => 0110010
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [2,1,6,5,4,3,8,7] => 1011101 => 0100010
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,3,7,1,2] => [2,1,7,3,4,5,6,8] => 1000010 => 0111101
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [8,5,4,6,3,7,1,2] => [2,1,7,3,6,4,5,8] => 1000110 => 0111001
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [8,5,4,3,6,7,1,2] => [2,1,7,6,3,4,5,8] => 1000110 => 0111001
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => [2,1,7,6,5,3,4,8] => 1001110 => 0110001
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [2,1,7,6,5,4,3,8] => 1011110 => 0100001
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [2,1,8,3,4,5,6,7] => 1000001 => 0111110
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2] => [2,1,8,3,4,7,5,6] => 1000011 => 0111100
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [5,6,7,4,3,8,1,2] => [2,1,8,3,4,7,6,5] => 1000111 => 0111000
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => [2,1,8,3,5,4,7,6] => 1001011 => 0110100
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,3,8,1,2] => [2,1,8,3,6,4,5,7] => 1000101 => 0111010
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [6,5,4,7,3,8,1,2] => [2,1,8,3,7,4,5,6] => 1000011 => 0111100
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => [2,1,8,3,7,4,6,5] => 1000111 => 0111000
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [6,4,5,7,3,8,1,2] => [2,1,8,3,7,5,4,6] => 1001011 => 0110100
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [5,4,6,7,3,8,1,2] => [2,1,8,3,7,6,4,5] => 1000111 => 0111000
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => [2,1,8,3,7,6,5,4] => 1001111 => 0110000
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [6,7,5,3,4,8,1,2] => [2,1,8,4,3,5,7,6] => 1010011 => 0101100
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => [2,1,8,4,3,6,5,7] => 1010101 => 0101010
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [6,5,7,3,4,8,1,2] => [2,1,8,4,3,7,5,6] => 1010011 => 0101100
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [5,6,7,3,4,8,1,2] => [2,1,8,4,3,7,6,5] => 1010111 => 0101000
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [7,6,4,3,5,8,1,2] => [2,1,8,5,3,4,6,7] => 1001001 => 0110110
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [6,7,4,3,5,8,1,2] => [2,1,8,5,3,4,7,6] => 1001011 => 0110100
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => [2,1,8,5,4,3,6,7] => 1011001 => 0100110
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [6,7,3,4,5,8,1,2] => [2,1,8,5,4,3,7,6] => 1011011 => 0100100
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [7,4,5,3,6,8,1,2] => [2,1,8,6,3,5,4,7] => 1001101 => 0110010
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [7,5,3,4,6,8,1,2] => [2,1,8,6,4,3,5,7] => 1010101 => 0101010
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [7,3,4,5,6,8,1,2] => [2,1,8,6,5,4,3,7] => 1011101 => 0100010
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [6,5,4,3,7,8,1,2] => [2,1,8,7,3,4,5,6] => 1000011 => 0111100
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [5,6,4,3,7,8,1,2] => [2,1,8,7,3,4,6,5] => 1000111 => 0111000
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [6,4,5,3,7,8,1,2] => [2,1,8,7,3,5,4,6] => 1001011 => 0110100
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => [2,1,8,7,3,6,4,5] => 1000111 => 0111000
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [4,5,6,3,7,8,1,2] => [2,1,8,7,3,6,5,4] => 1001111 => 0110000
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [6,5,3,4,7,8,1,2] => [2,1,8,7,4,3,5,6] => 1010011 => 0101100
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => [2,1,8,7,4,3,6,5] => 1010111 => 0101000
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => [2,1,8,7,5,3,4,6] => 1001011 => 0110100
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => [2,1,8,7,5,4,3,6] => 1011011 => 0100100
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => [2,1,8,7,6,3,4,5] => 1000111 => 0111000
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => [2,1,8,7,6,3,5,4] => 1001111 => 0110000
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [5,3,4,6,7,8,1,2] => [2,1,8,7,6,4,3,5] => 1010111 => 0101000
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => [2,1,8,7,6,5,3,4] => 1001111 => 0110000
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [2,1,8,7,6,5,4,3] => 1011111 => 0100000
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,8] => 0100000 => 1011111
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,2,1,3] => [3,1,2,4,5,6,8,7] => 0100001 => 1011110
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [8,6,7,5,4,2,1,3] => [3,1,2,4,5,7,6,8] => 0100010 => 1011101
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => [3,1,2,4,5,8,6,7] => 0100001 => 1011110
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,2,1,3] => [3,1,2,4,6,5,8,7] => 0100101 => 1011010
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,2,1,3] => [3,1,2,4,7,5,6,8] => 0100010 => 1011101
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,2,1,3] => [3,1,2,4,8,5,6,7] => 0100001 => 1011110
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,2,1,3] => [3,1,2,4,8,5,7,6] => 0100011 => 1011100
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,2,1,3] => [3,1,2,4,8,6,5,7] => 0100101 => 1011010
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,2,1,3] => [3,1,2,4,8,7,5,6] => 0100011 => 1011100
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => [3,1,2,4,8,7,6,5] => 0100111 => 1011000
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [7,8,6,4,5,2,1,3] => [3,1,2,5,4,6,8,7] => 0101001 => 1010110
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,2,1,3] => [3,1,2,5,4,7,6,8] => 0101010 => 1010101
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [7,8,5,4,6,2,1,3] => [3,1,2,6,4,5,8,7] => 0100101 => 1011010
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,2,1,3] => [3,1,2,7,4,5,6,8] => 0100010 => 1011101
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,2,1,3] => [3,1,2,7,5,4,6,8] => 0101010 => 1010101
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [8,5,4,6,7,2,1,3] => [3,1,2,7,6,4,5,8] => 0100110 => 1011001
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,2,1,3] => [3,1,2,8,4,5,6,7] => 0100001 => 1011110
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,2,1,3] => [3,1,2,8,4,5,7,6] => 0100011 => 1011100
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,2,1,3] => [3,1,2,8,4,7,5,6] => 0100011 => 1011100
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,2,1,3] => [3,1,2,8,5,4,7,6] => 0101011 => 1010100
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,2,1,3] => [3,1,2,8,6,4,5,7] => 0100101 => 1011010
[[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,2,1,3] => [3,1,2,8,6,5,4,7] => 0101101 => 1010010
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,2,1,3] => [3,1,2,8,7,4,5,6] => 0100011 => 1011100
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [5,6,4,7,8,2,1,3] => [3,1,2,8,7,4,6,5] => 0100111 => 1011000
[[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [6,4,5,7,8,2,1,3] => [3,1,2,8,7,5,4,6] => 0101011 => 1010100
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,2,1,3] => [3,1,2,8,7,6,4,5] => 0100111 => 1011000
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => [3,1,2,8,7,6,5,4] => 0101111 => 1010000
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [3,2,1,4,5,6,7,8] => 1100000 => 0011111
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => [3,2,1,4,5,6,8,7] => 1100001 => 0011110
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [8,6,7,5,4,1,2,3] => [3,2,1,4,5,7,6,8] => 1100010 => 0011101
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,1,2,3] => [3,2,1,4,5,8,6,7] => 1100001 => 0011110
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => [3,2,1,4,5,8,7,6] => 1100011 => 0011100
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [3,2,1,4,7,6,5,8] => 1100110 => 0011001
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,1,2,3] => [3,2,1,4,8,5,6,7] => 1100001 => 0011110
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,1,2,3] => [3,2,1,4,8,5,7,6] => 1100011 => 0011100
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,1,2,3] => [3,2,1,4,8,6,5,7] => 1100101 => 0011010
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => [3,2,1,4,8,7,5,6] => 1100011 => 0011100
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => [3,2,1,4,8,7,6,5] => 1100111 => 0011000
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [3,2,1,5,4,6,7,8] => 1101000 => 0010111
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [3,2,1,5,4,7,6,8] => 1101010 => 0010101
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [8,7,5,4,6,1,2,3] => [3,2,1,6,4,5,7,8] => 1100100 => 0011011
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [3,2,1,6,5,4,7,8] => 1101100 => 0010011
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [3,2,1,6,5,4,8,7] => 1101101 => 0010010
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,1,2,3] => [3,2,1,7,4,5,6,8] => 1100010 => 0011101
[[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [8,5,6,4,7,1,2,3] => [3,2,1,7,4,6,5,8] => 1100110 => 0011001
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => [3,2,1,7,5,4,6,8] => 1101010 => 0010101
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [8,5,4,6,7,1,2,3] => [3,2,1,7,6,4,5,8] => 1100110 => 0011001
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => [3,2,1,7,6,5,4,8] => 1101110 => 0010001
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,1,2,3] => [3,2,1,8,4,5,6,7] => 1100001 => 0011110
[[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,1,2,3] => [3,2,1,8,4,5,7,6] => 1100011 => 0011100
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [7,5,6,4,8,1,2,3] => [3,2,1,8,4,6,5,7] => 1100101 => 0011010
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,1,2,3] => [3,2,1,8,4,7,5,6] => 1100011 => 0011100
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,1,2,3] => [3,2,1,8,4,7,6,5] => 1100111 => 0011000
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,1,2,3] => [3,2,1,8,5,4,6,7] => 1101001 => 0010110
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => [3,2,1,8,5,4,7,6] => 1101011 => 0010100
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,1,2,3] => [3,2,1,8,6,4,5,7] => 1100101 => 0011010
[[[.,.],.],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,1,2,3] => [3,2,1,8,6,5,4,7] => 1101101 => 0010010
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => [3,2,1,8,7,4,5,6] => 1100011 => 0011100
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [5,6,4,7,8,1,2,3] => [3,2,1,8,7,4,6,5] => 1100111 => 0011000
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [6,4,5,7,8,1,2,3] => [3,2,1,8,7,5,4,6] => 1101011 => 0010100
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,1,2,3] => [3,2,1,8,7,6,4,5] => 1100111 => 0011000
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => [3,2,1,8,7,6,5,4] => 1101111 => 0010000
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => [4,1,2,3,5,6,7,8] => 0010000 => 1101111
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,2,1,4] => [4,1,2,3,5,6,8,7] => 0010001 => 1101110
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,2,1,4] => [4,1,2,3,5,7,6,8] => 0010010 => 1101101
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,2,1,4] => [4,1,2,3,5,8,6,7] => 0010001 => 1101110
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,2,1,4] => [4,1,2,3,5,8,7,6] => 0010011 => 1101100
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,2,1,4] => [4,1,2,3,6,5,7,8] => 0010100 => 1101011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => [4,1,2,3,6,5,8,7] => 0010101 => 1101010
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,2,1,4] => [4,1,2,3,7,5,6,8] => 0010010 => 1101101
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,2,1,4] => [4,1,2,3,7,6,5,8] => 0010110 => 1101001
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => [4,1,2,3,8,5,6,7] => 0010001 => 1101110
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,2,1,4] => [4,1,2,3,8,5,7,6] => 0010011 => 1101100
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,2,1,4] => [4,1,2,3,8,6,5,7] => 0010101 => 1101010
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,2,1,4] => [4,1,2,3,8,7,5,6] => 0010011 => 1101100
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => [4,1,2,3,8,7,6,5] => 0010111 => 1101000
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,3,1,4] => [4,1,3,2,5,6,7,8] => 0110000 => 1001111
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,3,1,4] => [4,1,3,2,5,7,6,8] => 0110010 => 1001101
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [7,8,5,6,2,3,1,4] => [4,1,3,2,6,5,8,7] => 0110101 => 1001010
