Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
[.,.] => [1] => =>
[.,[.,.]] => [2,1] => 1 => 1
[[.,.],.] => [1,2] => 0 => 0
[.,[.,[.,.]]] => [3,2,1] => 11 => 11
[.,[[.,.],.]] => [2,3,1] => 10 => 01
[[.,.],[.,.]] => [1,3,2] => 01 => 10
[[.,[.,.]],.] => [2,1,3] => 10 => 01
[[[.,.],.],.] => [1,2,3] => 00 => 00
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 111 => 111
[.,[.,[[.,.],.]]] => [3,4,2,1] => 110 => 011
[.,[[.,.],[.,.]]] => [2,4,3,1] => 101 => 101
[.,[[.,[.,.]],.]] => [3,2,4,1] => 110 => 011
[.,[[[.,.],.],.]] => [2,3,4,1] => 100 => 001
[[.,.],[.,[.,.]]] => [1,4,3,2] => 011 => 110
[[.,.],[[.,.],.]] => [1,3,4,2] => 010 => 010
[[.,[.,.]],[.,.]] => [2,1,4,3] => 101 => 101
[[[.,.],.],[.,.]] => [1,2,4,3] => 001 => 100
[[.,[.,[.,.]]],.] => [3,2,1,4] => 110 => 011
[[.,[[.,.],.]],.] => [2,3,1,4] => 100 => 001
[[[.,.],[.,.]],.] => [1,3,2,4] => 010 => 010
[[[.,[.,.]],.],.] => [2,1,3,4] => 100 => 001
[[[[.,.],.],.],.] => [1,2,3,4] => 000 => 000
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 1111 => 1111
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 1110 => 0111
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 1101 => 1011
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1110 => 0111
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 1100 => 0011
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 1011 => 1101
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 1010 => 0101
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 1101 => 1011
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 1001 => 1001
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 1110 => 0111
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 1100 => 0011
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 1010 => 0101
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 1100 => 0011
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 1000 => 0001
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 0111 => 1110
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 0110 => 0110
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 0101 => 1010
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 0110 => 0110
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 0100 => 0010
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 1011 => 1101
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 1010 => 0101
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 0011 => 1100
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 0010 => 0100
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 1101 => 1011
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 1001 => 1001
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 0101 => 1010
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 1001 => 1001
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 0001 => 1000
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1110 => 0111
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 1100 => 0011
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 1010 => 0101
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 1100 => 0011
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 1000 => 0001
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 0110 => 0110
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 0100 => 0010
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 1010 => 0101
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 0010 => 0100
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 1100 => 0011
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 1000 => 0001
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 0100 => 0010
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1000 => 0001
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0000 => 0000
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 11111 => 11111
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 11110 => 01111
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 11101 => 10111
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 11110 => 01111
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 11100 => 00111
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 11011 => 11011
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 11010 => 01011
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 11101 => 10111
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 11001 => 10011
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 11110 => 01111
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 11100 => 00111
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 11010 => 01011
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 11100 => 00111
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 11000 => 00011
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 10111 => 11101
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 10110 => 01101
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 10101 => 10101
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 10110 => 01101
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 10100 => 00101
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 11011 => 11011
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 11010 => 01011
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 10011 => 11001
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 10010 => 01001
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 11101 => 10111
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 11001 => 10011
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 10101 => 10101
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 11001 => 10011
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 10001 => 10001
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 11110 => 01111
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 11100 => 00111
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 11010 => 01011
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 11100 => 00111
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 11000 => 00011
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 10110 => 01101
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 10100 => 00101
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 11010 => 01011
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 10010 => 01001
>>> Load all 2149 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 11100 => 00111
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 11000 => 00011
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 10100 => 00101
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 11000 => 00011
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 10000 => 00001
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 01111 => 11110
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 01110 => 01110
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 01101 => 10110
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 01110 => 01110
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 01100 => 00110
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 01011 => 11010
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 01010 => 01010
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 01101 => 10110
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => 01001 => 10010
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 01110 => 01110
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 01100 => 00110
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => 01010 => 01010
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 01100 => 00110
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => 01000 => 00010
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 10111 => 11101
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 10110 => 01101
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 10101 => 10101
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 10110 => 01101
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => 10100 => 00101
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 00111 => 11100
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 00110 => 01100
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 00101 => 10100
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 00110 => 01100
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 00100 => 00100
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 11011 => 11011
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 11010 => 01011
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 10011 => 11001
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => 10010 => 01001
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 01011 => 11010
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 01010 => 01010
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 10011 => 11001
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 10010 => 01001
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 00011 => 11000
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 00010 => 01000
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 11101 => 10111
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => 11001 => 10011
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => 10101 => 10101
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => 11001 => 10011
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => 10001 => 10001
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 01101 => 10110
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 01001 => 10010
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 10101 => 10101
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 00101 => 10100
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 11001 => 10011
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => 10001 => 10001
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 01001 => 10010
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 10001 => 10001
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 00001 => 10000
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 11110 => 01111
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 11100 => 00111
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 11010 => 01011
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 11100 => 00111
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 11000 => 00011
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 10110 => 01101
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 10100 => 00101
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 11010 => 01011
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 10010 => 01001
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 11100 => 00111
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 11000 => 00011
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 10100 => 00101
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 11000 => 00011
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 10000 => 00001
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 01110 => 01110
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 01100 => 00110
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 01010 => 01010
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 01100 => 00110
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => 01000 => 00010
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 10110 => 01101
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 10100 => 00101
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 00110 => 01100
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 00100 => 00100
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 11010 => 01011
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => 10010 => 01001
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 01010 => 01010
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 10010 => 01001
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 00010 => 01000
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 11100 => 00111
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 11000 => 00011
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 10100 => 00101
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 11000 => 00011
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 10000 => 00001
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 01100 => 00110
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 01000 => 00010
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 10100 => 00101
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 00100 => 00100
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 11000 => 00011
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 10000 => 00001
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 01000 => 00010
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 10000 => 00001
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 00000 => 00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 111111 => 111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => 111110 => 011111
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => 111101 => 101111
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => 111110 => 011111
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => 111100 => 001111
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => 111011 => 110111
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => 111010 => 010111
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => 111101 => 101111
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => 111001 => 100111
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => 111110 => 011111
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => 111100 => 001111
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => 111010 => 010111
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => 111100 => 001111
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => 111000 => 000111
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => 110111 => 111011
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => 110110 => 011011
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => 110101 => 101011
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => 110110 => 011011
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => 110100 => 001011
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => 111011 => 110111
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => 111010 => 010111
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => 110011 => 110011
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => 110010 => 010011
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => 111101 => 101111
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => 111001 => 100111
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => 110101 => 101011
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => 111001 => 100111
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => 110001 => 100011
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => 111110 => 011111
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => 111100 => 001111
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => 111010 => 010111
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => 111100 => 001111
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => 111000 => 000111
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => 110110 => 011011
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => 110100 => 001011
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => 111010 => 010111
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => 110010 => 010011
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => 111100 => 001111
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => 111000 => 000111
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => 110100 => 001011
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => 111000 => 000111
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => 110000 => 000011
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => 101111 => 111101
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => 101110 => 011101
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => 101101 => 101101
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => 101110 => 011101
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => 101100 => 001101
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => 101011 => 110101
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => 101010 => 010101
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => 101101 => 101101
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => 101001 => 100101
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => 101110 => 011101
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => 101100 => 001101
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => 101010 => 010101
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => 101100 => 001101
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => 101000 => 000101
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => 110111 => 111011
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => 110110 => 011011
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => 110101 => 101011
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => 110110 => 011011
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => 110100 => 001011
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => 100111 => 111001
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => 100110 => 011001
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => 100101 => 101001
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => 100110 => 011001
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => 100100 => 001001
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => 111011 => 110111
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => 111010 => 010111
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => 110011 => 110011
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => 110010 => 010011
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => 101011 => 110101
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => 101010 => 010101
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => 110011 => 110011
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => 110010 => 010011
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => 100011 => 110001
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => 100010 => 010001
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => 111101 => 101111
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => 111001 => 100111
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => 110101 => 101011
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => 111001 => 100111
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => 110001 => 100011
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => 101101 => 101101
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => 101001 => 100101
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => 110101 => 101011
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => 100101 => 101001
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => 111001 => 100111
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => 110001 => 100011
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => 101001 => 100101
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => 110001 => 100011
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => 100001 => 100001
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => 111110 => 011111
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => 111100 => 001111
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => 111010 => 010111
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => 111100 => 001111
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => 111000 => 000111
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => 110110 => 011011
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => 110100 => 001011
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => 111010 => 010111
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => 110010 => 010011
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => 111100 => 001111
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => 111000 => 000111
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => 110100 => 001011
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => 111000 => 000111
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 110000 => 000011
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => 101110 => 011101
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => 101100 => 001101
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => 101010 => 010101
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => 101100 => 001101
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => 101000 => 000101
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => 110110 => 011011
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => 110100 => 001011
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => 100110 => 011001
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => 100100 => 001001
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => 111010 => 010111
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => 110010 => 010011
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => 101010 => 010101
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => 110010 => 010011
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => 100010 => 010001
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => 111100 => 001111
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => 111000 => 000111
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => 110100 => 001011
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 111000 => 000111
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 110000 => 000011
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => 101100 => 001101
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => 101000 => 000101
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => 110100 => 001011
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => 100100 => 001001
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 111000 => 000111
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 110000 => 000011
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => 101000 => 000101
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 110000 => 000011
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 100000 => 000001