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,3,1,4] => [4,1,3,2,8,5,6,7] => 0110001 => 1001110
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [6,7,5,8,2,3,1,4] => [4,1,3,2,8,5,7,6] => 0110011 => 1001100
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => [4,1,3,2,8,6,5,7] => 0110101 => 1001010
[[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [6,5,7,8,2,3,1,4] => [4,1,3,2,8,7,5,6] => 0110011 => 1001100
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [5,6,7,8,2,3,1,4] => [4,1,3,2,8,7,6,5] => 0110111 => 1001000
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [4,2,1,3,5,6,7,8] => 1010000 => 0101111
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,1,2,4] => [4,2,1,3,5,6,8,7] => 1010001 => 0101110
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,1,2,4] => [4,2,1,3,5,7,6,8] => 1010010 => 0101101
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,1,2,4] => [4,2,1,3,5,8,6,7] => 1010001 => 0101110
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,1,2,4] => [4,2,1,3,5,8,7,6] => 1010011 => 0101100
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,1,2,4] => [4,2,1,3,6,5,7,8] => 1010100 => 0101011
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => [4,2,1,3,6,5,8,7] => 1010101 => 0101010
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,1,2,4] => [4,2,1,3,7,5,6,8] => 1010010 => 0101101
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,1,2,4] => [4,2,1,3,7,6,5,8] => 1010110 => 0101001
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,1,2,4] => [4,2,1,3,8,5,6,7] => 1010001 => 0101110
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => [4,2,1,3,8,5,7,6] => 1010011 => 0101100
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => [4,2,1,3,8,6,5,7] => 1010101 => 0101010
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,1,2,4] => [4,2,1,3,8,7,5,6] => 1010011 => 0101100
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => [4,2,1,3,8,7,6,5] => 1010111 => 0101000
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => [4,3,1,2,5,6,7,8] => 0110000 => 1001111
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => [4,3,1,2,5,6,8,7] => 0110001 => 1001110
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,1,3,4] => [4,3,1,2,5,7,6,8] => 0110010 => 1001101
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => [4,3,1,2,5,8,7,6] => 0110011 => 1001100
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,1,3,4] => [4,3,1,2,6,5,7,8] => 0110100 => 1001011
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => [4,3,1,2,6,5,8,7] => 0110101 => 1001010
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,1,3,4] => [4,3,1,2,8,5,6,7] => 0110001 => 1001110
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [6,7,5,8,2,1,3,4] => [4,3,1,2,8,5,7,6] => 0110011 => 1001100
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [7,5,6,8,2,1,3,4] => [4,3,1,2,8,6,5,7] => 0110101 => 1001010
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => [4,3,1,2,8,7,5,6] => 0110011 => 1001100
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => [4,3,1,2,8,7,6,5] => 0110111 => 1001000
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [4,3,2,1,5,6,7,8] => 1110000 => 0001111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [4,3,2,1,5,6,8,7] => 1110001 => 0001110
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [4,3,2,1,5,7,6,8] => 1110010 => 0001101
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => [4,3,2,1,5,8,6,7] => 1110001 => 0001110
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => [4,3,2,1,5,8,7,6] => 1110011 => 0001100
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [4,3,2,1,6,5,7,8] => 1110100 => 0001011
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [4,3,2,1,6,5,8,7] => 1110101 => 0001010
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => [4,3,2,1,7,5,6,8] => 1110010 => 0001101
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [4,3,2,1,7,6,5,8] => 1110110 => 0001001
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => [4,3,2,1,8,5,6,7] => 1110001 => 0001110
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => [4,3,2,1,8,5,7,6] => 1110011 => 0001100
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => [4,3,2,1,8,6,5,7] => 1110101 => 0001010
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => [4,3,2,1,8,7,5,6] => 1110011 => 0001100
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => 1110111 => 0001000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => [5,1,2,3,4,6,7,8] => 0001000 => 1110111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [7,8,6,4,3,2,1,5] => [5,1,2,3,4,6,8,7] => 0001001 => 1110110
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [7,6,8,4,3,2,1,5] => [5,1,2,3,4,8,6,7] => 0001001 => 1110110
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [6,7,8,4,3,2,1,5] => [5,1,2,3,4,8,7,6] => 0001011 => 1110100
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => [5,1,2,4,3,6,7,8] => 0011000 => 1100111
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [7,8,6,3,4,2,1,5] => [5,1,2,4,3,6,8,7] => 0011001 => 1100110
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [8,6,7,3,4,2,1,5] => [5,1,2,4,3,7,6,8] => 0011010 => 1100101
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [6,7,8,3,4,2,1,5] => [5,1,2,4,3,8,7,6] => 0011011 => 1100100
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,2,3,1,5] => [5,1,3,2,4,6,7,8] => 0101000 => 1010111
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [7,8,6,4,2,3,1,5] => [5,1,3,2,4,6,8,7] => 0101001 => 1010110
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [8,6,7,4,2,3,1,5] => [5,1,3,2,4,7,6,8] => 0101010 => 1010101
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [7,6,8,4,2,3,1,5] => [5,1,3,2,4,8,6,7] => 0101001 => 1010110
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [6,7,8,4,2,3,1,5] => [5,1,3,2,4,8,7,6] => 0101011 => 1010100
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => [5,1,4,2,3,6,7,8] => 0011000 => 1100111
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [7,6,8,3,2,4,1,5] => [5,1,4,2,3,8,6,7] => 0011001 => 1100110
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [6,7,8,3,2,4,1,5] => [5,1,4,2,3,8,7,6] => 0011011 => 1100100
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [8,7,6,2,3,4,1,5] => [5,1,4,3,2,6,7,8] => 0111000 => 1000111
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [7,8,6,2,3,4,1,5] => [5,1,4,3,2,6,8,7] => 0111001 => 1000110
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [6,7,8,2,3,4,1,5] => [5,1,4,3,2,8,7,6] => 0111011 => 1000100
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => [5,2,1,3,4,6,7,8] => 1001000 => 0110111
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => [5,2,1,3,4,8,7,6] => 1001011 => 0110100
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => [5,2,1,4,3,6,7,8] => 1011000 => 0100111
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [7,8,6,3,4,1,2,5] => [5,2,1,4,3,6,8,7] => 1011001 => 0100110
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [8,6,7,3,4,1,2,5] => [5,2,1,4,3,7,6,8] => 1011010 => 0100101
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [7,6,8,3,4,1,2,5] => [5,2,1,4,3,8,6,7] => 1011001 => 0100110
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => [5,2,1,4,3,8,7,6] => 1011011 => 0100100
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => [5,3,1,2,4,6,7,8] => 0101000 => 1010111
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,2,1,3,5] => [5,3,1,2,4,6,8,7] => 0101001 => 1010110
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,2,1,3,5] => [5,3,1,2,4,7,6,8] => 0101010 => 1010101
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [7,6,8,4,2,1,3,5] => [5,3,1,2,4,8,6,7] => 0101001 => 1010110
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => [5,3,1,2,4,8,7,6] => 0101011 => 1010100
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [5,3,2,1,4,6,7,8] => 1101000 => 0010111
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => [5,3,2,1,4,6,8,7] => 1101001 => 0010110
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,1,2,3,5] => [5,3,2,1,4,7,6,8] => 1101010 => 0010101
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [7,6,8,4,1,2,3,5] => [5,3,2,1,4,8,6,7] => 1101001 => 0010110
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => [5,3,2,1,4,8,7,6] => 1101011 => 0010100
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => [5,4,1,2,3,6,7,8] => 0011000 => 1100111
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [7,6,8,3,2,1,4,5] => [5,4,1,2,3,8,6,7] => 0011001 => 1100110
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [6,7,8,3,2,1,4,5] => [5,4,1,2,3,8,7,6] => 0011011 => 1100100
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [8,7,6,2,3,1,4,5] => [5,4,1,3,2,6,7,8] => 0111000 => 1000111
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [7,6,8,2,3,1,4,5] => [5,4,1,3,2,8,6,7] => 0111001 => 1000110
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [6,7,8,2,3,1,4,5] => [5,4,1,3,2,8,7,6] => 0111011 => 1000100
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [8,7,6,3,1,2,4,5] => [5,4,2,1,3,6,7,8] => 1011000 => 0100111
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [6,7,8,3,1,2,4,5] => [5,4,2,1,3,8,7,6] => 1011011 => 0100100
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => [5,4,3,1,2,6,7,8] => 0111000 => 1000111
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [8,6,7,2,1,3,4,5] => [5,4,3,1,2,7,6,8] => 0111010 => 1000101
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [7,6,8,2,1,3,4,5] => [5,4,3,1,2,8,6,7] => 0111001 => 1000110
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => [5,4,3,1,2,8,7,6] => 0111011 => 1000100
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [5,4,3,2,1,6,7,8] => 1111000 => 0000111
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [5,4,3,2,1,6,8,7] => 1111001 => 0000110
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [5,4,3,2,1,7,6,8] => 1111010 => 0000101
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => [5,4,3,2,1,8,6,7] => 1111001 => 0000110
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => [5,4,3,2,1,8,7,6] => 1111011 => 0000100
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [8,7,5,4,3,2,1,6] => [6,1,2,3,4,5,7,8] => 0000100 => 1111011
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => [6,1,2,3,4,5,8,7] => 0000101 => 1111010
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [8,7,4,5,3,2,1,6] => [6,1,2,3,5,4,7,8] => 0001100 => 1110011
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [8,7,5,3,4,2,1,6] => [6,1,2,4,3,5,7,8] => 0010100 => 1101011
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [7,8,5,3,4,2,1,6] => [6,1,2,4,3,5,8,7] => 0010101 => 1101010
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [8,7,4,3,5,2,1,6] => [6,1,2,5,3,4,7,8] => 0001100 => 1110011
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [7,8,3,4,5,2,1,6] => [6,1,2,5,4,3,8,7] => 0011101 => 1100010
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [7,8,5,4,2,3,1,6] => [6,1,3,2,4,5,8,7] => 0100101 => 1011010
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [7,8,4,5,2,3,1,6] => [6,1,3,2,5,4,8,7] => 0101101 => 1010010
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [8,7,5,3,2,4,1,6] => [6,1,4,2,3,5,7,8] => 0010100 => 1101011
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [7,8,5,3,2,4,1,6] => [6,1,4,2,3,5,8,7] => 0010101 => 1101010
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [8,7,4,3,2,5,1,6] => [6,1,5,2,3,4,7,8] => 0001100 => 1110011
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [7,8,4,3,2,5,1,6] => [6,1,5,2,3,4,8,7] => 0001101 => 1110010
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [7,8,3,4,2,5,1,6] => [6,1,5,2,4,3,8,7] => 0011101 => 1100010
[[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [7,8,3,2,4,5,1,6] => [6,1,5,4,2,3,8,7] => 0011101 => 1100010
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [7,8,2,3,4,5,1,6] => [6,1,5,4,3,2,8,7] => 0111101 => 1000010
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => [6,2,1,3,4,5,7,8] => 1000100 => 0111011
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [8,7,5,3,4,1,2,6] => [6,2,1,4,3,5,7,8] => 1010100 => 0101011
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [7,8,5,3,4,1,2,6] => [6,2,1,4,3,5,8,7] => 1010101 => 0101010
[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [7,8,4,3,5,1,2,6] => [6,2,1,5,3,4,8,7] => 1001101 => 0110010
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [8,7,3,4,5,1,2,6] => [6,2,1,5,4,3,7,8] => 1011100 => 0100011
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [7,8,3,4,5,1,2,6] => [6,2,1,5,4,3,8,7] => 1011101 => 0100010
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,2,1,3,6] => [6,3,1,2,4,5,7,8] => 0100100 => 1011011
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => [6,3,1,2,4,5,8,7] => 0100101 => 1011010