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => 011111 => 111110
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => 011110 => 011110
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => 011101 => 101110
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => 011110 => 011110
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => 011100 => 001110
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => 011011 => 110110
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => 011010 => 010110
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => 011101 => 101110
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => 011001 => 100110
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => 011110 => 011110
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => 011100 => 001110
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => 011010 => 010110
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => 011100 => 001110
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => 011000 => 000110
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 010111 => 111010
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 010110 => 011010
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 010101 => 101010
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 010110 => 011010
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => 010100 => 001010
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 011011 => 110110
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 011010 => 010110
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => 010011 => 110010
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => 010010 => 010010
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => 011101 => 101110
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => 011001 => 100110
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => 010101 => 101010
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => 011001 => 100110
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => 010001 => 100010
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => 011110 => 011110
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => 011100 => 001110
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => 011010 => 010110
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => 011100 => 001110
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => 011000 => 000110
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => 010110 => 011010
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => 010100 => 001010
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => 011010 => 010110
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => 010010 => 010010
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => 011100 => 001110
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => 011000 => 000110
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => 010100 => 001010
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => 011000 => 000110
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => 010000 => 000010
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => 101111 => 111101
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => 101110 => 011101
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => 101101 => 101101
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => 101110 => 011101
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => 101100 => 001101
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => 101011 => 110101
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => 101010 => 010101
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => 101101 => 101101
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => 101001 => 100101
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => 101110 => 011101
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => 101100 => 001101
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => 101010 => 010101
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => 101100 => 001101
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => 101000 => 000101
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => 001111 => 111100
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => 001110 => 011100
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => 001101 => 101100
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => 001110 => 011100
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => 001100 => 001100
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => 001011 => 110100
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => 001010 => 010100
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => 001101 => 101100
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => 001001 => 100100
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => 001110 => 011100
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => 001100 => 001100
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => 001010 => 010100
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => 001100 => 001100
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => 001000 => 000100
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => 110111 => 111011
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => 110110 => 011011
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => 110101 => 101011
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => 110110 => 011011
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => 110100 => 001011
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => 100111 => 111001
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => 100110 => 011001
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => 100101 => 101001
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => 100110 => 011001
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => 100100 => 001001
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => 010111 => 111010
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => 010110 => 011010
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => 010101 => 101010
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => 010110 => 011010
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => 010100 => 001010
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => 100111 => 111001
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => 100110 => 011001
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => 100101 => 101001
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => 100110 => 011001
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => 100100 => 001001
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => 000111 => 111000
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => 000110 => 011000
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => 000101 => 101000
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => 000110 => 011000
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => 000100 => 001000
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => 111011 => 110111
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => 111010 => 010111
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => 110011 => 110011
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => 110010 => 010011
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => 101011 => 110101
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => 101010 => 010101
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => 110011 => 110011
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => 110010 => 010011
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => 100011 => 110001
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => 100010 => 010001
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => 011011 => 110110
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => 011010 => 010110
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => 010011 => 110010
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => 010010 => 010010
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => 101011 => 110101
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => 101010 => 010101
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => 001011 => 110100
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => 001010 => 010100
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => 110011 => 110011
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => 110010 => 010011
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => 100011 => 110001
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => 100010 => 010001
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => 010011 => 110010
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => 010010 => 010010
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => 100011 => 110001
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => 100010 => 010001
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => 000011 => 110000
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => 000010 => 010000
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => 111101 => 101111
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => 111001 => 100111
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => 110101 => 101011
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => 111001 => 100111
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => 110001 => 100011
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => 101101 => 101101
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => 101001 => 100101
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => 110101 => 101011
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => 100101 => 101001
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => 111001 => 100111
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => 110001 => 100011
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => 101001 => 100101
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => 110001 => 100011
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => 100001 => 100001
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => 011101 => 101110
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => 011001 => 100110
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => 010101 => 101010
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => 011001 => 100110
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => 010001 => 100010
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => 101101 => 101101
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => 101001 => 100101
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => 001101 => 101100
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => 001001 => 100100
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => 110101 => 101011
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => 100101 => 101001
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => 010101 => 101010
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => 100101 => 101001
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => 000101 => 101000
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => 111001 => 100111
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => 110001 => 100011
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => 101001 => 100101
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => 110001 => 100011
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => 100001 => 100001
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => 011001 => 100110
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => 010001 => 100010
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => 101001 => 100101
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => 001001 => 100100
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => 110001 => 100011
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => 100001 => 100001
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => 010001 => 100010
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => 100001 => 100001
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 000001 => 100000
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 111110 => 011111
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 111100 => 001111
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => 111010 => 010111
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 111100 => 001111
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 111000 => 000111
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => 110110 => 011011
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => 110100 => 001011
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => 111010 => 010111
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => 110010 => 010011
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 111100 => 001111
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 111000 => 000111
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => 110100 => 001011
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => 111000 => 000111
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => 110000 => 000011
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => 101110 => 011101
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => 101100 => 001101
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => 101010 => 010101
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => 101100 => 001101
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => 101000 => 000101
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => 110110 => 011011
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => 110100 => 001011
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => 100110 => 011001
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => 100100 => 001001
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => 111010 => 010111
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => 110010 => 010011
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => 101010 => 010101
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => 110010 => 010011
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => 100010 => 010001
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 111100 => 001111
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => 111000 => 000111
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => 110100 => 001011
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => 111000 => 000111
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => 110000 => 000011
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => 101100 => 001101
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => 101000 => 000101
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => 110100 => 001011
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => 100100 => 001001
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => 111000 => 000111
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => 110000 => 000011
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => 101000 => 000101
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => 110000 => 000011
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 100000 => 000001
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => 011110 => 011110
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => 011100 => 001110
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => 011010 => 010110
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => 011100 => 001110
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => 011000 => 000110
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => 010110 => 011010
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => 010100 => 001010
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => 011010 => 010110
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => 010010 => 010010
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => 011100 => 001110
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => 011000 => 000110
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => 010100 => 001010
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => 011000 => 000110
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => 010000 => 000010
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => 101110 => 011101
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => 101100 => 001101
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => 101010 => 010101
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => 101100 => 001101
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => 101000 => 000101
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => 001110 => 011100
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => 001100 => 001100
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => 001010 => 010100
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => 001100 => 001100
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => 001000 => 000100
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => 110110 => 011011
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => 110100 => 001011
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => 100110 => 011001
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => 100100 => 001001
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => 010110 => 011010
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => 010100 => 001010
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => 100110 => 011001
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => 100100 => 001001
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => 000110 => 011000
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => 000100 => 001000
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => 111010 => 010111
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => 110010 => 010011
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => 101010 => 010101
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => 110010 => 010011
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => 100010 => 010001
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => 011010 => 010110
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => 010010 => 010010
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => 101010 => 010101
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => 001010 => 010100
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => 110010 => 010011
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => 100010 => 010001
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => 010010 => 010010
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => 100010 => 010001
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 000010 => 010000
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 111100 => 001111
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => 111000 => 000111
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => 110100 => 001011
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => 111000 => 000111
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => 110000 => 000011
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => 101100 => 001101
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => 101000 => 000101
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => 110100 => 001011
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => 100100 => 001001
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => 111000 => 000111
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => 110000 => 000011
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => 101000 => 000101
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => 110000 => 000011
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 100000 => 000001
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => 011100 => 001110
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => 011000 => 000110
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => 010100 => 001010
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => 011000 => 000110
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => 010000 => 000010
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => 101100 => 001101
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => 101000 => 000101
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => 001100 => 001100
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => 001000 => 000100
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => 110100 => 001011
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => 100100 => 001001
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => 010100 => 001010
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => 100100 => 001001
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => 000100 => 001000
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 111000 => 000111
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => 110000 => 000011
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => 101000 => 000101
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => 110000 => 000011
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 100000 => 000001
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => 011000 => 000110
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => 010000 => 000010
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => 101000 => 000101
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => 001000 => 000100
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 110000 => 000011
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 100000 => 000001
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 010000 => 000010
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 100000 => 000001
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 000000 => 000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 1111111 => 1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => 1111110 => 0111111
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [6,8,7,5,4,3,2,1] => 1111101 => 1011111
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 1111110 => 0111111
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => 1111100 => 0011111
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [5,8,7,6,4,3,2,1] => 1111011 => 1101111
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [5,7,8,6,4,3,2,1] => 1111010 => 0101111
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => 1111101 => 1011111
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [5,6,8,7,4,3,2,1] => 1111001 => 1001111
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => 1111110 => 0111111