[[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [7,8,4,5,2,1,3,6] => [6,3,1,2,5,4,8,7] => 0101101 => 1010010
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => [6,3,2,1,4,5,7,8] => 1100100 => 0011011
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => [6,3,2,1,4,5,8,7] => 1100101 => 0011010
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => [6,3,2,1,5,4,7,8] => 1101100 => 0010011
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => [6,3,2,1,5,4,8,7] => 1101101 => 0010010
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [8,7,5,3,2,1,4,6] => [6,4,1,2,3,5,7,8] => 0010100 => 1101011
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]] => [8,7,5,2,3,1,4,6] => [6,4,1,3,2,5,7,8] => 0110100 => 1001011
[[[.,[[.,.],.]],[.,.]],[[.,.],.]] => [7,8,5,2,3,1,4,6] => [6,4,1,3,2,5,8,7] => 0110101 => 1001010
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [8,7,5,3,1,2,4,6] => [6,4,2,1,3,5,7,8] => 1010100 => 0101011
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [7,8,5,3,1,2,4,6] => [6,4,2,1,3,5,8,7] => 1010101 => 0101010
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => [6,4,3,1,2,5,7,8] => 0110100 => 1001011
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => [6,4,3,1,2,5,8,7] => 0110101 => 1001010
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => [6,4,3,2,1,5,7,8] => 1110100 => 0001011
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [6,4,3,2,1,5,8,7] => 1110101 => 0001010
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => [6,5,1,2,3,4,8,7] => 0001101 => 1110010
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [7,8,3,4,2,1,5,6] => [6,5,1,2,4,3,8,7] => 0011101 => 1100010
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [7,8,3,2,4,1,5,6] => [6,5,1,4,2,3,8,7] => 0011101 => 1100010
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [8,7,2,3,4,1,5,6] => [6,5,1,4,3,2,7,8] => 0111100 => 1000011
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [7,8,2,3,4,1,5,6] => [6,5,1,4,3,2,8,7] => 0111101 => 1000010
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [7,8,4,3,1,2,5,6] => [6,5,2,1,3,4,8,7] => 1001101 => 0110010
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => [6,5,2,1,4,3,8,7] => 1011101 => 0100010
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => [6,5,3,1,2,4,8,7] => 0101101 => 1010010
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => [6,5,3,2,1,4,7,8] => 1101100 => 0010011
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [7,8,4,1,2,3,5,6] => [6,5,3,2,1,4,8,7] => 1101101 => 0010010
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => [6,5,4,1,2,3,7,8] => 0011100 => 1100011
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => [6,5,4,1,2,3,8,7] => 0011101 => 1100010
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [7,8,2,3,1,4,5,6] => [6,5,4,1,3,2,8,7] => 0111101 => 1000010
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [8,7,3,1,2,4,5,6] => [6,5,4,2,1,3,7,8] => 1011100 => 0100011
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [7,8,3,1,2,4,5,6] => [6,5,4,2,1,3,8,7] => 1011101 => 0100010
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [8,7,2,1,3,4,5,6] => [6,5,4,3,1,2,7,8] => 0111100 => 1000011
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => [6,5,4,3,1,2,8,7] => 0111101 => 1000010
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [6,5,4,3,2,1,7,8] => 1111100 => 0000011
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [6,5,4,3,2,1,8,7] => 1111101 => 0000010
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,8] => 0000010 => 1111101
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [8,5,6,4,3,2,1,7] => [7,1,2,3,4,6,5,8] => 0000110 => 1111001
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [8,6,4,5,3,2,1,7] => [7,1,2,3,5,4,6,8] => 0001010 => 1110101
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [8,5,4,6,3,2,1,7] => [7,1,2,3,6,4,5,8] => 0000110 => 1111001
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => [7,1,2,3,6,5,4,8] => 0001110 => 1110001
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [8,6,5,3,4,2,1,7] => [7,1,2,4,3,5,6,8] => 0010010 => 1101101
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [8,6,4,3,5,2,1,7] => [7,1,2,5,3,4,6,8] => 0001010 => 1110101
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [8,5,4,3,6,2,1,7] => [7,1,2,6,3,4,5,8] => 0000110 => 1111001
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [8,4,5,3,6,2,1,7] => [7,1,2,6,3,5,4,8] => 0001110 => 1110001
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [8,5,3,4,6,2,1,7] => [7,1,2,6,4,3,5,8] => 0010110 => 1101001
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [8,4,3,5,6,2,1,7] => [7,1,2,6,5,3,4,8] => 0001110 => 1110001
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [8,3,4,5,6,2,1,7] => [7,1,2,6,5,4,3,8] => 0011110 => 1100001
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,2,3,1,7] => [7,1,3,2,4,5,6,8] => 0100010 => 1011101
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,2,3,1,7] => [7,1,3,2,5,4,6,8] => 0101010 => 1010101
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [8,6,5,3,2,4,1,7] => [7,1,4,2,3,5,6,8] => 0010010 => 1101101
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [8,6,5,2,3,4,1,7] => [7,1,4,3,2,5,6,8] => 0110010 => 1001101
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [8,6,3,4,2,5,1,7] => [7,1,5,2,4,3,6,8] => 0011010 => 1100101
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [8,6,4,2,3,5,1,7] => [7,1,5,3,2,4,6,8] => 0101010 => 1010101
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [8,6,3,2,4,5,1,7] => [7,1,5,4,2,3,6,8] => 0011010 => 1100101
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [8,5,4,3,2,6,1,7] => [7,1,6,2,3,4,5,8] => 0000110 => 1111001
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [8,4,3,5,2,6,1,7] => [7,1,6,2,5,3,4,8] => 0001110 => 1110001
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [8,3,4,5,2,6,1,7] => [7,1,6,2,5,4,3,8] => 0011110 => 1100001
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [8,4,5,2,3,6,1,7] => [7,1,6,3,2,5,4,8] => 0101110 => 1010001
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [8,5,3,2,4,6,1,7] => [7,1,6,4,2,3,5,8] => 0010110 => 1101001
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [8,3,4,2,5,6,1,7] => [7,1,6,5,2,4,3,8] => 0011110 => 1100001
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [8,4,2,3,5,6,1,7] => [7,1,6,5,3,2,4,8] => 0101110 => 1010001
[[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [8,3,2,4,5,6,1,7] => [7,1,6,5,4,2,3,8] => 0011110 => 1100001
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [8,2,3,4,5,6,1,7] => [7,1,6,5,4,3,2,8] => 0111110 => 1000001
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => [7,2,1,3,4,5,6,8] => 1000010 => 0111101
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,3,1,2,7] => [7,2,1,3,5,4,6,8] => 1001010 => 0110101
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [8,6,5,3,4,1,2,7] => [7,2,1,4,3,5,6,8] => 1010010 => 0101101
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [7,2,1,4,3,6,5,8] => 1010110 => 0101001
[[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [8,6,3,4,5,1,2,7] => [7,2,1,5,4,3,6,8] => 1011010 => 0100101
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [8,4,5,3,6,1,2,7] => [7,2,1,6,3,5,4,8] => 1001110 => 0110001
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [8,4,3,5,6,1,2,7] => [7,2,1,6,5,3,4,8] => 1001110 => 0110001
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => [7,2,1,6,5,4,3,8] => 1011110 => 0100001
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => [7,3,1,2,4,5,6,8] => 0100010 => 1011101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,2,1,3,7] => [7,3,1,2,4,6,5,8] => 0100110 => 1011001
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,2,1,3,7] => [7,3,1,2,5,4,6,8] => 0101010 => 1010101
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [8,5,4,6,2,1,3,7] => [7,3,1,2,6,4,5,8] => 0100110 => 1011001
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => [7,3,2,1,4,5,6,8] => 1100010 => 0011101
[[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,1,2,3,7] => [7,3,2,1,4,6,5,8] => 1100110 => 0011001
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [7,3,2,1,5,4,6,8] => 1101010 => 0010101
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [8,5,4,6,1,2,3,7] => [7,3,2,1,6,4,5,8] => 1100110 => 0011001
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [8,6,5,3,2,1,4,7] => [7,4,1,2,3,5,6,8] => 0010010 => 1101101
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => [7,4,1,3,2,5,6,8] => 0110010 => 1001101
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [8,5,6,2,3,1,4,7] => [7,4,1,3,2,6,5,8] => 0110110 => 1001001
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [8,6,5,2,1,3,4,7] => [7,4,3,1,2,5,6,8] => 0110010 => 1001101
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => [7,4,3,1,2,6,5,8] => 0110110 => 1001001
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => [7,4,3,2,1,5,6,8] => 1110010 => 0001101
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => [7,4,3,2,1,6,5,8] => 1110110 => 0001001
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => [7,5,1,2,3,4,6,8] => 0001010 => 1110101
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [8,6,3,4,2,1,5,7] => [7,5,1,2,4,3,6,8] => 0011010 => 1100101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [8,6,4,2,3,1,5,7] => [7,5,1,3,2,4,6,8] => 0101010 => 1010101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [8,6,3,2,4,1,5,7] => [7,5,1,4,2,3,6,8] => 0011010 => 1100101
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => [7,5,3,1,2,4,6,8] => 0101010 => 1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [8,6,4,1,2,3,5,7] => [7,5,3,2,1,4,6,8] => 1101010 => 0010101
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [8,6,2,3,1,4,5,7] => [7,5,4,1,3,2,6,8] => 0111010 => 1000101
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [8,6,2,1,3,4,5,7] => [7,5,4,3,1,2,6,8] => 0111010 => 1000101
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => [7,5,4,3,2,1,6,8] => 1111010 => 0000101
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [8,5,4,3,2,1,6,7] => [7,6,1,2,3,4,5,8] => 0000110 => 1111001
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [8,4,5,3,2,1,6,7] => [7,6,1,2,3,5,4,8] => 0001110 => 1110001
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [8,3,4,5,2,1,6,7] => [7,6,1,2,5,4,3,8] => 0011110 => 1100001
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [8,5,3,2,4,1,6,7] => [7,6,1,4,2,3,5,8] => 0010110 => 1101001
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [8,5,2,3,4,1,6,7] => [7,6,1,4,3,2,5,8] => 0110110 => 1001001
[[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [8,3,4,2,5,1,6,7] => [7,6,1,5,2,4,3,8] => 0011110 => 1100001
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [8,3,4,5,1,2,6,7] => [7,6,2,1,5,4,3,8] => 1011110 => 0100001
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [8,4,5,2,1,3,6,7] => [7,6,3,1,2,5,4,8] => 0101110 => 1010001
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [8,5,4,1,2,3,6,7] => [7,6,3,2,1,4,5,8] => 1100110 => 0011001
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [8,4,5,1,2,3,6,7] => [7,6,3,2,1,5,4,8] => 1101110 => 0010001
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [8,5,3,1,2,4,6,7] => [7,6,4,2,1,3,5,8] => 1010110 => 0101001
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [8,5,2,1,3,4,6,7] => [7,6,4,3,1,2,5,8] => 0110110 => 1001001
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => [7,6,4,3,2,1,5,8] => 1110110 => 0001001
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => [7,6,5,1,2,3,4,8] => 0001110 => 1110001
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [8,3,4,2,1,5,6,7] => [7,6,5,1,2,4,3,8] => 0011110 => 1100001
[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [8,4,2,3,1,5,6,7] => [7,6,5,1,3,2,4,8] => 0101110 => 1010001
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [8,3,2,4,1,5,6,7] => [7,6,5,1,4,2,3,8] => 0011110 => 1100001
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => [7,6,5,1,4,3,2,8] => 0111110 => 1000001
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [8,4,3,1,2,5,6,7] => [7,6,5,2,1,3,4,8] => 1001110 => 0110001
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [8,3,4,1,2,5,6,7] => [7,6,5,2,1,4,3,8] => 1011110 => 0100001
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => [7,6,5,3,2,1,4,8] => 1101110 => 0010001
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => [7,6,5,4,1,2,3,8] => 0011110 => 1100001
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => [7,6,5,4,1,3,2,8] => 0111110 => 1000001
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => [7,6,5,4,2,1,3,8] => 1011110 => 0100001
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => [7,6,5,4,3,1,2,8] => 0111110 => 1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,8] => 1111110 => 0000001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7] => 0000001 => 1111110
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [8,1,2,3,4,5,7,6] => 0000011 => 1111100
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [7,5,6,4,3,2,1,8] => [8,1,2,3,4,6,5,7] => 0000101 => 1111010
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [8,1,2,3,4,7,5,6] => 0000011 => 1111100
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [8,1,2,3,4,7,6,5] => 0000111 => 1111000
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => [8,1,2,3,5,4,6,7] => 0001001 => 1110110
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [6,7,4,5,3,2,1,8] => [8,1,2,3,5,4,7,6] => 0001011 => 1110100
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [7,5,4,6,3,2,1,8] => [8,1,2,3,6,4,5,7] => 0000101 => 1111010
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => [8,1,2,3,6,5,4,7] => 0001101 => 1110010
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [8,1,2,3,7,4,5,6] => 0000011 => 1111100
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [6,4,5,7,3,2,1,8] => [8,1,2,3,7,5,4,6] => 0001011 => 1110100
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => [8,1,2,3,7,6,5,4] => 0001111 => 1110000
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [7,6,5,3,4,2,1,8] => [8,1,2,4,3,5,6,7] => 0010001 => 1101110
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [6,7,5,3,4,2,1,8] => [8,1,2,4,3,5,7,6] => 0010011 => 1101100
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => [8,1,2,4,3,6,5,7] => 0010101 => 1101010
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [5,6,7,3,4,2,1,8] => [8,1,2,4,3,7,6,5] => 0010111 => 1101000
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => [8,1,2,5,3,4,6,7] => 0001001 => 1110110
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [6,7,4,3,5,2,1,8] => [8,1,2,5,3,4,7,6] => 0001011 => 1110100
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => [8,1,2,5,4,3,6,7] => 0011001 => 1100110
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => [8,1,2,6,3,4,5,7] => 0000101 => 1111010
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [7,4,3,5,6,2,1,8] => [8,1,2,6,5,3,4,7] => 0001101 => 1110010
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [7,3,4,5,6,2,1,8] => [8,1,2,6,5,4,3,7] => 0011101 => 1100010
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => [8,1,2,7,3,4,5,6] => 0000011 => 1111100
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => [8,1,2,7,3,4,6,5] => 0000111 => 1111000
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [6,4,5,3,7,2,1,8] => [8,1,2,7,3,5,4,6] => 0001011 => 1110100
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => [8,1,2,7,3,6,4,5] => 0000111 => 1111000
[[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [4,5,6,3,7,2,1,8] => [8,1,2,7,3,6,5,4] => 0001111 => 1110000
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [5,6,3,4,7,2,1,8] => [8,1,2,7,4,3,6,5] => 0010111 => 1101000
[[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [6,3,4,5,7,2,1,8] => [8,1,2,7,5,4,3,6] => 0011011 => 1100100
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => [8,1,2,7,6,3,4,5] => 0000111 => 1111000
[[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [4,5,3,6,7,2,1,8] => [8,1,2,7,6,3,5,4] => 0001111 => 1110000
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => [8,1,2,7,6,5,4,3] => 0011111 => 1100000
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,2,3,1,8] => [8,1,3,2,4,5,6,7] => 0100001 => 1011110
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => [8,1,3,2,4,5,7,6] => 0100011 => 1011100
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,2,3,1,8] => [8,1,3,2,4,6,5,7] => 0100101 => 1011010
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [5,6,7,4,2,3,1,8] => [8,1,3,2,4,7,6,5] => 0100111 => 1011000
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => [8,1,3,2,5,4,6,7] => 0101001 => 1010110
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [6,7,4,5,2,3,1,8] => [8,1,3,2,5,4,7,6] => 0101011 => 1010100
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [7,4,5,6,2,3,1,8] => [8,1,3,2,6,5,4,7] => 0101101 => 1010010
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [5,6,4,7,2,3,1,8] => [8,1,3,2,7,4,6,5] => 0100111 => 1011000
[[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [6,4,5,7,2,3,1,8] => [8,1,3,2,7,5,4,6] => 0101011 => 1010100
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [5,4,6,7,2,3,1,8] => [8,1,3,2,7,6,4,5] => 0100111 => 1011000
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [4,5,6,7,2,3,1,8] => [8,1,3,2,7,6,5,4] => 0101111 => 1010000
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [7,6,5,3,2,4,1,8] => [8,1,4,2,3,5,6,7] => 0010001 => 1101110
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [6,7,5,3,2,4,1,8] => [8,1,4,2,3,5,7,6] => 0010011 => 1101100
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [7,5,6,3,2,4,1,8] => [8,1,4,2,3,6,5,7] => 0010101 => 1101010
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => [8,1,4,2,3,7,5,6] => 0010011 => 1101100
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => [8,1,4,2,3,7,6,5] => 0010111 => 1101000
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => [8,1,4,3,2,5,6,7] => 0110001 => 1001110
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [6,7,5,2,3,4,1,8] => [8,1,4,3,2,5,7,6] => 0110011 => 1001100
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [7,5,6,2,3,4,1,8] => [8,1,4,3,2,6,5,7] => 0110101 => 1001010
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => [8,1,4,3,2,7,5,6] => 0110011 => 1001100
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => [8,1,4,3,2,7,6,5] => 0110111 => 1001000
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [7,6,4,3,2,5,1,8] => [8,1,5,2,3,4,6,7] => 0001001 => 1110110
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [6,7,3,4,2,5,1,8] => [8,1,5,2,4,3,7,6] => 0011011 => 1100100
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [7,6,4,2,3,5,1,8] => [8,1,5,3,2,4,6,7] => 0101001 => 1010110
[[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [6,7,4,2,3,5,1,8] => [8,1,5,3,2,4,7,6] => 0101011 => 1010100
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [7,6,3,2,4,5,1,8] => [8,1,5,4,2,3,6,7] => 0011001 => 1100110
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [7,6,2,3,4,5,1,8] => [8,1,5,4,3,2,6,7] => 0111001 => 1000110
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [6,7,2,3,4,5,1,8] => [8,1,5,4,3,2,7,6] => 0111011 => 1000100
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [7,5,4,3,2,6,1,8] => [8,1,6,2,3,4,5,7] => 0000101 => 1111010
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [7,4,5,3,2,6,1,8] => [8,1,6,2,3,5,4,7] => 0001101 => 1110010
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [7,5,3,4,2,6,1,8] => [8,1,6,2,4,3,5,7] => 0010101 => 1101010
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [7,4,3,5,2,6,1,8] => [8,1,6,2,5,3,4,7] => 0001101 => 1110010
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [7,5,4,2,3,6,1,8] => [8,1,6,3,2,4,5,7] => 0100101 => 1011010
[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [7,4,5,2,3,6,1,8] => [8,1,6,3,2,5,4,7] => 0101101 => 1010010
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [7,5,3,2,4,6,1,8] => [8,1,6,4,2,3,5,7] => 0010101 => 1101010
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [7,4,3,2,5,6,1,8] => [8,1,6,5,2,3,4,7] => 0001101 => 1110010
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [7,2,3,4,5,6,1,8] => [8,1,6,5,4,3,2,7] => 0111101 => 1000010
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => [8,1,7,2,3,4,5,6] => 0000011 => 1111100
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => [8,1,7,2,3,6,4,5] => 0000111 => 1111000
[[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [4,5,6,3,2,7,1,8] => [8,1,7,2,3,6,5,4] => 0001111 => 1110000
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [6,5,3,4,2,7,1,8] => [8,1,7,2,4,3,5,6] => 0010011 => 1101100
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [5,6,3,4,2,7,1,8] => [8,1,7,2,4,3,6,5] => 0010111 => 1101000
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [6,4,3,5,2,7,1,8] => [8,1,7,2,5,3,4,6] => 0001011 => 1110100
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [6,3,4,5,2,7,1,8] => [8,1,7,2,5,4,3,6] => 0011011 => 1100100
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [8,1,7,2,6,3,4,5] => 0000111 => 1111000
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [8,1,7,2,6,3,5,4] => 0001111 => 1110000
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [5,3,4,6,2,7,1,8] => [8,1,7,2,6,4,3,5] => 0010111 => 1101000
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [8,1,7,2,6,5,4,3] => 0011111 => 1100000
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [6,5,4,2,3,7,1,8] => [8,1,7,3,2,4,5,6] => 0100011 => 1011100
[[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [6,4,5,2,3,7,1,8] => [8,1,7,3,2,5,4,6] => 0101011 => 1010100
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [5,4,6,2,3,7,1,8] => [8,1,7,3,2,6,4,5] => 0100111 => 1011000
[[.,[[[.,.],[[[.,.],.],.]],.]],.] => [4,5,6,2,3,7,1,8] => [8,1,7,3,2,6,5,4] => 0101111 => 1010000
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [6,5,3,2,4,7,1,8] => [8,1,7,4,2,3,5,6] => 0010011 => 1101100
[[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [5,6,3,2,4,7,1,8] => [8,1,7,4,2,3,6,5] => 0010111 => 1101000
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [5,6,2,3,4,7,1,8] => [8,1,7,4,3,2,6,5] => 0110111 => 1001000
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [6,3,4,2,5,7,1,8] => [8,1,7,5,2,4,3,6] => 0011011 => 1100100
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [6,4,2,3,5,7,1,8] => [8,1,7,5,3,2,4,6] => 0101011 => 1010100
[[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [6,3,2,4,5,7,1,8] => [8,1,7,5,4,2,3,6] => 0011011 => 1100100
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [6,2,3,4,5,7,1,8] => [8,1,7,5,4,3,2,6] => 0111011 => 1000100
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [8,1,7,6,2,3,4,5] => 0000111 => 1111000
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [5,3,4,2,6,7,1,8] => [8,1,7,6,2,4,3,5] => 0010111 => 1101000
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => [8,1,7,6,2,5,4,3] => 0011111 => 1100000
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [5,4,2,3,6,7,1,8] => [8,1,7,6,3,2,4,5] => 0100111 => 1011000
[[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [5,3,2,4,6,7,1,8] => [8,1,7,6,4,2,3,5] => 0010111 => 1101000
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [5,2,3,4,6,7,1,8] => [8,1,7,6,4,3,2,5] => 0110111 => 1001000
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => [8,1,7,6,5,2,3,4] => 0001111 => 1110000
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => [8,1,7,6,5,2,4,3] => 0011111 => 1100000
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [4,2,3,5,6,7,1,8] => [8,1,7,6,5,3,2,4] => 0101111 => 1010000
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [8,1,7,6,5,4,2,3] => 0011111 => 1100000
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [8,1,7,6,5,4,3,2] => 0111111 => 1000000
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [8,2,1,3,4,5,6,7] => 1000001 => 0111110
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,3,1,2,8] => [8,2,1,3,4,5,7,6] => 1000011 => 0111100
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => [8,2,1,3,4,6,5,7] => 1000101 => 0111010
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [6,5,7,4,3,1,2,8] => [8,2,1,3,4,7,5,6] => 1000011 => 0111100
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [7,5,4,6,3,1,2,8] => [8,2,1,3,6,4,5,7] => 1000101 => 0111010
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [7,4,5,6,3,1,2,8] => [8,2,1,3,6,5,4,7] => 1001101 => 0110010
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [5,6,4,7,3,1,2,8] => [8,2,1,3,7,4,6,5] => 1000111 => 0111000
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [5,4,6,7,3,1,2,8] => [8,2,1,3,7,6,4,5] => 1000111 => 0111000
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [4,5,6,7,3,1,2,8] => [8,2,1,3,7,6,5,4] => 1001111 => 0110000
[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [6,7,5,3,4,1,2,8] => [8,2,1,4,3,5,7,6] => 1010011 => 0101100
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [7,5,6,3,4,1,2,8] => [8,2,1,4,3,6,5,7] => 1010101 => 0101010
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [6,5,7,3,4,1,2,8] => [8,2,1,4,3,7,5,6] => 1010011 => 0101100
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [5,6,7,3,4,1,2,8] => [8,2,1,4,3,7,6,5] => 1010111 => 0101000
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [6,7,3,4,5,1,2,8] => [8,2,1,5,4,3,7,6] => 1011011 => 0100100