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => 1111100 => 0011111
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => 1111010 => 0101111
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => 1111100 => 0011111
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => 1111000 => 0001111
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => 1110111 => 1110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [4,7,8,6,5,3,2,1] => 1110110 => 0110111
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => 1110101 => 1010111
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [4,7,6,8,5,3,2,1] => 1110110 => 0110111
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [4,6,7,8,5,3,2,1] => 1110100 => 0010111
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [5,4,7,8,6,3,2,1] => 1111010 => 0101111
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [4,5,8,7,6,3,2,1] => 1110011 => 1100111
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [4,5,7,8,6,3,2,1] => 1110010 => 0100111
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [6,5,4,8,7,3,2,1] => 1111101 => 1011111
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [5,6,4,8,7,3,2,1] => 1111001 => 1001111
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [4,6,5,8,7,3,2,1] => 1110101 => 1010111
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => 1110001 => 1000111
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 1111110 => 0111111
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => 1111100 => 0011111
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [5,7,6,4,8,3,2,1] => 1111010 => 0101111
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 1111100 => 0011111
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => 1111000 => 0001111
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1] => 1110110 => 0110111
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [4,6,7,5,8,3,2,1] => 1110100 => 0010111
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [5,4,7,6,8,3,2,1] => 1111010 => 0101111
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [4,5,7,6,8,3,2,1] => 1110010 => 0100111
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => 1111100 => 0011111
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => 1111000 => 0001111
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [4,6,5,7,8,3,2,1] => 1110100 => 0010111
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => 1111000 => 0001111
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => 1110000 => 0000111
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [3,8,7,6,5,4,2,1] => 1101111 => 1111011
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [3,7,8,6,5,4,2,1] => 1101110 => 0111011
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [3,6,8,7,5,4,2,1] => 1101101 => 1011011
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [3,7,6,8,5,4,2,1] => 1101110 => 0111011
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => 1101011 => 1101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => 1101010 => 0101011
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [3,5,6,8,7,4,2,1] => 1101001 => 1001011
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [3,7,6,5,8,4,2,1] => 1101110 => 0111011
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [3,6,7,5,8,4,2,1] => 1101100 => 0011011
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [3,5,7,6,8,4,2,1] => 1101010 => 0101011
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [3,5,6,7,8,4,2,1] => 1101000 => 0001011
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => 1110111 => 1110111
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [4,3,7,8,6,5,2,1] => 1110110 => 0110111
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [4,3,6,7,8,5,2,1] => 1110100 => 0010111
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [3,4,8,7,6,5,2,1] => 1100111 => 1110011
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => 1100100 => 0010011
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [5,4,3,8,7,6,2,1] => 1111011 => 1101111
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [5,4,3,7,8,6,2,1] => 1111010 => 0101111
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [4,5,3,7,8,6,2,1] => 1110010 => 0100111
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [3,5,4,7,8,6,2,1] => 1101010 => 0101011
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [4,3,5,7,8,6,2,1] => 1110010 => 0100111
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [3,4,5,8,7,6,2,1] => 1100011 => 1100011
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [3,4,5,7,8,6,2,1] => 1100010 => 0100011
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [6,5,4,3,8,7,2,1] => 1111101 => 1011111
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [5,6,4,3,8,7,2,1] => 1111001 => 1001111
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [4,5,6,3,8,7,2,1] => 1110001 => 1000111
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [3,6,5,4,8,7,2,1] => 1101101 => 1011011
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => 1110101 => 1010111
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [5,4,3,6,8,7,2,1] => 1111001 => 1001111
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [4,5,3,6,8,7,2,1] => 1110001 => 1000111
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [4,3,5,6,8,7,2,1] => 1110001 => 1000111
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [3,4,5,6,8,7,2,1] => 1100001 => 1000011
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => 1111110 => 0111111
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => 1111100 => 0011111
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [5,7,6,4,3,8,2,1] => 1111010 => 0101111
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [6,5,7,4,3,8,2,1] => 1111100 => 0011111
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => 1111000 => 0001111
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [4,7,6,5,3,8,2,1] => 1110110 => 0110111
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [5,4,7,6,3,8,2,1] => 1111010 => 0101111
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => 1111100 => 0011111
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => 1111000 => 0001111
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => 1110000 => 0000111
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [3,7,6,5,4,8,2,1] => 1101110 => 0111011
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [3,5,7,6,4,8,2,1] => 1101010 => 0101011
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [3,5,6,7,4,8,2,1] => 1101000 => 0001011
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [4,3,7,6,5,8,2,1] => 1110110 => 0110111
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [3,4,7,6,5,8,2,1] => 1100110 => 0110011
[.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [3,4,6,7,5,8,2,1] => 1100100 => 0010011
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [4,5,3,7,6,8,2,1] => 1110010 => 0100111
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [3,5,4,7,6,8,2,1] => 1101010 => 0101011
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [4,3,5,7,6,8,2,1] => 1110010 => 0100111
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [3,4,5,7,6,8,2,1] => 1100010 => 0100011
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => 1111100 => 0011111
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => 1110000 => 0000111
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [3,6,5,4,7,8,2,1] => 1101100 => 0011011
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [3,5,6,4,7,8,2,1] => 1101000 => 0001011
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [4,3,6,5,7,8,2,1] => 1110100 => 0010111
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [3,4,6,5,7,8,2,1] => 1100100 => 0010011
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => 1111000 => 0001111
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [3,5,4,6,7,8,2,1] => 1101000 => 0001011
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => 1110000 => 0000111
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => 1100000 => 0000011
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => 1011111 => 1111101
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [2,7,8,6,5,4,3,1] => 1011110 => 0111101
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => 1011101 => 1011101
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [2,7,6,8,5,4,3,1] => 1011110 => 0111101
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [2,6,7,8,5,4,3,1] => 1011100 => 0011101
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [2,5,8,7,6,4,3,1] => 1011011 => 1101101
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [2,6,7,5,8,4,3,1] => 1011100 => 0011101
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [2,6,5,7,8,4,3,1] => 1011100 => 0011101
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [2,5,6,7,8,4,3,1] => 1011000 => 0001101
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [2,4,8,7,6,5,3,1] => 1010111 => 1110101
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [2,4,7,8,6,5,3,1] => 1010110 => 0110101
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => 1010101 => 1010101
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [2,4,6,7,8,5,3,1] => 1010100 => 0010101
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [2,5,4,8,7,6,3,1] => 1011011 => 1101101
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [2,5,4,7,8,6,3,1] => 1011010 => 0101101
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [2,4,5,7,8,6,3,1] => 1010010 => 0100101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [2,6,5,4,8,7,3,1] => 1011101 => 1011101
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [2,5,6,4,8,7,3,1] => 1011001 => 1001101
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [2,4,6,5,8,7,3,1] => 1010101 => 1010101
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [2,4,5,6,8,7,3,1] => 1010001 => 1000101
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [2,7,6,5,4,8,3,1] => 1011110 => 0111101
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [2,6,7,5,4,8,3,1] => 1011100 => 0011101
[.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [2,5,6,7,4,8,3,1] => 1011000 => 0001101
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [2,4,7,6,5,8,3,1] => 1010110 => 0110101
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [2,4,6,7,5,8,3,1] => 1010100 => 0010101
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [2,5,4,7,6,8,3,1] => 1011010 => 0101101
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [2,6,5,4,7,8,3,1] => 1011100 => 0011101
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [2,5,6,4,7,8,3,1] => 1011000 => 0001101
[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [2,4,6,5,7,8,3,1] => 1010100 => 0010101
[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [2,5,4,6,7,8,3,1] => 1011000 => 0001101
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [2,4,5,6,7,8,3,1] => 1010000 => 0000101
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => 1101111 => 1111011
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [3,2,6,8,7,5,4,1] => 1101101 => 1011011
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [3,2,5,7,8,6,4,1] => 1101010 => 0101011
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [3,2,6,5,8,7,4,1] => 1101101 => 1011011
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [3,2,5,7,6,8,4,1] => 1101010 => 0101011
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [3,2,5,6,7,8,4,1] => 1101000 => 0001011
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => 1001111 => 1111001
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [2,3,6,7,8,5,4,1] => 1001100 => 0011001
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [2,3,5,8,7,6,4,1] => 1001011 => 1101001
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [2,3,5,7,8,6,4,1] => 1001010 => 0101001
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [2,3,6,5,8,7,4,1] => 1001101 => 1011001
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => 1001001 => 1001001
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [2,3,7,6,5,8,4,1] => 1001110 => 0111001
[.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [2,3,5,7,6,8,4,1] => 1001010 => 0101001
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [2,3,5,6,7,8,4,1] => 1001000 => 0001001
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => 1110111 => 1110111
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [4,3,2,7,8,6,5,1] => 1110110 => 0110111
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [4,3,2,6,8,7,5,1] => 1110101 => 1010111
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => 1100111 => 1110011
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [3,4,2,7,8,6,5,1] => 1100110 => 0110011
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [2,4,3,8,7,6,5,1] => 1010111 => 1110101
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [2,4,3,6,8,7,5,1] => 1010101 => 1010101
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [2,4,3,6,7,8,5,1] => 1010100 => 0010101
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [3,2,4,8,7,6,5,1] => 1100111 => 1110011
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [3,2,4,7,8,6,5,1] => 1100110 => 0110011
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => 1000111 => 1110001
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [2,3,4,7,8,6,5,1] => 1000110 => 0110001
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [2,3,4,6,8,7,5,1] => 1000101 => 1010001
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [2,3,4,7,6,8,5,1] => 1000110 => 0110001
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [2,3,4,6,7,8,5,1] => 1000100 => 0010001
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [5,4,3,2,8,7,6,1] => 1111011 => 1101111
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [5,4,3,2,7,8,6,1] => 1111010 => 0101111
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [4,5,3,2,8,7,6,1] => 1110011 => 1100111
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [3,5,4,2,7,8,6,1] => 1101010 => 0101011
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [4,3,5,2,8,7,6,1] => 1110011 => 1100111
[.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [3,4,5,2,7,8,6,1] => 1100010 => 0100011
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => 1011011 => 1101101
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [2,5,4,3,7,8,6,1] => 1011010 => 0101101
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [2,4,5,3,8,7,6,1] => 1010011 => 1100101
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [2,4,5,3,7,8,6,1] => 1010010 => 0100101
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [3,2,5,4,7,8,6,1] => 1101010 => 0101011
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [2,3,5,4,8,7,6,1] => 1001011 => 1101001
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [2,3,5,4,7,8,6,1] => 1001010 => 0101001
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [4,3,2,5,8,7,6,1] => 1110011 => 1100111
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [4,3,2,5,7,8,6,1] => 1110010 => 0100111
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [3,4,2,5,8,7,6,1] => 1100011 => 1100011
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [3,4,2,5,7,8,6,1] => 1100010 => 0100011
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [2,4,3,5,8,7,6,1] => 1010011 => 1100101
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [3,2,4,5,7,8,6,1] => 1100010 => 0100011
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [2,3,4,5,8,7,6,1] => 1000011 => 1100001
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [2,3,4,5,7,8,6,1] => 1000010 => 0100001
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [6,5,4,3,2,8,7,1] => 1111101 => 1011111
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [4,6,5,3,2,8,7,1] => 1110101 => 1010111
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [5,4,6,3,2,8,7,1] => 1111001 => 1001111
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [4,5,6,3,2,8,7,1] => 1110001 => 1000111
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [3,6,5,4,2,8,7,1] => 1101101 => 1011011
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [3,5,6,4,2,8,7,1] => 1101001 => 1001011
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [4,3,6,5,2,8,7,1] => 1110101 => 1010111
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [5,4,3,6,2,8,7,1] => 1111001 => 1001111
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => 1110001 => 1000111
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [3,5,4,6,2,8,7,1] => 1101001 => 1001011
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [3,4,5,6,2,8,7,1] => 1100001 => 1000011
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [2,6,5,4,3,8,7,1] => 1011101 => 1011101
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [2,4,6,5,3,8,7,1] => 1010101 => 1010101
[.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [2,4,5,6,3,8,7,1] => 1010001 => 1000101
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => 1101101 => 1011011
[.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [2,3,5,6,4,8,7,1] => 1001001 => 1001001
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [4,3,2,6,5,8,7,1] => 1110101 => 1010111
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [3,4,2,6,5,8,7,1] => 1100101 => 1010011
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => 1010101 => 1010101
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [3,2,4,6,5,8,7,1] => 1100101 => 1010011
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [2,3,4,6,5,8,7,1] => 1000101 => 1010001
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [5,4,3,2,6,8,7,1] => 1111001 => 1001111
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [4,5,3,2,6,8,7,1] => 1110001 => 1000111
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [2,5,4,3,6,8,7,1] => 1011001 => 1001101
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [2,4,5,3,6,8,7,1] => 1010001 => 1000101
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [3,2,5,4,6,8,7,1] => 1101001 => 1001011
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [4,3,2,5,6,8,7,1] => 1110001 => 1000111
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [3,4,2,5,6,8,7,1] => 1100001 => 1000011
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => 1010001 => 1000101
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [3,2,4,5,6,8,7,1] => 1100001 => 1000011
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => 1000001 => 1000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 1111110 => 0111111
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => 1111100 => 0011111
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [5,7,6,4,3,2,8,1] => 1111010 => 0101111
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 1111100 => 0011111
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => 1111000 => 0001111
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [4,7,6,5,3,2,8,1] => 1110110 => 0110111
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [4,6,7,5,3,2,8,1] => 1110100 => 0010111
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1] => 1111100 => 0011111
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [4,6,5,7,3,2,8,1] => 1110100 => 0010111
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => 1110000 => 0000111
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [3,5,7,6,4,2,8,1] => 1101010 => 0101011
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [3,5,6,7,4,2,8,1] => 1101000 => 0001011
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [4,3,7,6,5,2,8,1] => 1110110 => 0110111
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [4,3,6,7,5,2,8,1] => 1110100 => 0010111
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [3,4,7,6,5,2,8,1] => 1100110 => 0110011
[.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [3,4,6,7,5,2,8,1] => 1100100 => 0010011
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [5,4,3,7,6,2,8,1] => 1111010 => 0101111
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [4,5,3,7,6,2,8,1] => 1110010 => 0100111
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [3,5,4,7,6,2,8,1] => 1101010 => 0101011
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [3,4,5,7,6,2,8,1] => 1100010 => 0100011
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 1111100 => 0011111
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [4,6,5,3,7,2,8,1] => 1110100 => 0010111
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 1111000 => 0001111
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => 1110000 => 0000111
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [3,6,5,4,7,2,8,1] => 1101100 => 0011011
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => 1101000 => 0001011
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => 1110100 => 0010111
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [3,4,6,5,7,2,8,1] => 1100100 => 0010011
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => 1111000 => 0001111
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => 1110000 => 0000111
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [3,5,4,6,7,2,8,1] => 1101000 => 0001011
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [4,3,5,6,7,2,8,1] => 1110000 => 0000111
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => 1100000 => 0000011
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1] => 1011110 => 0111101
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [2,6,5,7,4,3,8,1] => 1011100 => 0011101
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [2,5,6,7,4,3,8,1] => 1011000 => 0001101
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [2,4,6,7,5,3,8,1] => 1010100 => 0010101
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [2,5,4,7,6,3,8,1] => 1011010 => 0101101
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => 1010100 => 0010101
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [2,5,4,6,7,3,8,1] => 1011000 => 0001101
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [2,4,5,6,7,3,8,1] => 1010000 => 0000101
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [3,2,7,6,5,4,8,1] => 1101110 => 0111011
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [3,2,6,7,5,4,8,1] => 1101100 => 0011011
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [3,2,5,7,6,4,8,1] => 1101010 => 0101011
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => 1101100 => 0011011
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [3,2,5,6,7,4,8,1] => 1101000 => 0001011
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [2,3,7,6,5,4,8,1] => 1001110 => 0111001
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [2,3,5,7,6,4,8,1] => 1001010 => 0101001
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [2,3,5,6,7,4,8,1] => 1001000 => 0001001
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1] => 1110110 => 0110111