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [7,5,4,3,6,1,2,8] => [8,2,1,6,3,4,5,7] => 1000101 => 0111010
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [7,5,3,4,6,1,2,8] => [8,2,1,6,4,3,5,7] => 1010101 => 0101010
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [7,4,3,5,6,1,2,8] => [8,2,1,6,5,3,4,7] => 1001101 => 0110010
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [6,5,4,3,7,1,2,8] => [8,2,1,7,3,4,5,6] => 1000011 => 0111100
[[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [6,4,5,3,7,1,2,8] => [8,2,1,7,3,5,4,6] => 1001011 => 0110100
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [6,5,3,4,7,1,2,8] => [8,2,1,7,4,3,5,6] => 1010011 => 0101100
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [5,6,3,4,7,1,2,8] => [8,2,1,7,4,3,6,5] => 1010111 => 0101000
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [6,4,3,5,7,1,2,8] => [8,2,1,7,5,3,4,6] => 1001011 => 0110100
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [6,3,4,5,7,1,2,8] => [8,2,1,7,5,4,3,6] => 1011011 => 0100100
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [5,4,3,6,7,1,2,8] => [8,2,1,7,6,3,4,5] => 1000111 => 0111000
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [4,5,3,6,7,1,2,8] => [8,2,1,7,6,3,5,4] => 1001111 => 0110000
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [5,3,4,6,7,1,2,8] => [8,2,1,7,6,4,3,5] => 1010111 => 0101000
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [4,3,5,6,7,1,2,8] => [8,2,1,7,6,5,3,4] => 1001111 => 0110000
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [3,4,5,6,7,1,2,8] => [8,2,1,7,6,5,4,3] => 1011111 => 0100000
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => [8,3,1,2,4,5,6,7] => 0100001 => 1011110
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [6,7,5,4,2,1,3,8] => [8,3,1,2,4,5,7,6] => 0100011 => 1011100
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,2,1,3,8] => [8,3,1,2,4,6,5,7] => 0100101 => 1011010
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => [8,3,1,2,4,7,5,6] => 0100011 => 1011100
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [5,6,7,4,2,1,3,8] => [8,3,1,2,4,7,6,5] => 0100111 => 1011000
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,2,1,3,8] => [8,3,1,2,5,4,6,7] => 0101001 => 1010110
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [6,7,4,5,2,1,3,8] => [8,3,1,2,5,4,7,6] => 0101011 => 1010100
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => [8,3,1,2,6,4,5,7] => 0100101 => 1011010
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [7,4,5,6,2,1,3,8] => [8,3,1,2,6,5,4,7] => 0101101 => 1010010
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [6,5,4,7,2,1,3,8] => [8,3,1,2,7,4,5,6] => 0100011 => 1011100
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [5,4,6,7,2,1,3,8] => [8,3,1,2,7,6,4,5] => 0100111 => 1011000
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [4,5,6,7,2,1,3,8] => [8,3,1,2,7,6,5,4] => 0101111 => 1010000
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [8,3,2,1,4,5,6,7] => 1100001 => 0011110
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [6,7,5,4,1,2,3,8] => [8,3,2,1,4,5,7,6] => 1100011 => 0011100
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,1,2,3,8] => [8,3,2,1,4,6,5,7] => 1100101 => 0011010
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,1,2,3,8] => [8,3,2,1,4,7,5,6] => 1100011 => 0011100
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => [8,3,2,1,4,7,6,5] => 1100111 => 0011000
[[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,1,2,3,8] => [8,3,2,1,5,4,6,7] => 1101001 => 0010110
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [6,7,4,5,1,2,3,8] => [8,3,2,1,5,4,7,6] => 1101011 => 0010100
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,1,2,3,8] => [8,3,2,1,6,4,5,7] => 1100101 => 0011010
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => [8,3,2,1,6,5,4,7] => 1101101 => 0010010
[[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [6,5,4,7,1,2,3,8] => [8,3,2,1,7,4,5,6] => 1100011 => 0011100
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => [8,3,2,1,7,4,6,5] => 1100111 => 0011000
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => [8,3,2,1,7,6,4,5] => 1100111 => 0011000
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => [8,3,2,1,7,6,5,4] => 1101111 => 0010000
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [7,6,5,3,2,1,4,8] => [8,4,1,2,3,5,6,7] => 0010001 => 1101110
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [6,5,7,3,2,1,4,8] => [8,4,1,2,3,7,5,6] => 0010011 => 1101100
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [7,6,5,2,3,1,4,8] => [8,4,1,3,2,5,6,7] => 0110001 => 1001110
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [6,7,5,2,3,1,4,8] => [8,4,1,3,2,5,7,6] => 0110011 => 1001100
[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [7,5,6,2,3,1,4,8] => [8,4,1,3,2,6,5,7] => 0110101 => 1001010
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [5,6,7,2,3,1,4,8] => [8,4,1,3,2,7,6,5] => 0110111 => 1001000
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [7,6,5,3,1,2,4,8] => [8,4,2,1,3,5,6,7] => 1010001 => 0101110
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [6,7,5,3,1,2,4,8] => [8,4,2,1,3,5,7,6] => 1010011 => 0101100
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [7,5,6,3,1,2,4,8] => [8,4,2,1,3,6,5,7] => 1010101 => 0101010
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [6,5,7,3,1,2,4,8] => [8,4,2,1,3,7,5,6] => 1010011 => 0101100
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => [8,4,2,1,3,7,6,5] => 1010111 => 0101000
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [6,7,5,2,1,3,4,8] => [8,4,3,1,2,5,7,6] => 0110011 => 1001100
[[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [7,5,6,2,1,3,4,8] => [8,4,3,1,2,6,5,7] => 0110101 => 1001010
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => [8,4,3,1,2,7,6,5] => 0110111 => 1001000
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [8,4,3,2,1,5,6,7] => 1110001 => 0001110
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => [8,4,3,2,1,5,7,6] => 1110011 => 0001100
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => [8,4,3,2,1,6,5,7] => 1110101 => 0001010
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => [8,4,3,2,1,7,5,6] => 1110011 => 0001100
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => [8,4,3,2,1,7,6,5] => 1110111 => 0001000
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => [8,5,1,2,3,4,6,7] => 0001001 => 1110110
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [7,6,3,4,2,1,5,8] => [8,5,1,2,4,3,6,7] => 0011001 => 1100110
[[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [6,7,3,4,2,1,5,8] => [8,5,1,2,4,3,7,6] => 0011011 => 1100100
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [7,6,4,2,3,1,5,8] => [8,5,1,3,2,4,6,7] => 0101001 => 1010110
[[[.,[[.,.],[.,.]]],[[.,.],.]],.] => [6,7,4,2,3,1,5,8] => [8,5,1,3,2,4,7,6] => 0101011 => 1010100
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [7,6,3,2,4,1,5,8] => [8,5,1,4,2,3,6,7] => 0011001 => 1100110
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [6,7,3,2,4,1,5,8] => [8,5,1,4,2,3,7,6] => 0011011 => 1100100
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => [8,5,2,1,3,4,6,7] => 1001001 => 0110110
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [7,6,3,4,1,2,5,8] => [8,5,2,1,4,3,6,7] => 1011001 => 0100110
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [6,7,3,4,1,2,5,8] => [8,5,2,1,4,3,7,6] => 1011011 => 0100100
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [7,6,4,2,1,3,5,8] => [8,5,3,1,2,4,6,7] => 0101001 => 1010110
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [6,7,4,2,1,3,5,8] => [8,5,3,1,2,4,7,6] => 0101011 => 1010100
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [7,6,4,1,2,3,5,8] => [8,5,3,2,1,4,6,7] => 1101001 => 0010110
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [6,7,4,1,2,3,5,8] => [8,5,3,2,1,4,7,6] => 1101011 => 0010100
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [7,6,3,2,1,4,5,8] => [8,5,4,1,2,3,6,7] => 0011001 => 1100110
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [6,7,3,2,1,4,5,8] => [8,5,4,1,2,3,7,6] => 0011011 => 1100100
[[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [7,6,2,3,1,4,5,8] => [8,5,4,1,3,2,6,7] => 0111001 => 1000110
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [6,7,2,3,1,4,5,8] => [8,5,4,1,3,2,7,6] => 0111011 => 1000100
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [7,6,3,1,2,4,5,8] => [8,5,4,2,1,3,6,7] => 1011001 => 0100110
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [6,7,3,1,2,4,5,8] => [8,5,4,2,1,3,7,6] => 1011011 => 0100100
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => [8,5,4,3,2,1,6,7] => 1111001 => 0000110
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => [8,5,4,3,2,1,7,6] => 1111011 => 0000100
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [7,5,4,3,2,1,6,8] => [8,6,1,2,3,4,5,7] => 0000101 => 1111010
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [7,4,5,3,2,1,6,8] => [8,6,1,2,3,5,4,7] => 0001101 => 1110010
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [7,5,3,4,2,1,6,8] => [8,6,1,2,4,3,5,7] => 0010101 => 1101010
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [7,4,3,5,2,1,6,8] => [8,6,1,2,5,3,4,7] => 0001101 => 1110010
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [7,3,4,5,2,1,6,8] => [8,6,1,2,5,4,3,7] => 0011101 => 1100010
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [7,5,4,2,3,1,6,8] => [8,6,1,3,2,4,5,7] => 0100101 => 1011010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [7,5,3,2,4,1,6,8] => [8,6,1,4,2,3,5,7] => 0010101 => 1101010
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [7,5,2,3,4,1,6,8] => [8,6,1,4,3,2,5,7] => 0110101 => 1001010
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [7,4,3,2,5,1,6,8] => [8,6,1,5,2,3,4,7] => 0001101 => 1110010
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [7,3,4,2,5,1,6,8] => [8,6,1,5,2,4,3,7] => 0011101 => 1100010
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [7,4,2,3,5,1,6,8] => [8,6,1,5,3,2,4,7] => 0101101 => 1010010
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [7,2,3,4,5,1,6,8] => [8,6,1,5,4,3,2,7] => 0111101 => 1000010
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [7,4,5,3,1,2,6,8] => [8,6,2,1,3,5,4,7] => 1001101 => 0110010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [7,5,3,4,1,2,6,8] => [8,6,2,1,4,3,5,7] => 1010101 => 0101010
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [7,4,3,5,1,2,6,8] => [8,6,2,1,5,3,4,7] => 1001101 => 0110010
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [7,3,4,5,1,2,6,8] => [8,6,2,1,5,4,3,7] => 1011101 => 0100010
[[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [7,4,5,2,1,3,6,8] => [8,6,3,1,2,5,4,7] => 0101101 => 1010010
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [7,5,4,1,2,3,6,8] => [8,6,3,2,1,4,5,7] => 1100101 => 0011010
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [7,4,5,1,2,3,6,8] => [8,6,3,2,1,5,4,7] => 1101101 => 0010010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [7,5,2,3,1,4,6,8] => [8,6,4,1,3,2,5,7] => 0110101 => 1001010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8] => [8,6,4,2,1,3,5,7] => 1010101 => 0101010
[[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [7,5,2,1,3,4,6,8] => [8,6,4,3,1,2,5,7] => 0110101 => 1001010
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [8,6,4,3,2,1,5,7] => 1110101 => 0001010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8] => [8,6,5,1,2,3,4,7] => 0001101 => 1110010
[[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [7,3,4,2,1,5,6,8] => [8,6,5,1,2,4,3,7] => 0011101 => 1100010
[[[[.,[[.,.],[.,.]]],.],[.,.]],.] => [7,4,2,3,1,5,6,8] => [8,6,5,1,3,2,4,7] => 0101101 => 1010010
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [7,2,3,4,1,5,6,8] => [8,6,5,1,4,3,2,7] => 0111101 => 1000010
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [7,4,3,1,2,5,6,8] => [8,6,5,2,1,3,4,7] => 1001101 => 0110010
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [7,3,4,1,2,5,6,8] => [8,6,5,2,1,4,3,7] => 1011101 => 0100010
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [7,4,1,2,3,5,6,8] => [8,6,5,3,2,1,4,7] => 1101101 => 0010010
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [7,3,2,1,4,5,6,8] => [8,6,5,4,1,2,3,7] => 0011101 => 1100010
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [7,2,3,1,4,5,6,8] => [8,6,5,4,1,3,2,7] => 0111101 => 1000010
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => [8,6,5,4,2,1,3,7] => 1011101 => 0100010
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => [8,6,5,4,3,1,2,7] => 0111101 => 1000010
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => [8,6,5,4,3,2,1,7] => 1111101 => 0000010
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [8,7,1,2,3,4,5,6] => 0000011 => 1111100