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [4,3,2,6,7,5,8,1] => 1110100 => 0010111
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [3,4,2,7,6,5,8,1] => 1100110 => 0110011
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [3,4,2,6,7,5,8,1] => 1100100 => 0010011
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [2,4,3,7,6,5,8,1] => 1010110 => 0110101
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [2,4,3,6,7,5,8,1] => 1010100 => 0010101
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [3,2,4,7,6,5,8,1] => 1100110 => 0110011
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [2,3,4,7,6,5,8,1] => 1000110 => 0110001
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [2,3,4,6,7,5,8,1] => 1000100 => 0010001
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [5,4,3,2,7,6,8,1] => 1111010 => 0101111
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [3,5,4,2,7,6,8,1] => 1101010 => 0101011
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => 1110010 => 0100111
[.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [3,4,5,2,7,6,8,1] => 1100010 => 0100011
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [2,5,4,3,7,6,8,1] => 1011010 => 0101101
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => 1101010 => 0101011
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [2,3,5,4,7,6,8,1] => 1001010 => 0101001
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [4,3,2,5,7,6,8,1] => 1110010 => 0100111
[.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [3,4,2,5,7,6,8,1] => 1100010 => 0100011
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [2,4,3,5,7,6,8,1] => 1010010 => 0100101
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1] => 1100010 => 0100011
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => 1000010 => 0100001
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => 1111100 => 0011111
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => 1111000 => 0001111
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => 1110000 => 0000111
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [3,6,5,4,2,7,8,1] => 1101100 => 0011011
[.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [3,5,6,4,2,7,8,1] => 1101000 => 0001011
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [3,4,6,5,2,7,8,1] => 1100100 => 0010011
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => 1111000 => 0001111
[.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [3,5,4,6,2,7,8,1] => 1101000 => 0001011
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => 1110000 => 0000111
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => 1100000 => 0000011
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [2,6,5,4,3,7,8,1] => 1011100 => 0011101
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [2,5,6,4,3,7,8,1] => 1011000 => 0001101
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [2,4,6,5,3,7,8,1] => 1010100 => 0010101
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [2,5,4,6,3,7,8,1] => 1011000 => 0001101
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [2,4,5,6,3,7,8,1] => 1010000 => 0000101
[.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [3,2,5,6,4,7,8,1] => 1101000 => 0001011
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [2,3,6,5,4,7,8,1] => 1001100 => 0011001
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [2,3,5,6,4,7,8,1] => 1001000 => 0001001
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [4,3,2,6,5,7,8,1] => 1110100 => 0010111
[.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [3,4,2,6,5,7,8,1] => 1100100 => 0010011
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [2,4,3,6,5,7,8,1] => 1010100 => 0010101
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [2,3,4,6,5,7,8,1] => 1000100 => 0010001
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => 1111000 => 0001111
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [4,5,3,2,6,7,8,1] => 1110000 => 0000111
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [3,5,4,2,6,7,8,1] => 1101000 => 0001011
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => 1110000 => 0000111
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 1100000 => 0000011
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1] => 1011000 => 0001101
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [2,4,5,3,6,7,8,1] => 1010000 => 0000101
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [3,2,5,4,6,7,8,1] => 1101000 => 0001011
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1] => 1001000 => 0001001
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 1110000 => 0000111
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 1100000 => 0000011
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [2,4,3,5,6,7,8,1] => 1010000 => 0000101
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 1100000 => 0000011
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 1000000 => 0000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => 0111111 => 1111110
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => 0111110 => 0111110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => 0111101 => 1011110
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => 0111110 => 0111110
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => 0111100 => 0011110
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => 0111011 => 1101110
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,6,5,8,7,4,3,2] => 0111101 => 1011110
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => 0111110 => 0111110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => 0111100 => 0011110
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,5,7,6,8,4,3,2] => 0111010 => 0101110
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,6,5,7,8,4,3,2] => 0111100 => 0011110
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => 0111000 => 0001110
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => 0110111 => 1110110
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => 0110110 => 0110110
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => 0110101 => 1010110
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,4,6,7,8,5,3,2] => 0110100 => 0010110
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,5,4,7,8,6,3,2] => 0111010 => 0101110
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,4,5,8,7,6,3,2] => 0110011 => 1100110
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,4,5,7,8,6,3,2] => 0110010 => 0100110
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,6,5,4,8,7,3,2] => 0111101 => 1011110
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,4,6,5,8,7,3,2] => 0110101 => 1010110
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,5,4,6,8,7,3,2] => 0111001 => 1001110
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => 0111110 => 0111110
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,4,7,6,5,8,3,2] => 0110110 => 0110110
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,4,6,7,5,8,3,2] => 0110100 => 0010110
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,6,5,4,7,8,3,2] => 0111100 => 0011110
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,5,6,4,7,8,3,2] => 0111000 => 0001110
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,5,4,6,7,8,3,2] => 0111000 => 0001110
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,4,5,6,7,8,3,2] => 0110000 => 0000110
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => 0101111 => 1111010
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,3,7,8,6,5,4,2] => 0101110 => 0111010
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,3,6,8,7,5,4,2] => 0101101 => 1011010
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,3,6,7,8,5,4,2] => 0101100 => 0011010
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,3,5,8,7,6,4,2] => 0101011 => 1101010
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => 0101010 => 0101010
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,3,5,6,8,7,4,2] => 0101001 => 1001010
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,3,5,7,6,8,4,2] => 0101010 => 0101010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => 0101100 => 0011010
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => 0101000 => 0001010
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => 0110111 => 1110110
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => 0110110 => 0110110
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,4,3,6,8,7,5,2] => 0110101 => 1010110
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,4,3,7,6,8,5,2] => 0110110 => 0110110
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,4,3,6,7,8,5,2] => 0110100 => 0010110
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => 0100111 => 1110010
[[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,3,4,7,6,8,5,2] => 0100110 => 0110010
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,3,4,6,7,8,5,2] => 0100100 => 0010010
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,5,4,3,8,7,6,2] => 0111011 => 1101110
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,4,5,3,8,7,6,2] => 0110011 => 1100110
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,3,5,4,8,7,6,2] => 0101011 => 1101010
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,3,5,4,7,8,6,2] => 0101010 => 0101010
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,4,3,5,8,7,6,2] => 0110011 => 1100110
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,4,3,5,7,8,6,2] => 0110010 => 0100110
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,3,4,5,8,7,6,2] => 0100011 => 1100010
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => 0100010 => 0100010
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => 0111101 => 1011110
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => 0111001 => 1001110
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,4,6,5,3,8,7,2] => 0110101 => 1010110
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,4,5,6,3,8,7,2] => 0110001 => 1000110
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,3,6,5,4,8,7,2] => 0101101 => 1011010
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => 0110101 => 1010110
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,5,4,3,6,8,7,2] => 0111001 => 1001110
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,4,5,3,6,8,7,2] => 0110001 => 1000110
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => 0100001 => 1000010
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => 0111110 => 0111110
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,6,7,5,4,3,8,2] => 0111100 => 0011110
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,6,5,7,4,3,8,2] => 0111100 => 0011110
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,5,6,7,4,3,8,2] => 0111000 => 0001110
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => 0110100 => 0010110
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => 0111000 => 0001110
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,4,6,5,7,3,8,2] => 0110100 => 0010110
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => 0111000 => 0001110
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => 0110000 => 0000110
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,3,5,7,6,4,8,2] => 0101010 => 0101010
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,3,6,5,7,4,8,2] => 0101100 => 0011010
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,3,5,6,7,4,8,2] => 0101000 => 0001010
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,4,3,6,7,5,8,2] => 0110100 => 0010110
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,3,4,7,6,5,8,2] => 0100110 => 0110010
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,3,4,6,7,5,8,2] => 0100100 => 0010010
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,3,5,4,7,6,8,2] => 0101010 => 0101010
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,3,4,5,7,6,8,2] => 0100010 => 0100010
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,6,5,4,3,7,8,2] => 0111100 => 0011110
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,5,4,6,3,7,8,2] => 0111000 => 0001110
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,3,5,6,4,7,8,2] => 0101000 => 0001010
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,4,3,6,5,7,8,2] => 0110100 => 0010110
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,3,4,6,5,7,8,2] => 0100100 => 0010010
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,5,4,3,6,7,8,2] => 0111000 => 0001110
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => 0110000 => 0000110
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,3,5,4,6,7,8,2] => 0101000 => 0001010
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => 0110000 => 0000110
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => 0100000 => 0000010
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => 1011111 => 1111101
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [2,1,7,8,6,5,4,3] => 1011110 => 0111101
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [2,1,6,8,7,5,4,3] => 1011101 => 1011101
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => 1011110 => 0111101
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => 1011100 => 0011101
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [2,1,5,8,7,6,4,3] => 1011011 => 1101101
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => 1011010 => 0101101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [2,1,6,5,8,7,4,3] => 1011101 => 1011101
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [2,1,5,6,8,7,4,3] => 1011001 => 1001101
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [2,1,7,6,5,8,4,3] => 1011110 => 0111101
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => 1011100 => 0011101
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [2,1,5,7,6,8,4,3] => 1011010 => 0101101
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => 1011100 => 0011101
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => 1011000 => 0001101
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => 1010111 => 1110101
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [2,1,4,7,8,6,5,3] => 1010110 => 0110101
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => 1010101 => 1010101
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [2,1,4,7,6,8,5,3] => 1010110 => 0110101
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [2,1,4,6,7,8,5,3] => 1010100 => 0010101
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [2,1,5,4,8,7,6,3] => 1011011 => 1101101
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [2,1,5,4,7,8,6,3] => 1011010 => 0101101
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => 1010011 => 1100101
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [2,1,4,5,7,8,6,3] => 1010010 => 0100101
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [2,1,6,5,4,8,7,3] => 1011101 => 1011101
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [2,1,5,6,4,8,7,3] => 1011001 => 1001101
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => 1010101 => 1010101
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [2,1,5,4,6,8,7,3] => 1011001 => 1001101
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [2,1,4,5,6,8,7,3] => 1010001 => 1000101
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [2,1,7,6,5,4,8,3] => 1011110 => 0111101
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [2,1,6,7,5,4,8,3] => 1011100 => 0011101
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [2,1,5,7,6,4,8,3] => 1011010 => 0101101
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => 1011100 => 0011101
[[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [2,1,5,6,7,4,8,3] => 1011000 => 0001101
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [2,1,4,7,6,5,8,3] => 1010110 => 0110101
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [2,1,4,6,7,5,8,3] => 1010100 => 0010101
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => 1011010 => 0101101
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [2,1,5,6,4,7,8,3] => 1011000 => 0001101
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [2,1,5,4,6,7,8,3] => 1011000 => 0001101
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => 1010000 => 0000101
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => 0011111 => 1111100
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => 0011110 => 0111100
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,2,7,6,8,5,4,3] => 0011110 => 0111100
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => 0011100 => 0011100
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,2,5,8,7,6,4,3] => 0011011 => 1101100
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,2,6,5,8,7,4,3] => 0011101 => 1011100
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,2,5,6,8,7,4,3] => 0011001 => 1001100
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => 0011110 => 0111100
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,2,5,7,6,8,4,3] => 0011010 => 0101100
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,2,6,5,7,8,4,3] => 0011100 => 0011100
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,2,5,6,7,8,4,3] => 0011000 => 0001100
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => 0010111 => 1110100
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,2,4,7,8,6,5,3] => 0010110 => 0110100
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,2,4,6,8,7,5,3] => 0010101 => 1010100
[[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,2,4,7,6,8,5,3] => 0010110 => 0110100
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => 0010100 => 0010100
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,2,5,4,8,7,6,3] => 0011011 => 1101100
[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,2,5,4,7,8,6,3] => 0011010 => 0101100
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,2,4,5,8,7,6,3] => 0010011 => 1100100
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,2,4,5,7,8,6,3] => 0010010 => 0100100
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,2,6,5,4,8,7,3] => 0011101 => 1011100
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,2,4,6,5,8,7,3] => 0010101 => 1010100
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,2,5,4,6,8,7,3] => 0011001 => 1001100
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,2,4,5,6,8,7,3] => 0010001 => 1000100
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,2,7,6,5,4,8,3] => 0011110 => 0111100
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,2,5,7,6,4,8,3] => 0011010 => 0101100
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => 0011000 => 0001100
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,2,4,7,6,5,8,3] => 0010110 => 0110100
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,2,5,4,7,6,8,3] => 0011010 => 0101100
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,2,6,5,4,7,8,3] => 0011100 => 0011100
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,2,5,6,4,7,8,3] => 0011000 => 0001100
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,2,4,6,5,7,8,3] => 0010100 => 0010100
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => 0011000 => 0001100
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => 0010000 => 0000100
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => 1101111 => 1111011
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [3,2,1,7,8,6,5,4] => 1101110 => 0111011
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [3,2,1,6,8,7,5,4] => 1101101 => 1011011
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [3,2,1,7,6,8,5,4] => 1101110 => 0111011
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => 1101100 => 0011011
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => 1101011 => 1101011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => 1101010 => 0101011
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => 1101101 => 1011011
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => 1101001 => 1001011
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => 1101110 => 0111011
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => 1101100 => 0011011
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [3,2,1,5,7,6,8,4] => 1101010 => 0101011
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [3,2,1,6,5,7,8,4] => 1101100 => 0011011
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => 1101000 => 0001011
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => 1001111 => 1111001
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [2,3,1,7,8,6,5,4] => 1001110 => 0111001
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [2,3,1,6,8,7,5,4] => 1001101 => 1011001
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [2,3,1,7,6,8,5,4] => 1001110 => 0111001
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [2,3,1,6,7,8,5,4] => 1001100 => 0011001
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [2,3,1,6,5,8,7,4] => 1001101 => 1011001
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [2,3,1,7,6,5,8,4] => 1001110 => 0111001
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [2,3,1,6,7,5,8,4] => 1001100 => 0011001
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [2,3,1,5,7,6,8,4] => 1001010 => 0101001
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [2,3,1,5,6,7,8,4] => 1001000 => 0001001
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => 0101111 => 1111010
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => 0101101 => 1011010
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,3,2,7,6,8,5,4] => 0101110 => 0111010
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,3,2,6,7,8,5,4] => 0101100 => 0011010
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,3,2,5,8,7,6,4] => 0101011 => 1101010
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,3,2,5,7,8,6,4] => 0101010 => 0101010
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,3,2,6,5,8,7,4] => 0101101 => 1011010
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,3,2,5,6,8,7,4] => 0101001 => 1001010
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,3,2,7,6,5,8,4] => 0101110 => 0111010
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,3,2,6,7,5,8,4] => 0101100 => 0011010
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,3,2,5,7,6,8,4] => 0101010 => 0101010
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,3,2,6,5,7,8,4] => 0101100 => 0011010
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,3,2,5,6,7,8,4] => 0101000 => 0001010
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => 1001111 => 1111001
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [2,1,3,7,8,6,5,4] => 1001110 => 0111001
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [2,1,3,6,8,7,5,4] => 1001101 => 1011001
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [2,1,3,6,7,8,5,4] => 1001100 => 0011001