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => [8,7,1,2,3,4,6,5] => 0000111 => 1111000
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => [8,7,1,2,3,6,4,5] => 0000111 => 1111000
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => [8,7,1,2,3,6,5,4] => 0001111 => 1110000
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [6,5,3,4,2,1,7,8] => [8,7,1,2,4,3,5,6] => 0010011 => 1101100
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [5,6,3,4,2,1,7,8] => [8,7,1,2,4,3,6,5] => 0010111 => 1101000
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [6,4,3,5,2,1,7,8] => [8,7,1,2,5,3,4,6] => 0001011 => 1110100
[[[.,[.,[[[.,.],.],[.,.]]]],.],.] => [6,3,4,5,2,1,7,8] => [8,7,1,2,5,4,3,6] => 0011011 => 1100100
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => [8,7,1,2,6,3,4,5] => 0000111 => 1111000
[[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [4,3,5,6,2,1,7,8] => [8,7,1,2,6,5,3,4] => 0001111 => 1110000
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => [8,7,1,2,6,5,4,3] => 0011111 => 1100000
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [6,5,4,2,3,1,7,8] => [8,7,1,3,2,4,5,6] => 0100011 => 1011100
[[[.,[[.,.],[.,[[.,.],.]]]],.],.] => [5,6,4,2,3,1,7,8] => [8,7,1,3,2,4,6,5] => 0100111 => 1011000
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [6,4,5,2,3,1,7,8] => [8,7,1,3,2,5,4,6] => 0101011 => 1010100
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [5,4,6,2,3,1,7,8] => [8,7,1,3,2,6,4,5] => 0100111 => 1011000
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [6,5,3,2,4,1,7,8] => [8,7,1,4,2,3,5,6] => 0010011 => 1101100
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [6,5,2,3,4,1,7,8] => [8,7,1,4,3,2,5,6] => 0110011 => 1001100
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [5,6,2,3,4,1,7,8] => [8,7,1,4,3,2,6,5] => 0110111 => 1001000
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [6,4,3,2,5,1,7,8] => [8,7,1,5,2,3,4,6] => 0001011 => 1110100
[[[.,[[[.,[.,.]],.],[.,.]]],.],.] => [6,3,2,4,5,1,7,8] => [8,7,1,5,4,2,3,6] => 0011011 => 1100100
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [8,7,1,6,2,3,4,5] => 0000111 => 1111000
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => [8,7,1,6,2,3,5,4] => 0001111 => 1110000
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [8,7,1,6,2,5,3,4] => 0001111 => 1110000
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => [8,7,1,6,2,5,4,3] => 0011111 => 1100000
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [5,3,2,4,6,1,7,8] => [8,7,1,6,4,2,3,5] => 0010111 => 1101000
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [5,2,3,4,6,1,7,8] => [8,7,1,6,4,3,2,5] => 0110111 => 1001000
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => [8,7,1,6,5,2,3,4] => 0001111 => 1110000
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => [8,7,1,6,5,2,4,3] => 0011111 => 1100000
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [4,2,3,5,6,1,7,8] => [8,7,1,6,5,3,2,4] => 0101111 => 1010000
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [8,7,1,6,5,4,3,2] => 0111111 => 1000000
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [6,5,4,3,1,2,7,8] => [8,7,2,1,3,4,5,6] => 1000011 => 0111100
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => [8,7,2,1,3,4,6,5] => 1000111 => 0111000
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [6,4,5,3,1,2,7,8] => [8,7,2,1,3,5,4,6] => 1001011 => 0110100
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => [8,7,2,1,3,6,4,5] => 1000111 => 0111000
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [4,5,6,3,1,2,7,8] => [8,7,2,1,3,6,5,4] => 1001111 => 0110000
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [6,5,3,4,1,2,7,8] => [8,7,2,1,4,3,5,6] => 1010011 => 0101100
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => [8,7,2,1,4,3,6,5] => 1010111 => 0101000
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [6,4,3,5,1,2,7,8] => [8,7,2,1,5,3,4,6] => 1001011 => 0110100
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [6,3,4,5,1,2,7,8] => [8,7,2,1,5,4,3,6] => 1011011 => 0100100
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => [8,7,2,1,6,3,4,5] => 1000111 => 0111000
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [3,4,5,6,1,2,7,8] => [8,7,2,1,6,5,4,3] => 1011111 => 0100000
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => [8,7,3,1,2,4,6,5] => 0100111 => 1011000
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [5,4,6,2,1,3,7,8] => [8,7,3,1,2,6,4,5] => 0100111 => 1011000
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8] => [8,7,3,2,1,4,5,6] => 1100011 => 0011100
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [5,6,4,1,2,3,7,8] => [8,7,3,2,1,4,6,5] => 1100111 => 0011000
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [6,4,5,1,2,3,7,8] => [8,7,3,2,1,5,4,6] => 1101011 => 0010100
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [5,4,6,1,2,3,7,8] => [8,7,3,2,1,6,4,5] => 1100111 => 0011000
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => [8,7,3,2,1,6,5,4] => 1101111 => 0010000
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [6,5,3,2,1,4,7,8] => [8,7,4,1,2,3,5,6] => 0010011 => 1101100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => [8,7,4,1,2,3,6,5] => 0010111 => 1101000
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [5,6,2,3,1,4,7,8] => [8,7,4,1,3,2,6,5] => 0110111 => 1001000
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [6,5,3,1,2,4,7,8] => [8,7,4,2,1,3,5,6] => 1010011 => 0101100
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [5,6,3,1,2,4,7,8] => [8,7,4,2,1,3,6,5] => 1010111 => 0101000
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [6,5,1,2,3,4,7,8] => [8,7,4,3,2,1,5,6] => 1110011 => 0001100
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [5,6,1,2,3,4,7,8] => [8,7,4,3,2,1,6,5] => 1110111 => 0001000
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8] => [8,7,5,1,2,3,4,6] => 0001011 => 1110100
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [6,3,4,2,1,5,7,8] => [8,7,5,1,2,4,3,6] => 0011011 => 1100100
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [6,3,2,4,1,5,7,8] => [8,7,5,1,4,2,3,6] => 0011011 => 1100100
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [6,2,3,4,1,5,7,8] => [8,7,5,1,4,3,2,6] => 0111011 => 1000100
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [6,4,3,1,2,5,7,8] => [8,7,5,2,1,3,4,6] => 1001011 => 0110100
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [6,4,2,1,3,5,7,8] => [8,7,5,3,1,2,4,6] => 0101011 => 1010100
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => [8,7,5,3,2,1,4,6] => 1101011 => 0010100
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [6,3,2,1,4,5,7,8] => [8,7,5,4,1,2,3,6] => 0011011 => 1100100
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [6,2,3,1,4,5,7,8] => [8,7,5,4,1,3,2,6] => 0111011 => 1000100
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [6,2,1,3,4,5,7,8] => [8,7,5,4,3,1,2,6] => 0111011 => 1000100
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => [8,7,5,4,3,2,1,6] => 1111011 => 0000100
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [8,7,6,1,2,3,4,5] => 0000111 => 1111000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => [8,7,6,1,2,3,5,4] => 0001111 => 1110000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [5,3,4,2,1,6,7,8] => [8,7,6,1,2,4,3,5] => 0010111 => 1101000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => [8,7,6,1,2,5,3,4] => 0001111 => 1110000
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => [8,7,6,1,2,5,4,3] => 0011111 => 1100000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [5,4,2,3,1,6,7,8] => [8,7,6,1,3,2,4,5] => 0100111 => 1011000
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [4,5,2,3,1,6,7,8] => [8,7,6,1,3,2,5,4] => 0101111 => 1010000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [5,3,2,4,1,6,7,8] => [8,7,6,1,4,2,3,5] => 0010111 => 1101000
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [5,2,3,4,1,6,7,8] => [8,7,6,1,4,3,2,5] => 0110111 => 1001000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => [8,7,6,1,5,2,3,4] => 0001111 => 1110000
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [8,7,6,1,5,2,4,3] => 0011111 => 1100000
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [4,2,3,5,1,6,7,8] => [8,7,6,1,5,3,2,4] => 0101111 => 1010000
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => [8,7,6,1,5,4,2,3] => 0011111 => 1100000
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [8,7,6,1,5,4,3,2] => 0111111 => 1000000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [5,4,3,1,2,6,7,8] => [8,7,6,2,1,3,4,5] => 1000111 => 0111000
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [5,3,4,1,2,6,7,8] => [8,7,6,2,1,4,3,5] => 1010111 => 0101000
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [4,3,5,1,2,6,7,8] => [8,7,6,2,1,5,3,4] => 1001111 => 0110000
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [5,4,2,1,3,6,7,8] => [8,7,6,3,1,2,4,5] => 0100111 => 1011000
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [5,4,1,2,3,6,7,8] => [8,7,6,3,2,1,4,5] => 1100111 => 0011000
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [4,5,1,2,3,6,7,8] => [8,7,6,3,2,1,5,4] => 1101111 => 0010000
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [5,3,2,1,4,6,7,8] => [8,7,6,4,1,2,3,5] => 0010111 => 1101000
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [5,2,3,1,4,6,7,8] => [8,7,6,4,1,3,2,5] => 0110111 => 1001000
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => [8,7,6,4,2,1,3,5] => 1010111 => 0101000
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [5,2,1,3,4,6,7,8] => [8,7,6,4,3,1,2,5] => 0110111 => 1001000
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => [8,7,6,4,3,2,1,5] => 1110111 => 0001000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [8,7,6,5,1,2,3,4] => 0001111 => 1110000
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => [8,7,6,5,1,2,4,3] => 0011111 => 1100000
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [4,2,3,1,5,6,7,8] => [8,7,6,5,1,3,2,4] => 0101111 => 1010000
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [8,7,6,5,1,4,2,3] => 0011111 => 1100000
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [8,7,6,5,1,4,3,2] => 0111111 => 1000000
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [4,3,1,2,5,6,7,8] => [8,7,6,5,2,1,3,4] => 1001111 => 0110000
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => [8,7,6,5,2,1,4,3] => 1011111 => 0100000
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [4,2,1,3,5,6,7,8] => [8,7,6,5,3,1,2,4] => 0101111 => 1010000
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => [8,7,6,5,3,2,1,4] => 1101111 => 0010000
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [8,7,6,5,4,1,2,3] => 0011111 => 1100000
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [8,7,6,5,4,1,3,2] => 0111111 => 1000000
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => [8,7,6,5,4,2,1,3] => 1011111 => 0100000
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [8,7,6,5,4,3,1,2] => 0111111 => 1000000
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => 1111111 => 0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => 00000000 => 11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => 00000001 => 11111110
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [1,2,3,4,5,6,9,8,7] => 00000011 => 11111100
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => [1,2,3,4,5,9,8,7,6] => 00000111 => 11111000
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => [1,2,3,4,9,8,7,6,5] => 00001111 => 11110000
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => [1,2,3,9,8,7,6,5,4] => 00011111 => 11100000
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => [1,2,9,8,7,6,5,4,3] => 00111111 => 11000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,3,2] => 01111111 => 10000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1] => 11111111 => 00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,10,9] => 000000001 => 111111110
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [9,7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,7,9] => 00000010 => 11111101
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,10,9,8] => 000000011 => 111111100
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [8,9,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,9,8] => 00000101 => 11111010
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => [1,2,3,4,5,6,10,9,8,7] => 000000111 => 111111000
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [7,8,9,5,6,4,3,2,1] => [1,2,3,4,6,5,9,8,7] => 00001011 => 11110100
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [1,2,3,4,5,10,9,8,7,6] => 000001111 => 111110000
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [6,7,8,9,4,5,3,2,1] => [1,2,3,5,4,9,8,7,6] => 00010111 => 11101000