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [2,1,3,6,5,8,7,4] => 1001101 => 1011001
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [2,1,3,5,7,6,8,4] => 1001010 => 0101001
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [2,1,3,5,6,7,8,4] => 1001000 => 0001001
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => 0001111 => 1111000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => 0001110 => 0111000
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => 0001101 => 1011000
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => 0001110 => 0111000
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => 0001100 => 0011000
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => 0001011 => 1101000
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => 0001010 => 0101000
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => 0001101 => 1011000
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => 0001001 => 1001000
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => 0001110 => 0111000
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => 0001100 => 0011000
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => 0001010 => 0101000
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => 0001100 => 0011000
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => 0001000 => 0001000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => 1110111 => 1110111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => 1110110 => 0110111
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => 1110101 => 1010111
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => 1110110 => 0110111
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => 1110100 => 0010111
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => 1100111 => 1110011
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => 1100110 => 0110011
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => 1100101 => 1010011
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => 1100110 => 0110011
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [3,4,2,1,6,7,8,5] => 1100100 => 0010011
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => 1010111 => 1110101
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [2,4,3,1,7,8,6,5] => 1010110 => 0110101
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => 1010101 => 1010101
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => 1010110 => 0110101
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [2,4,3,1,6,7,8,5] => 1010100 => 0010101
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => 1100111 => 1110011
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => 1100110 => 0110011
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => 1100101 => 1010011
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => 1100110 => 0110011
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [3,2,4,1,6,7,8,5] => 1100100 => 0010011
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => 1000111 => 1110001
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [2,3,4,1,7,8,6,5] => 1000110 => 0110001
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [2,3,4,1,6,8,7,5] => 1000101 => 1010001
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => 1000110 => 0110001
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => 1000100 => 0010001
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => 0110111 => 1110110
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,4,3,2,6,8,7,5] => 0110101 => 1010110
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => 0110110 => 0110110
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => 0110100 => 0010110
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => 0100111 => 1110010
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,3,4,2,7,8,6,5] => 0100110 => 0110010
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,3,4,2,6,8,7,5] => 0100101 => 1010010
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => 0100110 => 0110010
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,3,4,2,6,7,8,5] => 0100100 => 0010010
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => 1010111 => 1110101
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => 1010110 => 0110101
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => 1010101 => 1010101
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => 1010110 => 0110101
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => 1010100 => 0010101
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => 0010111 => 1110100
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,2,4,3,7,8,6,5] => 0010110 => 0110100
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => 0010101 => 1010100
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => 0010110 => 0110100
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => 0010100 => 0010100
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => 1100111 => 1110011
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [3,2,1,4,7,8,6,5] => 1100110 => 0110011
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [3,2,1,4,6,8,7,5] => 1100101 => 1010011
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [3,2,1,4,7,6,8,5] => 1100110 => 0110011
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [3,2,1,4,6,7,8,5] => 1100100 => 0010011
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => 1000111 => 1110001
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [2,3,1,4,7,8,6,5] => 1000110 => 0110001
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => 1000110 => 0110001
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [2,3,1,4,6,7,8,5] => 1000100 => 0010001
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => 0100111 => 1110010
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,3,2,4,6,8,7,5] => 0100101 => 1010010
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => 0100110 => 0110010
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,3,2,4,6,7,8,5] => 0100100 => 0010010
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => 1000111 => 1110001
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [2,1,3,4,7,8,6,5] => 1000110 => 0110001
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => 1000110 => 0110001
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => 1000100 => 0010001
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => 0000111 => 1110000
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => 0000110 => 0110000
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => 0000101 => 1010000
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => 0000110 => 0110000
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => 0000100 => 0010000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => 1111011 => 1101111
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => 1111010 => 0101111
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [4,5,3,2,1,8,7,6] => 1110011 => 1100111
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [3,5,4,2,1,8,7,6] => 1101011 => 1101011
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [3,5,4,2,1,7,8,6] => 1101010 => 0101011
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [4,3,5,2,1,8,7,6] => 1110011 => 1100111
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [3,4,5,2,1,8,7,6] => 1100011 => 1100011
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [3,4,5,2,1,7,8,6] => 1100010 => 0100011
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [2,5,4,3,1,8,7,6] => 1011011 => 1101101
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [2,5,4,3,1,7,8,6] => 1011010 => 0101101
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [2,4,5,3,1,8,7,6] => 1010011 => 1100101
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [2,4,5,3,1,7,8,6] => 1010010 => 0100101
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => 1101011 => 1101011
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [3,2,5,4,1,7,8,6] => 1101010 => 0101011
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [2,3,5,4,1,8,7,6] => 1001011 => 1101001
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => 1110011 => 1100111
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [4,3,2,5,1,7,8,6] => 1110010 => 0100111
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => 1100011 => 1100011
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [3,4,2,5,1,7,8,6] => 1100010 => 0100011
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [2,4,3,5,1,8,7,6] => 1010011 => 1100101
[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [2,4,3,5,1,7,8,6] => 1010010 => 0100101
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [3,2,4,5,1,8,7,6] => 1100011 => 1100011
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [2,3,4,5,1,8,7,6] => 1000011 => 1100001
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => 1000010 => 0100001
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => 0111011 => 1101110
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,5,4,3,2,7,8,6] => 0111010 => 0101110
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,4,5,3,2,8,7,6] => 0110011 => 1100110
[[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,4,5,3,2,7,8,6] => 0110010 => 0100110
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,3,5,4,2,7,8,6] => 0101010 => 0101010
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,4,3,5,2,8,7,6] => 0110011 => 1100110
[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,4,3,5,2,7,8,6] => 0110010 => 0100110
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,3,4,5,2,8,7,6] => 0100011 => 1100010
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,3,4,5,2,7,8,6] => 0100010 => 0100010
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [2,1,5,4,3,8,7,6] => 1011011 => 1101101
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [2,1,4,5,3,8,7,6] => 1010011 => 1100101
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => 0011011 => 1101100
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,2,5,4,3,7,8,6] => 0011010 => 0101100
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => 0010011 => 1100100
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,2,4,5,3,7,8,6] => 0010010 => 0100100
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => 0101011 => 1101010
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,3,2,5,4,7,8,6] => 0101010 => 0101010
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [2,1,3,5,4,8,7,6] => 1001011 => 1101001
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [2,1,3,5,4,7,8,6] => 1001010 => 0101001
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => 0001011 => 1101000
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,2,3,5,4,7,8,6] => 0001010 => 0101000
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => 1110011 => 1100111
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => 1110010 => 0100111
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [3,4,2,1,5,8,7,6] => 1100011 => 1100011
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [2,4,3,1,5,8,7,6] => 1010011 => 1100101
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => 1100011 => 1100011
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => 1100010 => 0100011
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [2,3,4,1,5,8,7,6] => 1000011 => 1100001
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [2,3,4,1,5,7,8,6] => 1000010 => 0100001
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => 0110011 => 1100110
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,4,3,2,5,7,8,6] => 0110010 => 0100110
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,3,4,2,5,8,7,6] => 0100011 => 1100010
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,3,4,2,5,7,8,6] => 0100010 => 0100010
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [2,1,4,3,5,8,7,6] => 1010011 => 1100101
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [2,1,4,3,5,7,8,6] => 1010010 => 0100101
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,2,4,3,5,8,7,6] => 0010011 => 1100100
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,2,4,3,5,7,8,6] => 0010010 => 0100100
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => 1100011 => 1100011
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [3,2,1,4,5,7,8,6] => 1100010 => 0100011
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => 1000010 => 0100001
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,3,2,4,5,8,7,6] => 0100011 => 1100010
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,3,2,4,5,7,8,6] => 0100010 => 0100010
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [2,1,3,4,5,8,7,6] => 1000011 => 1100001
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [2,1,3,4,5,7,8,6] => 1000010 => 0100001
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => 0000011 => 1100000
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => 0000010 => 0100000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => 1111101 => 1011111
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [5,6,4,3,2,1,8,7] => 1111001 => 1001111
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [4,6,5,3,2,1,8,7] => 1110101 => 1010111
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [5,4,6,3,2,1,8,7] => 1111001 => 1001111
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => 1110001 => 1000111
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [3,6,5,4,2,1,8,7] => 1101101 => 1011011
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => 1101001 => 1001011
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [4,3,6,5,2,1,8,7] => 1110101 => 1010111
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [3,4,6,5,2,1,8,7] => 1100101 => 1010011
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [5,4,3,6,2,1,8,7] => 1111001 => 1001111
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [4,5,3,6,2,1,8,7] => 1110001 => 1000111
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [4,3,5,6,2,1,8,7] => 1110001 => 1000111
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [3,4,5,6,2,1,8,7] => 1100001 => 1000011
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [2,6,5,4,3,1,8,7] => 1011101 => 1011101
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [2,5,6,4,3,1,8,7] => 1011001 => 1001101
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [2,4,6,5,3,1,8,7] => 1010101 => 1010101
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [3,2,6,5,4,1,8,7] => 1101101 => 1011011
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [3,2,5,6,4,1,8,7] => 1101001 => 1001011
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [2,3,6,5,4,1,8,7] => 1001101 => 1011001
[[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [2,3,5,6,4,1,8,7] => 1001001 => 1001001
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [4,3,2,6,5,1,8,7] => 1110101 => 1010111
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [3,4,2,6,5,1,8,7] => 1100101 => 1010011
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => 1010101 => 1010101
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [5,4,3,2,6,1,8,7] => 1111001 => 1001111
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [4,5,3,2,6,1,8,7] => 1110001 => 1000111
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [3,5,4,2,6,1,8,7] => 1101001 => 1001011
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => 1110001 => 1000111
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [3,4,5,2,6,1,8,7] => 1100001 => 1000011
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [2,5,4,3,6,1,8,7] => 1011001 => 1001101
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [2,4,5,3,6,1,8,7] => 1010001 => 1000101
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => 1101001 => 1001011
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [4,3,2,5,6,1,8,7] => 1110001 => 1000111
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [3,4,2,5,6,1,8,7] => 1100001 => 1000011
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [2,4,3,5,6,1,8,7] => 1010001 => 1000101
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => 1000001 => 1000001
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => 0111101 => 1011110
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => 0111001 => 1001110
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,5,4,6,3,2,8,7] => 0111001 => 1001110
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,3,6,5,4,2,8,7] => 0101101 => 1011010
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,3,4,5,6,2,8,7] => 0100001 => 1000010
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => 1011101 => 1011101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => 1011001 => 1001101
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => 1010101 => 1010101
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => 1011001 => 1001101
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => 1010001 => 1000101
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,2,4,5,6,3,8,7] => 0010001 => 1000100
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [3,2,1,6,5,4,8,7] => 1101101 => 1011011
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [2,3,1,6,5,4,8,7] => 1001101 => 1011001
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,3,2,6,5,4,8,7] => 0101101 => 1011010
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,3,2,5,6,4,8,7] => 0101001 => 1001010
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [2,1,3,6,5,4,8,7] => 1001101 => 1011001
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [2,1,3,5,6,4,8,7] => 1001001 => 1001001
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,2,3,6,5,4,8,7] => 0001101 => 1011000
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,2,3,5,6,4,8,7] => 0001001 => 1001000
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => 1110101 => 1010111
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => 1100101 => 1010011
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => 1010101 => 1010101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => 1100101 => 1010011
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => 1000101 => 1010001
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => 0100101 => 1010010
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => 1010101 => 1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => 0010101 => 1010100
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [2,3,1,4,6,5,8,7] => 1000101 => 1010001
[[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,3,2,4,6,5,8,7] => 0100101 => 1010010
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [2,1,3,4,6,5,8,7] => 1000101 => 1010001
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => 0000101 => 1010000
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => 1111001 => 1001111
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [4,5,3,2,1,6,8,7] => 1110001 => 1000111
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => [3,5,4,2,1,6,8,7] => 1101001 => 1001011
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [4,3,5,2,1,6,8,7] => 1110001 => 1000111
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [3,4,5,2,1,6,8,7] => 1100001 => 1000011
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [2,5,4,3,1,6,8,7] => 1011001 => 1001101
[[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [2,4,5,3,1,6,8,7] => 1010001 => 1000101
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [3,2,5,4,1,6,8,7] => 1101001 => 1001011
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [2,3,5,4,1,6,8,7] => 1001001 => 1001001
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [2,4,3,5,1,6,8,7] => 1010001 => 1000101
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [2,3,4,5,1,6,8,7] => 1000001 => 1000001
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,4,5,3,2,6,8,7] => 0110001 => 1000110
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,3,5,4,2,6,8,7] => 0101001 => 1001010
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,3,4,5,2,6,8,7] => 0100001 => 1000010
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => 1011001 => 1001101
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => 1010001 => 1000101
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,2,5,4,3,6,8,7] => 0011001 => 1001100
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [2,1,3,5,4,6,8,7] => 1001001 => 1001001
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => 0001001 => 1001000
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => 1110001 => 1000111
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [3,4,2,1,5,6,8,7] => 1100001 => 1000011
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => 1100001 => 1000011
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [2,3,4,1,5,6,8,7] => 1000001 => 1000001
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,4,3,2,5,6,8,7] => 0110001 => 1000110
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,3,4,2,5,6,8,7] => 0100001 => 1000010
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [2,1,4,3,5,6,8,7] => 1010001 => 1000101
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => 0010001 => 1000100
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [3,2,1,4,5,6,8,7] => 1100001 => 1000011
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [2,3,1,4,5,6,8,7] => 1000001 => 1000001
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => 0100001 => 1000010
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => 1000001 => 1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => 0000001 => 1000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 1111110 => 0111111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 1111100 => 0011111
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => 1111010 => 0101111
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 1111100 => 0011111
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 1111000 => 0001111
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => 1110110 => 0110111
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [4,6,7,5,3,2,1,8] => 1110100 => 0010111
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [5,4,7,6,3,2,1,8] => 1111010 => 0101111
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [4,5,7,6,3,2,1,8] => 1110010 => 0100111
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 1111100 => 0011111
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => 1111000 => 0001111
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [4,6,5,7,3,2,1,8] => 1110100 => 0010111
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => 1111000 => 0001111
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => 1110000 => 0000111
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [3,5,7,6,4,2,1,8] => 1101010 => 0101011
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [3,5,6,7,4,2,1,8] => 1101000 => 0001011