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => [1,2,3,4,10,9,8,7,6,5] => 000011111 => 111100000
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [5,6,7,8,9,3,4,2,1] => [1,2,4,3,9,8,7,6,5] => 00101111 => 11010000
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => [1,2,3,10,9,8,7,6,5,4] => 000111111 => 111000000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,2,3,1] => [1,3,2,9,8,7,6,5,4] => 01011111 => 10100000
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => [1,2,10,9,8,7,6,5,4,3] => 001111111 => 110000000
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => [2,1,9,8,7,6,5,4,3] => 10111111 => 01000000
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 100000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [1,2,3,4,5,6,9,7,8] => 00000001 => 11111110
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [1,2,3,4,5,9,6,7,8] => 00000001 => 11111110
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [1,2,3,4,9,5,6,7,8] => 00000001 => 11111110
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [1,2,3,9,4,5,6,7,8] => 00000001 => 11111110
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [1,2,9,3,4,5,6,7,8] => 00000001 => 11111110
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,7,8] => 00000001 => 11111110
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,7,8] => 00000001 => 11111110
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,10,8,9] => 000000001 => 111111110
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [8,6,7,9,5,4,3,2,1] => [1,2,3,4,5,9,7,6,8] => 00000101 => 11111010
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [1,2,3,4,5,6,10,7,8,9] => 000000001 => 111111110
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [8,7,5,6,9,4,3,2,1] => [1,2,3,4,9,6,5,7,8] => 00001001 => 11110110
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [1,2,3,4,5,10,6,7,8,9] => 000000001 => 111111110
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [8,7,6,4,5,9,3,2,1] => [1,2,3,9,5,4,6,7,8] => 00010001 => 11101110
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [1,2,3,4,10,5,6,7,8,9] => 000000001 => 111111110
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [8,7,6,5,3,4,9,2,1] => [1,2,9,4,3,5,6,7,8] => 00100001 => 11011110
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [1,2,3,10,4,5,6,7,8,9] => 000000001 => 111111110
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,2,3,9,1] => [1,9,3,2,4,5,6,7,8] => 01000001 => 10111110
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [1,2,10,3,4,5,6,7,8,9] => 000000001 => 111111110
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9] => [9,2,1,3,4,5,6,7,8] => 10000001 => 01111110
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [1,10,2,3,4,5,6,7,8,9] => 000000001 => 111111110
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,8,9] => 000000001 => 111111110
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9] => 101010101 => 010101010
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => [8,9,7,10,5,6,3,4,1,2] => [2,1,4,3,6,5,10,7,9,8] => 101010011 => 010101100
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => [9,10,6,7,5,8,3,4,1,2] => [2,1,4,3,8,5,7,6,10,9] => 101001101 => 010110010
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => [9,10,7,8,4,5,3,6,1,2] => [2,1,6,3,5,4,8,7,10,9] => 100110101 => 011001010
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => [8,9,7,10,4,5,3,6,1,2] => [2,1,6,3,5,4,10,7,9,8] => 100110011 => 011001100
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => [9,10,7,8,5,6,2,3,1,4] => [4,1,3,2,6,5,8,7,10,9] => 011010101 => 100101010
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]] => [8,9,7,10,5,6,2,3,1,4] => [4,1,3,2,6,5,10,7,9,8] => 011010011 => 100101100
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]] => [9,10,6,7,5,8,2,3,1,4] => [4,1,3,2,8,5,7,6,10,9] => 011001101 => 100110010
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => [8,9,6,7,4,5,2,3,1,10] => [10,1,3,2,5,4,7,6,9,8] => 010101011 => 101010100
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => [10,1,9,2,8,3,7,4,6,5] => 000011111 => 111100000
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [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 => 01010101010
[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]] => [10,11,9,12,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,12,9,11,10] => 10101010011 => 01010101100
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]] => [11,12,8,9,7,10,5,6,3,4,1,2] => [2,1,4,3,6,5,10,7,9,8,12,11] => 10101001101 => 01010110010
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]] => [11,12,9,10,6,7,5,8,3,4,1,2] => [2,1,4,3,8,5,7,6,10,9,12,11] => 10100110101 => 01011001010
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]] => [10,11,9,12,6,7,5,8,3,4,1,2] => [2,1,4,3,8,5,7,6,12,9,11,10] => 10100110011 => 01011001100
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]] => [11,12,9,10,7,8,4,5,3,6,1,2] => [2,1,6,3,5,4,8,7,10,9,12,11] => 10011010101 => 01100101010
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]] => [10,11,9,12,7,8,4,5,3,6,1,2] => [2,1,6,3,5,4,8,7,12,9,11,10] => 10011010011 => 01100101100
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]] => [11,12,8,9,7,10,4,5,3,6,1,2] => [2,1,6,3,5,4,10,7,9,8,12,11] => 10011001101 => 01100110010
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [11,12,9,10,7,8,5,6,2,3,1,4] => [4,1,3,2,6,5,8,7,10,9,12,11] => 01101010101 => 10010101010
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => [10,11,9,12,6,7,5,8,2,3,1,4] => [4,1,3,2,8,5,7,6,12,9,11,10] => 01100110011 => 10011001100
[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.] => [10,11,8,9,6,7,4,5,2,3,1,12] => [12,1,3,2,5,4,7,6,9,8,11,10] => 01010101011 => 10101010100
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [10,8,6,4,2,1,3,5,7,9] => [9,7,5,3,1,2,4,6,8,10] => 010101010 => 101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,9] => 11111110 => 00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1,10] => 111111110 => 000000001
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => [8,7,6,5,4,3,1,2,9] => 01111110 => 10000001
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,2,3] => 00111111 => 11000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110 => 0000000001
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,1,2,10] => 011111110 => 100000001
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => [8,7,6,5,4,2,1,3,9] => 10111110 => 01000001
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => [1,9,8,7,6,5,3,2,4] => 01011111 => 10100000
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => [1,9,8,7,6,5,2,4,3] => 00111111 => 11000000
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,4,2,3] => 001111111 => 110000000
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 1000000000
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,9,8] => 11111101 => 00000010
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => [6,5,4,3,2,1,9,8,7] => 11111011 => 00000100
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => [5,4,3,2,1,9,8,7,6] => 11110111 => 00001000
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [5,6,7,8,9,1,2,3,4] => [4,3,2,1,9,8,7,6,5] => 11101111 => 00010000
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,1,2,3] => [3,2,1,9,8,7,6,5,4] => 11011111 => 00100000
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,8,9] => 11111100 => 00000011
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,10,9] => 111111101 => 000000010
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,10,9,8] => 111111011 => 000000100
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => [6,5,4,3,2,1,10,9,8,7] => 111110111 => 000001000
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => 111101111 => 000010000
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [5,6,7,8,9,10,1,2,3,4] => [4,3,2,1,10,9,8,7,6,5] => 111011111 => 000100000
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [4,3,5,6,7,8,9,1,2] => [2,1,9,8,7,6,5,3,4] => 10011111 => 01100000
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [4,5,6,7,8,9,10,1,2,3] => [3,2,1,10,9,8,7,6,5,4] => 110111111 => 001000000
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 010000000
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,9] => 10000000 => 01111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,8,7] => 00000011 => 11111100
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,9,8] => 10000001 => 01111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,9,10] => 100000000 => 011111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => [11,1,2,3,4,5,6,7,8,9,10] => 0000000001 => 1111111110
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,9,8] => 000000011 => 111111100
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [9,1,2,3,4,5,8,6,7] => 00000011 => 11111100
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => [8,6,7,5,4,3,2,1,9] => [9,1,2,3,4,5,7,6,8] => 00000101 => 11111010
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,3,1,2] => [2,1,3,4,5,6,9,7,8] => 10000001 => 01111110
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => [2,1,3,4,5,6,8,7,9] => 10000010 => 01111101
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [9,10,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,10,9] => 100000001 => 011111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000 => 0111111111
[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] => [9,7,8,5,6,3,4,1,2,10] => [10,2,1,4,3,6,5,8,7,9] => 101010101 => 010101010
[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.] => [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 => 01010101010
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,8,9] => 01000000 => 10111111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,2,1,4] => [4,1,2,3,5,6,7,8,9] => 00100000 => 11011111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,3,2,1,5] => [5,1,2,3,4,6,7,8,9] => 00010000 => 11101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [9,8,7,5,4,3,2,1,6] => [6,1,2,3,4,5,7,8,9] => 00001000 => 11110111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [9,8,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,8,9] => 00000100 => 11111011
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [9,7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7,9] => 00000010 => 11111101
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => [3,2,1,4,5,6,7,8,9] => 11000000 => 00111111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,8,9,10] => 010000000 => 101111111
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,2,3,1,4] => [4,1,3,2,5,6,7,8,9] => 01100000 => 10011111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,3,2,1,4] => [4,1,2,3,5,6,7,8,9,10] => 001000000 => 110111111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,4,3,2,1,5] => [5,1,2,3,4,6,7,8,9,10] => 000100000 => 111011111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [10,9,8,7,5,4,3,2,1,6] => [6,1,2,3,4,5,7,8,9,10] => 000010000 => 111101111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [10,9,8,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,8,9,10] => 000001000 => 111110111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [9,6,7,5,4,3,2,1,8] => [8,1,2,3,4,5,7,6,9] => 00000110 => 11111001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [10,9,7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7,9,10] => 000000100 => 111111011
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [10,8,7,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,7,8,10] => 000000010 => 111111101
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [9,8,1,2,3,4,5,6,7] => 00000011 => 11111100
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => [9,8,7,1,2,3,4,5,6] => 00000111 => 11111000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => [9,8,7,6,1,2,3,4,5] => 00001111 => 11110000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => [9,8,7,6,5,1,2,3,4] => 00011111 => 11100000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [9,8,7,6,5,4,1,2,3] => 00111111 => 11000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,1,2] => 01111111 => 10000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => [10,9,1,2,3,4,5,6,7,8] => 000000011 => 111111100
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => [10,9,8,1,2,3,4,5,6,7] => 000000111 => 111111000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => [10,9,8,7,1,2,3,4,5,6] => 000001111 => 111110000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => [10,9,8,7,6,1,2,3,4,5] => 000011111 => 111100000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => [10,9,8,7,6,5,1,2,3,4] => 000111111 => 111000000