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [4,3,7,6,5,2,1,8] => 1110110 => 0110111
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => 1100110 => 0110011
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [5,4,3,7,6,2,1,8] => 1111010 => 0101111
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [4,5,3,7,6,2,1,8] => 1110010 => 0100111
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [3,5,4,7,6,2,1,8] => 1101010 => 0101011
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [4,3,5,7,6,2,1,8] => 1110010 => 0100111
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => 1111100 => 0011111
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => 1111000 => 0001111
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => 1111000 => 0001111
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [3,6,5,4,7,2,1,8] => 1101100 => 0011011
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [3,5,6,4,7,2,1,8] => 1101000 => 0001011
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [4,3,6,5,7,2,1,8] => 1110100 => 0010111
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => 1111000 => 0001111
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => 1100000 => 0000011
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => 1011110 => 0111101
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [2,6,7,5,4,3,1,8] => 1011100 => 0011101
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [2,5,7,6,4,3,1,8] => 1011010 => 0101101
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [2,5,6,7,4,3,1,8] => 1011000 => 0001101
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => 1010100 => 0010101
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [2,5,4,7,6,3,1,8] => 1011010 => 0101101
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [2,5,6,4,7,3,1,8] => 1011000 => 0001101
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [2,5,4,6,7,3,1,8] => 1011000 => 0001101
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [2,4,5,6,7,3,1,8] => 1010000 => 0000101
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => 1101110 => 0111011
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [3,2,6,7,5,4,1,8] => 1101100 => 0011011
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [3,2,5,7,6,4,1,8] => 1101010 => 0101011
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [3,2,6,5,7,4,1,8] => 1101100 => 0011011
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [3,2,5,6,7,4,1,8] => 1101000 => 0001011
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [2,3,7,6,5,4,1,8] => 1001110 => 0111001
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [2,3,6,7,5,4,1,8] => 1001100 => 0011001
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [2,3,5,7,6,4,1,8] => 1001010 => 0101001
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [2,3,6,5,7,4,1,8] => 1001100 => 0011001
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [2,3,5,6,7,4,1,8] => 1001000 => 0001001
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [4,3,2,6,7,5,1,8] => 1110100 => 0010111
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [3,4,2,7,6,5,1,8] => 1100110 => 0110011
[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [3,2,4,6,7,5,1,8] => 1100100 => 0010011
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [2,3,4,7,6,5,1,8] => 1000110 => 0110001
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [2,3,4,6,7,5,1,8] => 1000100 => 0010001
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => 1111010 => 0101111
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [4,5,3,2,7,6,1,8] => 1110010 => 0100111
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [3,5,4,2,7,6,1,8] => 1101010 => 0101011
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [4,3,5,2,7,6,1,8] => 1110010 => 0100111
[[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [3,4,5,2,7,6,1,8] => 1100010 => 0100011
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => 1101010 => 0101011
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [4,3,2,5,7,6,1,8] => 1110010 => 0100111
[[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [3,4,2,5,7,6,1,8] => 1100010 => 0100011
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => 1000010 => 0100001
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => 1111100 => 0011111
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => 1111000 => 0001111
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => 1111000 => 0001111
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [3,6,5,4,2,7,1,8] => 1101100 => 0011011
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [3,4,6,5,2,7,1,8] => 1100100 => 0010011
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => 1111000 => 0001111
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => 1110000 => 0000111
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => 1101000 => 0001011
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => 1110000 => 0000111
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => 1100000 => 0000011
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [2,5,4,6,3,7,1,8] => 1011000 => 0001101
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [3,2,6,5,4,7,1,8] => 1101100 => 0011011
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [2,3,5,6,4,7,1,8] => 1001000 => 0001001
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [4,3,2,6,5,7,1,8] => 1110100 => 0010111
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [3,4,2,6,5,7,1,8] => 1100100 => 0010011
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [2,4,3,6,5,7,1,8] => 1010100 => 0010101
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => 1000100 => 0010001
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => 1111000 => 0001111
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [3,5,4,2,6,7,1,8] => 1101000 => 0001011
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => 1100000 => 0000011
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [2,5,4,3,6,7,1,8] => 1011000 => 0001101
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [2,4,5,3,6,7,1,8] => 1010000 => 0000101
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [2,3,5,4,6,7,1,8] => 1001000 => 0001001
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => 1110000 => 0000111
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => 1100000 => 0000011
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => 1100000 => 0000011
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 1000000 => 0000001
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => 0111110 => 0111110
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => 0111100 => 0011110
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,6,5,7,4,3,2,8] => 0111100 => 0011110
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,5,6,7,4,3,2,8] => 0111000 => 0001110
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,4,7,6,5,3,2,8] => 0110110 => 0110110
[[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,4,6,7,5,3,2,8] => 0110100 => 0010110
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,5,4,7,6,3,2,8] => 0111010 => 0101110
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,5,6,4,7,3,2,8] => 0111000 => 0001110
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,4,6,5,7,3,2,8] => 0110100 => 0010110
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,5,4,6,7,3,2,8] => 0111000 => 0001110
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => 0110000 => 0000110
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,3,7,6,5,4,2,8] => 0101110 => 0111010
[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,3,6,7,5,4,2,8] => 0101100 => 0011010
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,3,5,7,6,4,2,8] => 0101010 => 0101010
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,3,6,5,7,4,2,8] => 0101100 => 0011010
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,3,5,6,7,4,2,8] => 0101000 => 0001010
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => 0100100 => 0010010
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,3,5,4,7,6,2,8] => 0101010 => 0101010
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,4,3,5,7,6,2,8] => 0110010 => 0100110
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,3,4,5,7,6,2,8] => 0100010 => 0100010
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,5,4,6,3,7,2,8] => 0111000 => 0001110
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,4,5,6,3,7,2,8] => 0110000 => 0000110
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,3,6,5,4,7,2,8] => 0101100 => 0011010
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => 0101000 => 0001010
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,4,3,6,5,7,2,8] => 0110100 => 0010110
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,3,4,6,5,7,2,8] => 0100100 => 0010010
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,5,4,3,6,7,2,8] => 0111000 => 0001110
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,4,5,3,6,7,2,8] => 0110000 => 0000110
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,3,5,4,6,7,2,8] => 0101000 => 0001010
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,3,4,5,6,7,2,8] => 0100000 => 0000010
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [2,1,7,6,5,4,3,8] => 1011110 => 0111101
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [2,1,6,7,5,4,3,8] => 1011100 => 0011101
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [2,1,5,6,7,4,3,8] => 1011000 => 0001101
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [2,1,4,6,7,5,3,8] => 1010100 => 0010101
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [2,1,5,4,6,7,3,8] => 1011000 => 0001101
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [2,1,4,5,6,7,3,8] => 1010000 => 0000101
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8] => 0011110 => 0111100
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,2,6,7,5,4,3,8] => 0011100 => 0011100
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,2,5,7,6,4,3,8] => 0011010 => 0101100
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,2,5,6,7,4,3,8] => 0011000 => 0001100
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,2,4,6,7,5,3,8] => 0010100 => 0010100
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,2,5,6,4,7,3,8] => 0011000 => 0001100
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,2,5,4,6,7,3,8] => 0011000 => 0001100
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,2,4,5,6,7,3,8] => 0010000 => 0000100
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => 1101110 => 0111011
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [3,2,1,6,7,5,4,8] => 1101100 => 0011011
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [3,2,1,5,7,6,4,8] => 1101010 => 0101011
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [3,2,1,6,5,7,4,8] => 1101100 => 0011011
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [3,2,1,5,6,7,4,8] => 1101000 => 0001011
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [2,3,1,6,7,5,4,8] => 1001100 => 0011001
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [2,3,1,6,5,7,4,8] => 1001100 => 0011001
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => 1001000 => 0001001
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,3,2,7,6,5,4,8] => 0101110 => 0111010
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,3,2,6,7,5,4,8] => 0101100 => 0011010
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,3,2,5,7,6,4,8] => 0101010 => 0101010
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,3,2,6,5,7,4,8] => 0101100 => 0011010
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,3,2,5,6,7,4,8] => 0101000 => 0001010
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [2,1,3,6,7,5,4,8] => 1001100 => 0011001
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => 0001110 => 0111000
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => 0001100 => 0011000
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,2,3,5,7,6,4,8] => 0001010 => 0101000
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,2,3,6,5,7,4,8] => 0001100 => 0011000
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => 0001000 => 0001000
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => 1110110 => 0110111
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => 1110100 => 0010111
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8] => 1100110 => 0110011
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => 1100100 => 0010011
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8] => 1000110 => 0110001
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [2,3,4,1,6,7,5,8] => 1000100 => 0010001
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => 0110110 => 0110110
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,4,3,2,6,7,5,8] => 0110100 => 0010110
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => 0100100 => 0010010
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [2,1,4,3,6,7,5,8] => 1010100 => 0010101
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,2,4,3,6,7,5,8] => 0010100 => 0010100
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => 1100110 => 0110011
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => 1000100 => 0010001
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8] => 0100110 => 0110010
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [2,1,3,4,6,7,5,8] => 1000100 => 0010001
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => 0000110 => 0110000
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => 0000100 => 0010000
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8] => 1111010 => 0101111
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [4,5,3,2,1,7,6,8] => 1110010 => 0100111
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [3,5,4,2,1,7,6,8] => 1101010 => 0101011
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [3,4,5,2,1,7,6,8] => 1100010 => 0100011
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [2,5,4,3,1,7,6,8] => 1011010 => 0101101
[[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [2,4,5,3,1,7,6,8] => 1010010 => 0100101
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [3,2,5,4,1,7,6,8] => 1101010 => 0101011
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [2,3,5,4,1,7,6,8] => 1001010 => 0101001
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [3,4,2,5,1,7,6,8] => 1100010 => 0100011
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8] => 1010010 => 0100101
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [2,3,4,5,1,7,6,8] => 1000010 => 0100001
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => 0111010 => 0101110
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,4,5,3,2,7,6,8] => 0110010 => 0100110
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => 0101010 => 0101010
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,4,3,5,2,7,6,8] => 0110010 => 0100110
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => 0100010 => 0100010
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [2,1,5,4,3,7,6,8] => 1011010 => 0101101
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,2,4,5,3,7,6,8] => 0010010 => 0100100
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => 1101010 => 0101011
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => 1001010 => 0101001
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => 0101010 => 0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => 0001010 => 0101000
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => 1110010 => 0100111
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => 1100010 => 0100011
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [2,3,4,1,5,7,6,8] => 1000010 => 0100001
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => 0110010 => 0100110
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,3,4,2,5,7,6,8] => 0100010 => 0100010
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => 0010010 => 0100100
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [3,2,1,4,5,7,6,8] => 1100010 => 0100011
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8] => 1000010 => 0100001
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => 0100010 => 0100010
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => 1000010 => 0100001
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => 0000010 => 0100000
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 1111100 => 0011111
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => 1111000 => 0001111
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => 1111000 => 0001111
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => 1110000 => 0000111
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [3,6,5,4,2,1,7,8] => 1101100 => 0011011
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [4,3,6,5,2,1,7,8] => 1110100 => 0010111
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => 1111000 => 0001111
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => 1100000 => 0000011
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [2,4,6,5,3,1,7,8] => 1010100 => 0010101
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [2,4,5,6,3,1,7,8] => 1010000 => 0000101
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [2,3,6,5,4,1,7,8] => 1001100 => 0011001
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [2,3,5,6,4,1,7,8] => 1001000 => 0001001
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [4,3,2,6,5,1,7,8] => 1110100 => 0010111
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [2,4,3,6,5,1,7,8] => 1010100 => 0010101
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => 1000100 => 0010001
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => 1111000 => 0001111
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => 1110000 => 0000111
[[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [3,5,4,2,6,1,7,8] => 1101000 => 0001011
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => 1110000 => 0000111
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => 1100000 => 0000011
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => 1001000 => 0001001
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => 1110000 => 0000111
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => 1100000 => 0000011
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => 1100000 => 0000011
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 1000000 => 0000001
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => 0111100 => 0011110
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,5,6,4,3,2,7,8] => 0111000 => 0001110
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,4,6,5,3,2,7,8] => 0110100 => 0010110
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,5,4,6,3,2,7,8] => 0111000 => 0001110
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,4,5,6,3,2,7,8] => 0110000 => 0000110
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => 0101000 => 0001010
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,4,3,6,5,2,7,8] => 0110100 => 0010110
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,5,4,3,6,2,7,8] => 0111000 => 0001110
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,4,5,3,6,2,7,8] => 0110000 => 0000110
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,3,5,4,6,2,7,8] => 0101000 => 0001010
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,4,3,5,6,2,7,8] => 0110000 => 0000110
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => 0100000 => 0000010
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [2,1,5,6,4,3,7,8] => 1011000 => 0001101
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [2,1,4,6,5,3,7,8] => 1010100 => 0010101
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => 0011100 => 0011100
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => 0011000 => 0001100
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,2,4,6,5,3,7,8] => 0010100 => 0010100
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => 0010000 => 0000100
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [3,2,1,6,5,4,7,8] => 1101100 => 0011011
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [3,2,1,5,6,4,7,8] => 1101000 => 0001011
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [2,3,1,6,5,4,7,8] => 1001100 => 0011001
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [2,3,1,5,6,4,7,8] => 1001000 => 0001001
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => 0101100 => 0011010
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,3,2,5,6,4,7,8] => 0101000 => 0001010
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => 0001100 => 0011000
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,2,3,5,6,4,7,8] => 0001000 => 0001000
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => 1110100 => 0010111
[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [2,4,3,1,6,5,7,8] => 1010100 => 0010101
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => 1100100 => 0010011
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [2,3,4,1,6,5,7,8] => 1000100 => 0010001
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => 1010100 => 0010101
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => 0010100 => 0010100
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => 0100100 => 0010010
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => 1000100 => 0010001
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => 0000100 => 0010000
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 1111000 => 0001111
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => 1110000 => 0000111
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [3,5,4,2,1,6,7,8] => 1101000 => 0001011
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => 1110000 => 0000111
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => 1100000 => 0000011
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [2,5,4,3,1,6,7,8] => 1011000 => 0001101
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => 1010000 => 0000101
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [3,2,5,4,1,6,7,8] => 1101000 => 0001011
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [2,3,5,4,1,6,7,8] => 1001000 => 0001001
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => 1110000 => 0000111
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => 1100000 => 0000011
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => 1010000 => 0000101
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => 1100000 => 0000011
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 1000000 => 0000001
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => 0111000 => 0001110
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,4,5,3,2,6,7,8] => 0110000 => 0000110
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,3,5,4,2,6,7,8] => 0101000 => 0001010
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => 0100000 => 0000010
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8] => 1011000 => 0001101
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => 1010000 => 0000101
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => 0011000 => 0001100
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [3,2,1,5,4,6,7,8] => 1101000 => 0001011
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [2,3,1,5,4,6,7,8] => 1001000 => 0001001
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => 0101000 => 0001010
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8] => 1001000 => 0001001
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => 0001000 => 0001000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 1110000 => 0000111
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => 1100000 => 0000011
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => 1010000 => 0000101
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => 1100000 => 0000011
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => 1000000 => 0000001
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => 0110000 => 0000110
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => 0100000 => 0000010
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => 1010000 => 0000101
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => 0010000 => 0000100
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 1100000 => 0000011
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => 1000000 => 0000001
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => 0100000 => 0000010
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 1000000 => 0000001
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 0000000 => 0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 11111111 => 11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => 11111110 => 01111111
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => 11111100 => 00111111
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => 11111000 => 00011111
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => 11110000 => 00001111
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => 11100000 => 00000111
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => 11000000 => 00000011
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 10000000 => 00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 00000000 => 00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => 111111110 => 011111111
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [7,9,8,6,5,4,3,2,1] => 11111101 => 10111111
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => 111111100 => 001111111
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => 111111000 => 000111111
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => 111110000 => 000011111
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => 111100000 => 000001111
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [3,5,6,7,8,9,4,2,1] => 11010000 => 00001011
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => 111000000 => 000000111
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [2,4,5,6,7,8,9,3,1] => 10100000 => 00000101
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => 110000000 => 000000011
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,2] => 01000000 => 00000010
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 100000000 => 000000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => 11111110 => 01111111
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => 11111110 => 01111111
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => 11111110 => 01111111
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => 11111110 => 01111111
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => 11111110 => 01111111
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => 11111110 => 01111111
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 11111110 => 01111111
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => 111111110 => 011111111
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [6,8,7,9,5,4,3,2,1] => 11111010 => 01011111
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => 111111110 => 011111111
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [5,8,7,6,9,4,3,2,1] => 11110110 => 01101111
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => 111111110 => 011111111
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [4,8,7,6,5,9,3,2,1] => 11101110 => 01110111
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => 111111110 => 011111111
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [3,8,7,6,5,4,9,2,1] => 11011110 => 01111011
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => 111111110 => 011111111
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [2,8,7,6,5,4,3,9,1] => 10111110 => 01111101
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => 111111110 => 011111111
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,8,7,6,5,4,3,2,9] => 01111110 => 01111110
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => 111111110 => 011111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 111111110 => 011111111
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,3,5,7,9,10,8,6,4,2] => 010101010 => 010101010
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [1,6,7,5,8,4,9,3,10,2] => 011110000 => 000011110
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => 111100000 => 000001111
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,10,9,1] => 101010101 => 101010101
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,1,4,6,5,3,8,10,9,7] => 101010101 => 101010101
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,1,4,6,5,3,8,7,10,9] => 101010101 => 101010101
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,9,8,1,10] => 110101010 => 010101011
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => 101010101 => 101010101
[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,10,9,12,11,1] => 10101010101 => 10101010101
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3,8,7,10,12,11,9] => 10101010101 => 10101010101
[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,10,9,7,12,11] => 10101010101 => 10101010101
[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [2,1,4,6,5,3,8,7,10,9,12,11] => 10101010101 => 10101010101
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,9,8,11,10,1,12] => 11010101010 => 01010101011
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => 10101010101 => 10101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => 00000001 => 10000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => 000000001 => 100000000
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,9,8] => 10000001 => 10000001
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 11000000 => 00000011
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001 => 1000000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,8,10,9] => 100000001 => 100000001
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,3,2,4,5,6,7,9,8] => 01000001 => 10000010
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [2,3,1,4,5,6,7,9,8] => 10000001 => 10000001
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [2,4,3,5,6,7,8,9,1] => 10100000 => 00000101
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 11000000 => 00000011
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 110000000 => 000000011
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 1000000000 => 0000000001
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => 00000010 => 01000000
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,7,8,9,6] => 00000100 => 00100000
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,6,7,8,9,5] => 00001000 => 00010000
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,5,6,7,8,9,4] => 00010000 => 00001000
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,3] => 00100000 => 00000100
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => 00000011 => 11000000
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,7,9,10,8] => 000000010 => 010000000
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,5,8,7,9,6] => 00000110 => 01100000
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,6,8,9,10,7] => 000000100 => 001000000
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,4,7,6,8,9,5] => 00001100 => 00110000
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,5,7,8,9,10,6] => 000001000 => 000100000
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [1,2,3,6,5,7,8,9,4] => 00011000 => 00011000
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,4,6,7,8,9,10,5] => 000010000 => 000010000
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [1,2,5,4,6,7,8,9,3] => 00110000 => 00001100
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,3,5,6,7,8,9,10,4] => 000100000 => 000001000
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,4,3,5,6,7,8,9,2] => 01100000 => 00000110
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,10,3] => 001000000 => 000000100
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,10,2] => 010000000 => 000000010
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => 01111111 => 11111110
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 11111100 => 00111111
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => 01111110 => 01111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 111111110
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110 => 0111111111
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 111111100 => 001111111
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 11111100 => 00111111
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,8,7,9,6,5,4,3,2] => 01111110 => 01111110
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,9,10,8,7,6,5,4,3,2] => 011111110 => 011111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 1111111110
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => 111110000 => 000011111
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [5,4,7,6,8,3,9,2,10,1] => 111101000 => 000101111
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [4,3,7,6,8,5,9,2,10,1] => 111011000 => 000110111
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [5,4,6,3,8,7,9,2,10,1] => 111100100 => 001001111
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [4,3,6,5,8,7,9,2,10,1] => 111010100 => 001010111
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [3,2,7,6,8,5,9,4,10,1] => 110111000 => 000111011
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [3,2,6,5,8,7,9,4,10,1] => 110110100 => 001011011
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [4,3,5,2,8,7,9,6,10,1] => 111001100 => 001100111
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [3,2,5,4,8,7,9,6,10,1] => 110101100 => 001101011
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [5,4,6,3,7,2,9,8,10,1] => 111100010 => 010001111
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [4,3,6,5,7,2,9,8,10,1] => 111010010 => 010010111
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [3,2,6,5,7,4,9,8,10,1] => 110110010 => 010011011
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [4,3,5,2,7,6,9,8,10,1] => 111001010 => 010100111
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,10,1] => 110101010 => 010101011
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [2,1,7,6,8,5,9,4,10,3] => 101111000 => 000111101
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [2,1,6,5,8,7,9,4,10,3] => 101110100 => 001011101
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [2,1,5,4,8,7,9,6,10,3] => 101101100 => 001101101
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [2,1,6,5,7,4,9,8,10,3] => 101110010 => 010011101
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [2,1,5,4,7,6,9,8,10,3] => 101101010 => 010101101
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [3,2,4,1,8,7,9,6,10,5] => 110011100 => 001110011
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [3,2,4,1,7,6,9,8,10,5] => 110011010 => 010110011
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,4,3,8,7,9,6,10,5] => 101011100 => 001110101
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,4,3,7,6,9,8,10,5] => 101011010 => 010110101
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [4,3,5,2,6,1,9,8,10,7] => 111000110 => 011000111
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [3,2,5,4,6,1,9,8,10,7] => 110100110 => 011001011
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [2,1,5,4,6,3,9,8,10,7] => 101100110 => 011001101
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [3,2,4,1,6,5,9,8,10,7] => 110010110 => 011010011
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,6,5,9,8,10,7] => 101010110 => 011010101
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [5,4,6,3,7,2,8,1,10,9] => 111100001 => 100001111
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [4,3,6,5,7,2,8,1,10,9] => 111010001 => 100010111
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [3,2,6,5,7,4,8,1,10,9] => 110110001 => 100011011
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [4,3,5,2,7,6,8,1,10,9] => 111001001 => 100100111
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,7,6,8,1,10,9] => 110101001 => 100101011
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [2,1,6,5,7,4,8,3,10,9] => 101110001 => 100011101
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [2,1,5,4,7,6,8,3,10,9] => 101101001 => 100101101
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [3,2,4,1,7,6,8,5,10,9] => 110011001 => 100110011
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,4,3,7,6,8,5,10,9] => 101011001 => 100110101
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [4,3,5,2,6,1,8,7,10,9] => 111000101 => 101000111
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => [3,2,5,4,6,1,8,7,10,9] => 110100101 => 101001011
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [2,1,5,4,6,3,8,7,10,9] => 101100101 => 101001101
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7,10,9] => 110010101 => 101010011
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [7,6,8,5,9,4,10,3,11,2,12,1] => 11111100000 => 00000111111
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]] => [6,5,8,7,9,4,10,3,11,2,12,1] => 11111010000 => 00001011111
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]] => [5,4,8,7,9,6,10,3,11,2,12,1] => 11110110000 => 00001101111
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]] => [6,5,7,4,9,8,10,3,11,2,12,1] => 11111001000 => 00010011111
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]] => [5,4,7,6,9,8,10,3,11,2,12,1] => 11110101000 => 00010101111
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]] => [4,3,8,7,9,6,10,5,11,2,12,1] => 11101110000 => 00001110111
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]] => [4,3,7,6,9,8,10,5,11,2,12,1] => 11101101000 => 00010110111
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]] => [5,4,6,3,9,8,10,7,11,2,12,1] => 11110011000 => 00011001111
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]] => [4,3,6,5,9,8,10,7,11,2,12,1] => 11101011000 => 00011010111
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]] => [6,5,7,4,8,3,10,9,11,2,12,1] => 11111000100 => 00100011111
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => [5,4,7,6,8,3,10,9,11,2,12,1] => 11110100100 => 00100101111
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => [4,3,7,6,8,5,10,9,11,2,12,1] => 11101100100 => 00100110111
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => [5,4,6,3,8,7,10,9,11,2,12,1] => 11110010100 => 00101001111
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => [4,3,6,5,8,7,10,9,11,2,12,1] => 11101010100 => 00101010111
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [3,2,8,7,9,6,10,5,11,4,12,1] => 11011110000 => 00001111011
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [3,2,7,6,9,8,10,5,11,4,12,1] => 11011101000 => 00010111011
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [3,2,6,5,9,8,10,7,11,4,12,1] => 11011011000 => 00011011011
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [3,2,7,6,8,5,10,9,11,4,12,1] => 11011100100 => 00100111011
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [3,2,6,5,8,7,10,9,11,4,12,1] => 11011010100 => 00101011011
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => [4,3,5,2,9,8,10,7,11,6,12,1] => 11100111000 => 00011100111
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]] => [4,3,5,2,8,7,10,9,11,6,12,1] => 11100110100 => 00101100111
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [3,2,5,4,9,8,10,7,11,6,12,1] => 11010111000 => 00011101011
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [3,2,5,4,8,7,10,9,11,6,12,1] => 11010110100 => 00101101011
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => [5,4,6,3,7,2,10,9,11,8,12,1] => 11110001100 => 00110001111
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]] => [4,3,6,5,7,2,10,9,11,8,12,1] => 11101001100 => 00110010111
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,10,9,11,8,12,1] => 11011001100 => 00110011011
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]] => [4,3,5,2,7,6,10,9,11,8,12,1] => 11100101100 => 00110100111
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [3,2,5,4,7,6,10,9,11,8,12,1] => 11010101100 => 00110101011
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => [6,5,7,4,8,3,9,2,11,10,12,1] => 11111000010 => 01000011111
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => [5,4,7,6,8,3,9,2,11,10,12,1] => 11110100010 => 01000101111
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => [4,3,7,6,8,5,9,2,11,10,12,1] => 11101100010 => 01000110111
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => [5,4,6,3,8,7,9,2,11,10,12,1] => 11110010010 => 01001001111
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => [4,3,6,5,8,7,9,2,11,10,12,1] => 11101010010 => 01001010111
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [3,2,7,6,8,5,9,4,11,10,12,1] => 11011100010 => 01000111011
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [3,2,6,5,8,7,9,4,11,10,12,1] => 11011010010 => 01001011011
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,8,7,9,6,11,10,12,1] => 11100110010 => 01001100111
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [3,2,5,4,8,7,9,6,11,10,12,1] => 11010110010 => 01001101011
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]] => [5,4,6,3,7,2,9,8,11,10,12,1] => 11110001010 => 01010001111
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => [4,3,6,5,7,2,9,8,11,10,12,1] => 11101001010 => 01010010111
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [3,2,6,5,7,4,9,8,11,10,12,1] => 11011001010 => 01010011011
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => [4,3,5,2,7,6,9,8,11,10,12,1] => 11100101010 => 01010100111
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,11,10,12,1] => 11010101010 => 01010101011
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [2,1,8,7,9,6,10,5,11,4,12,3] => 10111110000 => 00001111101
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [2,1,7,6,9,8,10,5,11,4,12,3] => 10111101000 => 00010111101
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [2,1,6,5,9,8,10,7,11,4,12,3] => 10111011000 => 00011011101
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [2,1,7,6,8,5,10,9,11,4,12,3] => 10111100100 => 00100111101
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [2,1,6,5,8,7,10,9,11,4,12,3] => 10111010100 => 00101011101
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [2,1,5,4,9,8,10,7,11,6,12,3] => 10110111000 => 00011101101
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [2,1,5,4,8,7,10,9,11,6,12,3] => 10110110100 => 00101101101
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,10,9,11,8,12,3] => 10111001100 => 00110011101
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [2,1,5,4,7,6,10,9,11,8,12,3] => 10110101100 => 00110101101
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [2,1,7,6,8,5,9,4,11,10,12,3] => 10111100010 => 01000111101
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [2,1,6,5,8,7,9,4,11,10,12,3] => 10111010010 => 01001011101
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [2,1,5,4,8,7,9,6,11,10,12,3] => 10110110010 => 01001101101
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [2,1,6,5,7,4,9,8,11,10,12,3] => 10111001010 => 01010011101
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [2,1,5,4,7,6,9,8,11,10,12,3] => 10110101010 => 01010101101
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [3,2,4,1,9,8,10,7,11,6,12,5] => 11001111000 => 00011110011
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [3,2,4,1,8,7,10,9,11,6,12,5] => 11001110100 => 00101110011
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,4,1,7,6,10,9,11,8,12,5] => 11001101100 => 00110110011
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [3,2,4,1,8,7,9,6,11,10,12,5] => 11001110010 => 01001110011
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,4,1,7,6,9,8,11,10,12,5] => 11001101010 => 01010110011
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [2,1,4,3,9,8,10,7,11,6,12,5] => 10101111000 => 00011110101
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [2,1,4,3,8,7,10,9,11,6,12,5] => 10101110100 => 00101110101
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [2,1,4,3,7,6,10,9,11,8,12,5] => 10101101100 => 00110110101
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [2,1,4,3,8,7,9,6,11,10,12,5] => 10101110010 => 01001110101
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [2,1,4,3,7,6,9,8,11,10,12,5] => 10101101010 => 01010110101
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1,10,9,11,8,12,7] => 11100011100 => 00111000111
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => [4,3,5,2,6,1,9,8,11,10,12,7] => 11100011010 => 01011000111
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [3,2,5,4,6,1,10,9,11,8,12,7] => 11010011100 => 00111001011
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1,9,8,11,10,12,7] => 11010011010 => 01011001011
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [2,1,5,4,6,3,10,9,11,8,12,7] => 10110011100 => 00111001101
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,6,3,9,8,11,10,12,7] => 10110011010 => 01011001101
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [3,2,4,1,6,5,10,9,11,8,12,7] => 11001011100 => 00111010011
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [3,2,4,1,6,5,9,8,11,10,12,7] => 11001011010 => 01011010011
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,4,3,6,5,10,9,11,8,12,7] => 10101011100 => 00111010101
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,4,3,6,5,9,8,11,10,12,7] => 10101011010 => 01011010101