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [4,3,1,2,5,6,7,8,9] => [9,8,7,6,5,2,1,3,4] => 10011111 => 01100000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,1,2,3] => 001111111 => 110000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9] => [9,8,7,6,5,4,2,1,3] => 10111111 => 01000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,1,2] => 011111111 => 100000000
[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => [9,8,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,8,9] => 00000100 => 11111011
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [9,8,7,5,6,4,3,2,1] => [1,2,3,4,6,5,7,8,9] => 00001000 => 11110111
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,4,5,3,2,1] => [1,2,3,5,4,6,7,8,9] => 00010000 => 11101111
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,3,4,2,1] => [1,2,4,3,5,6,7,8,9] => 00100000 => 11011111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,8,9] => 01000000 => 10111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [10,8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8,10] => 000000010 => 111111101
[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] => [10,9,7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,7,9,10] => 000000100 => 111111011
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [10,9,8,6,7,5,4,3,2,1] => [1,2,3,4,5,7,6,8,9,10] => 000001000 => 111110111
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,5,6,4,3,2,1] => [1,2,3,4,6,5,7,8,9,10] => 000010000 => 111101111
[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,4,5,3,2,1] => [1,2,3,5,4,6,7,8,9,10] => 000100000 => 111011111
[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,3,4,2,1] => [1,2,4,3,5,6,7,8,9,10] => 001000000 => 110111111
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,8,9,10] => 010000000 => 101111111
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [10,8,9,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,9,8,10] => 010101010 => 101010101
[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [10,8,9,6,7,4,5,2,1,3] => [3,1,2,5,4,7,6,9,8,10] => 010101010 => 101010101
[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]] => [10,8,9,6,7,4,2,1,3,5] => [5,3,1,2,4,7,6,9,8,10] => 010101010 => 101010101
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [10,8,9,6,4,2,1,3,5,7] => [7,5,3,1,2,4,6,9,8,10] => 010101010 => 101010101
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [9,2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2,9] => 01111110 => 10000001
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [11,10,9,8,7,6,5,4,3,1,2] => 0111111111 => 1000000000
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [8,2,1,3,4,5,6,7,9] => [9,7,6,5,4,3,1,2,8] => 01111101 => 10000010
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [8,9,2,1,3,4,5,6,7] => [7,6,5,4,3,1,2,9,8] => 01111101 => 10000010
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => [8,2,3,4,5,6,7,9,1] => [1,9,7,6,5,4,3,2,8] => 01111101 => 10000010
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [8,9,2,3,4,5,6,7,1] => [1,7,6,5,4,3,2,9,8] => 01111101 => 10000010
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [10,2,3,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,3,2,10] => 011111110 => 100000001
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [4,2,1,3,5,6,7,8,9] => [9,8,7,6,5,3,1,2,4] => 01011111 => 10100000
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [5,3,2,1,4,6,7,8,9] => [9,8,7,6,4,1,2,3,5] => 00101111 => 11010000
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.] => [6,4,3,2,1,5,7,8,9] => [9,8,7,5,1,2,3,4,6] => 00010111 => 11101000
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.] => [7,5,4,3,2,1,6,8,9] => [9,8,6,1,2,3,4,5,7] => 00001011 => 11110100
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [8,6,5,4,3,2,1,7,9] => [9,7,1,2,3,4,5,6,8] => 00000101 => 11111010
[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]] => [7,8,6,9,5,4,3,2,1] => [1,2,3,4,5,9,6,8,7] => 00000011 => 11111100
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => [1,9,2,8,7,6,5,4,3] => 00111111 => 11000000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [9,1,8,7,6,5,4,3,2] => 01111111 => 10000000
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => [9,8,7,6,5,4,1,3,2] => 01111111 => 10000000
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.] => [2,3,4,5,1,6,7,8,9] => [9,8,7,6,1,5,4,3,2] => 01111111 => 10000000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [9,8,1,7,6,5,4,3,2] => 01111111 => 10000000
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [10,1,9,8,7,6,5,4,3,2] => 011111111 => 100000000
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9] => [9,8,7,6,5,3,2,1,4] => 11011111 => 00100000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [5,1,2,3,4,6,7,8,9] => [9,8,7,6,4,3,2,1,5] => 11101111 => 00010000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [6,1,2,3,4,5,7,8,9] => [9,8,7,5,4,3,2,1,6] => 11110111 => 00001000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => [9,8,6,5,4,3,2,1,7] => 11111011 => 00000100
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => [9,7,6,5,4,3,2,1,8] => 11111101 => 00000010
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,2,1,3] => 101111111 => 010000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9,10] => [10,9,8,7,6,5,3,2,1,4] => 110111111 => 001000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [5,1,2,3,4,6,7,8,9,10] => [10,9,8,7,6,4,3,2,1,5] => 111011111 => 000100000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [6,1,2,3,4,5,7,8,9,10] => [10,9,8,7,5,4,3,2,1,6] => 111101111 => 000010000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [7,1,2,3,4,5,6,8,9,10] => [10,9,8,6,5,4,3,2,1,7] => 111110111 => 000001000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [8,1,2,3,4,5,6,7,9,10] => [10,9,7,6,5,4,3,2,1,8] => 111111011 => 000000100
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => [10,8,7,6,5,4,3,2,1,9] => 111111101 => 000000010
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [9,3,4,5,6,7,8,1,2] => [2,1,8,7,6,5,4,3,9] => 10111110 => 01000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [9,7,6,5,4,3,2,8,1] => [1,8,2,3,4,5,6,7,9] => 00000010 => 11111101
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [9,7,6,5,4,3,1,2,8] => [8,2,1,3,4,5,6,7,9] => 10000010 => 01111101
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [8,9,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,9,8] => 00000101 => 11111010
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => [11,10,9,8,7,6,5,4,3,2,1] => 1111111111 => 0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => [3,2,1,4,5,6,7,8,9,10] => 110000000 => 001111111
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,2,1,3,9] => [9,3,1,2,4,5,6,7,8] => 01000001 => 10111110
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [9,8,7,6,5,4,3,1,2,10] => [10,2,1,3,4,5,6,7,8,9] => 100000001 => 011111110
[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,2,3,1] => [1,3,2,4,5,6,9,7,8] => 01000001 => 10111110
[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]] => [7,2,3,4,5,6,8,9,1] => [1,9,8,6,5,4,3,2,7] => 01111011 => 10000100
[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]] => [7,8,2,3,4,5,6,9,1] => [1,9,6,5,4,3,2,8,7] => 01111011 => 10000100
[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]] => [6,2,3,4,5,7,8,9,10,1] => [1,10,9,8,7,5,4,3,2,6] => 011101111 => 100010000
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [10,8,7,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,7,8,10] => 000000010 => 111111101
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [3,4,5,6,7,8,1,2,9] => [9,2,1,8,7,6,5,4,3] => 10111111 => 01000000
[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]] => [8,9,6,5,4,3,2,7,1] => [1,7,2,3,4,5,6,9,8] => 00000101 => 11111010
[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]] => [6,7,8,5,4,3,2,9,1] => [1,9,2,3,4,5,8,7,6] => 00000111 => 11111000
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] => [8,9,7,6,5,4,2,1,3] => [3,1,2,4,5,6,7,9,8] => 01000001 => 10111110
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,9,10] => 111111100 => 000000011
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => [9,1,2,3,4,5,8,7,6] => 00000111 => 11111000
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,9,8,7] => 000000111 => 111111000
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]] => [10,9,8,7,6,5,4,3,2,11,1] => [1,11,2,3,4,5,6,7,8,9,10] => 0000000001 => 1111111110
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => [6,5,4,3,2,1,7,8,9] => 11111000 => 00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => [5,4,3,2,1,6,7,8,9] => 11110000 => 00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => [4,3,2,1,5,6,7,8,9] => 11100000 => 00011111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [9,7,1,2,3,4,5,6,8] => [8,6,5,4,3,2,1,7,9] => 11111010 => 00000101
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => [7,6,5,4,3,2,1,8,9,10] => 111111000 => 000000111
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => [6,5,4,3,2,1,7,8,9,10] => 111110000 => 000001111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => [5,4,3,2,1,6,7,8,9,10] => 111100000 => 000011111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => [4,3,2,1,5,6,7,8,9,10] => 111000000 => 000111111
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [10,8,1,2,3,4,5,6,7,9] => [9,7,6,5,4,3,2,1,8,10] => 111111010 => 000000101
[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]] => [8,9,2,3,1,4,5,6,7] => [7,6,5,4,1,3,2,9,8] => 01111101 => 10000010
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,11,9,10] => 0000000001 => 1111111110
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [9,8,10,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,10,8,9] => 100000001 => 011111110
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,2,3,1] => [1,3,2,4,5,6,7,9,8] => 01000001 => 10111110
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001 => 1111111110
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,8,7] => 00000011 => 11111100
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]] => [8,9,7,6,5,4,3,2,10,1] => [1,10,2,3,4,5,6,7,9,8] => 000000011 => 111111100
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => [9,1,8,2,3,4,5,6,7] => 00000011 => 11111100
[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.] => [6,5,4,3,2,7,1,8,9] => [9,8,1,7,2,3,4,5,6] => 00000111 => 11111000
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => [8,7,1,2,3,4,5,6,9] => [9,6,5,4,3,2,1,7,8] => 11111001 => 00000110
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [8,7,5,4,3,2,1,6,9] => [9,6,1,2,3,4,5,7,8] => 00001001 => 11110110
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,3,9,1,2] => [2,1,9,3,4,5,6,7,8] => 10000001 => 01111110
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,2,3,1,9] => [9,1,3,2,4,5,6,7,8] => 01000001 => 10111110
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => [9,8,7,6,5,2,1,4,3] => 10111111 => 01000000
[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => [4,5,6,7,8,9,10,2,3,1] => [1,3,2,10,9,8,7,6,5,4] => 010111111 => 101000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [10,11,1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1,11,10] => 1111111101 => 0000000010
[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]] => [9,10,2,1,3,4,5,6,7,8] => [8,7,6,5,4,3,1,2,10,9] => 011111101 => 100000010
[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]] => [8,9,3,1,2,4,5,6,7] => [7,6,5,4,2,1,3,9,8] => 10111101 => 01000010
[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.] => [8,7,6,1,2,3,4,5,9] => [9,5,4,3,2,1,6,7,8] => 11110001 => 00001110
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => [10,3,1,2,4,5,6,7,8,9] => [9,8,7,6,5,4,2,1,3,10] => 101111110 => 010000001
[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => [9,10,11,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,11,10,9] => 0000000011 => 1111111100
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [9,10,7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7,10,9] => 000000101 => 111111010
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => [11,9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010 => 1111111101
[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]] => [9,7,8,5,6,4,3,2,1] => [1,2,3,4,6,5,8,7,9] => 00001010 => 11110101
[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]] => [8,9,6,5,7,4,3,2,1] => [1,2,3,4,7,5,6,9,8] => 00000101 => 11111010
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
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
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
searching the database
Sorry, this map was not found in the database.