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]] => [5,4,6,3,7,2,8,1,11,10,12,9] => 11110000110 => 01100001111
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => [4,3,6,5,7,2,8,1,11,10,12,9] => 11101000110 => 01100010111
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [3,2,6,5,7,4,8,1,11,10,12,9] => 11011000110 => 01100011011
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => [4,3,5,2,7,6,8,1,11,10,12,9] => 11100100110 => 01100100111
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [3,2,5,4,7,6,8,1,11,10,12,9] => 11010100110 => 01100101011
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [2,1,6,5,7,4,8,3,11,10,12,9] => 10111000110 => 01100011101
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [2,1,5,4,7,6,8,3,11,10,12,9] => 10110100110 => 01100101101
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5,11,10,12,9] => 11001100110 => 01100110011
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5,11,10,12,9] => 10101100110 => 01100110101
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]] => [4,3,5,2,6,1,8,7,11,10,12,9] => 11100010110 => 01101000111
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [3,2,5,4,6,1,8,7,11,10,12,9] => 11010010110 => 01101001011
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3,8,7,11,10,12,9] => 10110010110 => 01101001101
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [3,2,4,1,6,5,8,7,11,10,12,9] => 11001010110 => 01101010011
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,6,5,8,7,11,10,12,9] => 10101010110 => 01101010101
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => [6,5,7,4,8,3,9,2,10,1,12,11] => 11111000001 => 10000011111
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]] => [5,4,7,6,8,3,9,2,10,1,12,11] => 11110100001 => 10000101111
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]] => [4,3,7,6,8,5,9,2,10,1,12,11] => 11101100001 => 10000110111
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => [5,4,6,3,8,7,9,2,10,1,12,11] => 11110010001 => 10001001111
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]] => [4,3,6,5,8,7,9,2,10,1,12,11] => 11101010001 => 10001010111
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [3,2,7,6,8,5,9,4,10,1,12,11] => 11011100001 => 10000111011
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [3,2,6,5,8,7,9,4,10,1,12,11] => 11011010001 => 10001011011
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,8,7,9,6,10,1,12,11] => 11100110001 => 10001100111
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [3,2,5,4,8,7,9,6,10,1,12,11] => 11010110001 => 10001101011
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => [5,4,6,3,7,2,9,8,10,1,12,11] => 11110001001 => 10010001111
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => [4,3,6,5,7,2,9,8,10,1,12,11] => 11101001001 => 10010010111
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [3,2,6,5,7,4,9,8,10,1,12,11] => 11011001001 => 10010011011
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => [4,3,5,2,7,6,9,8,10,1,12,11] => 11100101001 => 10010100111
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,7,6,9,8,10,1,12,11] => 11010101001 => 10010101011
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [2,1,7,6,8,5,9,4,10,3,12,11] => 10111100001 => 10000111101
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [2,1,6,5,8,7,9,4,10,3,12,11] => 10111010001 => 10001011101
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [2,1,5,4,8,7,9,6,10,3,12,11] => 10110110001 => 10001101101
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [2,1,6,5,7,4,9,8,10,3,12,11] => 10111001001 => 10010011101
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [2,1,5,4,7,6,9,8,10,3,12,11] => 10110101001 => 10010101101
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [3,2,4,1,8,7,9,6,10,5,12,11] => 11001110001 => 10001110011
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,4,1,7,6,9,8,10,5,12,11] => 11001101001 => 10010110011
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [2,1,4,3,8,7,9,6,10,5,12,11] => 10101110001 => 10001110101
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [2,1,4,3,7,6,9,8,10,5,12,11] => 10101101001 => 10010110101
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => [4,3,5,2,6,1,9,8,10,7,12,11] => 11100011001 => 10011000111
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [3,2,5,4,6,1,9,8,10,7,12,11] => 11010011001 => 10011001011
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,9,8,10,7,12,11] => 10110011001 => 10011001101
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5,9,8,10,7,12,11] => 11001011001 => 10011010011
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,4,3,6,5,9,8,10,7,12,11] => 10101011001 => 10011010101
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]] => [5,4,6,3,7,2,8,1,10,9,12,11] => 11110000101 => 10100001111
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]] => [4,3,6,5,7,2,8,1,10,9,12,11] => 11101000101 => 10100010111
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [3,2,6,5,7,4,8,1,10,9,12,11] => 11011000101 => 10100011011
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => [4,3,5,2,7,6,8,1,10,9,12,11] => 11100100101 => 10100100111
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]] => [3,2,5,4,7,6,8,1,10,9,12,11] => 11010100101 => 10100101011
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [2,1,6,5,7,4,8,3,10,9,12,11] => 10111000101 => 10100011101
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => [2,1,5,4,7,6,8,3,10,9,12,11] => 10110100101 => 10100101101
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,7,6,8,5,10,9,12,11] => 11001100101 => 10100110011
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [2,1,4,3,7,6,8,5,10,9,12,11] => 10101100101 => 10100110101
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => [4,3,5,2,6,1,8,7,10,9,12,11] => 11100010101 => 10101000111
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => [3,2,5,4,6,1,8,7,10,9,12,11] => 11010010101 => 10101001011
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [2,1,5,4,6,3,8,7,10,9,12,11] => 10110010101 => 10101001101
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7,10,9,12,11] => 11001010101 => 10101010011
[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,10,9,2] => 011010101 => 101010110
[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,10,9,12,11,2] => 01101010101 => 10101010110
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [2,1,9,8,7,6,5,4,3] => 10111111 => 11111101
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [3,2,1,9,8,7,6,5,4] => 11011111 => 11111011
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [4,3,2,1,9,8,7,6,5] => 11101111 => 11110111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [5,4,3,2,1,9,8,7,6] => 11110111 => 11101111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [6,5,4,3,2,1,9,8,7] => 11111011 => 11011111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [7,6,5,4,3,2,1,9,8] => 11111101 => 10111111
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,9,8,7,6,5,4,3] => 00111111 => 11111100
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 111111101
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [2,3,1,9,8,7,6,5,4] => 10011111 => 11111001
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [3,2,1,10,9,8,7,6,5,4] => 110111111 => 111111011
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]] => [3,4,2,1,9,8,7,6,5] => 11001111 => 11110011
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => 111011111 => 111110111
[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => [4,5,3,2,1,9,8,7,6] => 11100111 => 11100111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [5,4,3,2,1,10,9,8,7,6] => 111101111 => 111101111
[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => [5,6,4,3,2,1,9,8,7] => 11110011 => 11001111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => 111110111 => 111011111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [6,7,5,4,3,2,1,9,8] => 11111001 => 10011111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [7,6,5,4,3,2,1,10,9,8] => 111111011 => 110111111
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => 111111101 => 101111111
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 11111100 => 00111111
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 11111000 => 00011111
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 11110000 => 00001111
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 11100000 => 00000111
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 11000000 => 00000011
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 10000000 => 00000001
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 111111100 => 001111111
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 111111000 => 000111111
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 111110000 => 000011111
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 111100000 => 000001111
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 111000000 => 000000111
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,4,3,2,5,6,7,8,9] => 01100000 => 00000110
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 110000000 => 000000011
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9] => 01000000 => 00000010
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 100000000 => 000000001
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [4,9,8,7,6,5,3,2,1] => 11101111 => 11110111
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [3,9,8,7,6,5,4,2,1] => 11011111 => 11111011
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => 10111111 => 11111101
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [6,10,9,8,7,5,4,3,2,1] => 111110111 => 111011111
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,8,7,5,10,9] => 101010101 => 101010101
[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => [2,4,3,1,6,5,8,10,9,7] => 101010101 => 101010101
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7,10,9] => 101010101 => 101010101
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,3,6,8,7,5,10,9] => 101010101 => 101010101
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,5,8,10,9,7] => 101010101 => 101010101
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5,10,12,11,9] => 10101010101 => 10101010101
[[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,8,7,5,10,9,12,11] => 10101010101 => 10101010101
[[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5,8,10,9,7,12,11] => 10101010101 => 10101010101
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,4,3,1,6,5,8,7,10,12,11,9] => 10101010101 => 10101010101
[[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7,10,9,12,11] => 10101010101 => 10101010101
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5,10,12,11,9] => 10101010101 => 10101010101
[[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,1,4,3,6,8,7,5,10,9,12,11] => 10101010101 => 10101010101
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,3,6,5,8,10,9,7,12,11] => 10101010101 => 10101010101
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,5,8,7,10,12,11,9] => 10101010101 => 10101010101
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,9,8,1] => 10000001 => 10000001
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000 => 0000000001
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [2,1,3,4,5,6,8,7,9] => 10000010 => 01000001
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [2,1,3,4,5,6,8,9,7] => 10000010 => 01000001
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [2,3,4,5,6,8,9,7,1] => 10000010 => 01000001
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,8,10,9,1] => 100000001 => 100000001
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [2,1,4,3,5,6,7,8,9] => 10100000 => 00000101
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [3,2,1,5,4,6,7,8,9] => 11010000 => 00001011
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [6,5,4,3,2,1,8,7,9] => 11111010 => 01011111
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => 11000000 => 00000011
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 10000000 => 00000001
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => 10000000 => 00000001
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 10000000 => 00000001
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10] => 100000000 => 000000001
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [2,4,3,1,5,6,7,8,9] => 10100000 => 00000101
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [2,3,5,4,1,6,7,8,9] => 10010000 => 00001001
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [2,3,4,6,5,1,7,8,9] => 10001000 => 00010001
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [2,3,4,5,7,6,1,8,9] => 10000100 => 00100001
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [2,3,4,5,6,8,7,1,9] => 10000010 => 01000001
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 100000000 => 000000001
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9] => 00100000 => 00000100
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,2,3,5,4,6,7,8,9] => 00010000 => 00001000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,6,5,7,8,9] => 00001000 => 00010000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,7,6,8,9] => 00000100 => 00100000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,8,7,9] => 00000010 => 01000000
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9,10] => 010000000 => 000000010
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9,10] => 001000000 => 000000100
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,2,3,5,4,6,7,8,9,10] => 000100000 => 000001000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,2,3,4,6,5,7,8,9,10] => 000010000 => 000010000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,5,7,6,8,9,10] => 000001000 => 000100000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,6,8,7,9,10] => 000000100 => 001000000
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,9,8,10] => 000000010 => 010000000
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [1,3,4,5,6,7,9,8,2] => 01000001 => 10000010
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [7,6,5,4,3,2,9,8,1] => 11111101 => 10111111
[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,1] => 11100000 => 00000111
[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => [5,4,3,2,6,7,8,9,1] => 11110000 => 00001111
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => 11111000 => 00011111
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => [7,6,5,4,3,2,8,9,1] => 11111100 => 00111111
[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,10,1] => 111000000 => 000000111
[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]] => [5,4,3,2,6,7,8,9,10,1] => 111100000 => 000001111
[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]] => [6,5,4,3,2,7,8,9,10,1] => 111110000 => 000011111
[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]] => [7,6,5,4,3,2,8,9,10,1] => 111111000 => 000111111
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]] => [8,7,6,5,4,3,2,9,10,1] => 111111100 => 001111111
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,7,6,5,4,3,2,9,8] => 01111101 => 10111110
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [6,5,4,3,2,1,8,9,7] => 11111010 => 01011111
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000 => 0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,2,10,9,8,7,6,5,4,3] => 001111111 => 111111100
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,3,2,9,8,7,6,5,4] => 01011111 => 11111010
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [2,1,8,7,6,5,4,3,9] => 10111110 => 01111101
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,9,8,7,6,5,4,3,2,10] => 011111110 => 011111110
[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [2,8,7,9,6,5,4,3,1] => 10111110 => 01111101
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [1,3,4,5,2,6,7,8,9] => 01000000 => 00000010
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [1,2,4,5,3,6,7,8,9] => 00100000 => 00000100
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [2,1,4,5,3,6,7,8,9] => 10100000 => 00000101
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [1,3,2,5,4,6,7,8,9] => 01010000 => 00001010
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [8,7,6,5,4,3,2,10,9,1] => 111111101 => 101111111
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [2,1,4,5,6,7,8,9,3] => 10100000 => 00000101
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,3,4,5,6,7,8,2,9] => 01000000 => 00000010
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,7,10,9,8] => 000000011 => 110000000
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => 11111000 => 00011111
[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.] => [6,5,7,8,4,3,2,1,9] => 11111000 => 00011111
[[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.] => [6,5,4,7,8,3,2,1,9] => 11111000 => 00011111
[[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.] => [6,5,4,3,7,8,2,1,9] => 11111000 => 00011111
[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => [6,5,4,3,2,7,8,1,9] => 11111000 => 00011111
[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]] => [5,4,3,2,1,7,8,9,6] => 11110100 => 00101111
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => 111111000 => 000111111
[[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]] => [4,3,2,1,6,7,8,9,5] => 11101000 => 00010111
[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.] => [7,6,8,9,5,4,3,2,1,10] => 111111000 => 000111111
[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.] => [7,6,5,8,9,4,3,2,1,10] => 111111000 => 000111111
[[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.] => [7,6,5,4,8,9,3,2,1,10] => 111111000 => 000111111
[[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.] => [7,6,5,4,3,8,9,2,1,10] => 111111000 => 000111111
[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.] => [7,6,5,4,3,2,8,9,1,10] => 111111000 => 000111111
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,9,8,7,6] => 00000111 => 11100000
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,9,8,7,6,5] => 00001111 => 11110000
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,9,8,7,6,5,4] => 00011111 => 11111000
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,7,6,9,8] => 00000101 => 10100000
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,6,10,9,8,7] => 000000111 => 111000000
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,4,6,5,9,8,7] => 00001011 => 11010000
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,5,10,9,8,7,6] => 000001111 => 111100000
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,3,5,4,9,8,7,6] => 00010111 => 11101000
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,4,10,9,8,7,6,5] => 000011111 => 111110000
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,2,4,3,9,8,7,6,5] => 00101111 => 11110100
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,3,10,9,8,7,6,5,4] => 000111111 => 111111000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,6,8,7,10,9] => 000000101 => 101000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => 1111111110 => 0111111111
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [1,9,8,10,7,6,5,4,3,2] => 011111110 => 011111110
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [2,8,9,7,6,5,4,3,1] => 10111110 => 01111101
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => 1111111110 => 0111111111
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => 11111100 => 00111111
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => 11000000 => 00000011
[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10,11] => 1000000000 => 0000000001
[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9,10] => 110000000 => 000000011
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.] => [3,4,2,5,1,6,7,8,9] => 11000000 => 00000011
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => 11111100 => 00111111
[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.] => [6,5,8,7,4,3,2,1,9] => 11111010 => 01011111
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => [7,6,5,8,4,3,2,1,9] => 11111100 => 00111111
[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.] => [6,7,5,8,4,3,2,1,9] => 11111000 => 00011111
[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]] => [4,3,2,1,8,9,7,6,5] => 11101110 => 01110111
[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [2,3,1,5,4,6,7,8,9] => 10010000 => 00001001
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => 11100000 => 00000111
[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]] => [4,3,2,1,6,7,8,9,10,5] => 111010000 => 000010111
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => 11000000 => 00000011
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [5,4,3,2,1,8,7,6,9] => 11110110 => 01101111
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [7,6,5,4,3,2,1,9,8,10] => 111111010 => 010111111
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [2,3,9,8,7,6,5,4,1] => 10011111 => 11111001
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [2,8,7,6,5,4,3,1,9] => 10111110 => 01111101
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [2,3,4,5,6,7,1,9,8] => 10000001 => 10000001
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,3,4,2,5,6,7,8,9] => 01000000 => 00000010
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => [8,7,6,5,4,3,2,9,1,10] => 111111100 => 001111111
[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [1,4,5,6,7,8,3,9,2] => 01100000 => 00000110
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010 => 0100000000
[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]] => [2,1,3,5,6,7,8,9,4] => 10010000 => 00001001
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.] => [5,6,4,3,2,1,7,8,9] => 11110000 => 00001111
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => [5,6,4,3,2,1,7,8,9,10] => 111100000 => 000001111
[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.] => [6,7,5,4,3,2,1,8,9,10,11] => 1111100000 => 0000011111
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.] => [6,7,5,4,3,2,1,8,9,10] => 111110000 => 000011111
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.] => [5,6,4,3,2,7,1,8,9] => 11110000 => 00001111
[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]] => [1,2,5,6,7,4,8,9,3] => 00110000 => 00001100
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => 11111000 => 00011111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [7,6,5,4,3,2,1,9,10,8] => 111111010 => 010111111
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
Map
reverse
Description
Return the reversal of a binary word.
searching the database
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