Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Images
[.,.] => [1] => =>
[.,[.,.]] => [2,1] => 1 => 0
[[.,.],.] => [1,2] => 0 => 1
[.,[.,[.,.]]] => [3,2,1] => 11 => 00
[.,[[.,.],.]] => [2,3,1] => 10 => 01
[[.,.],[.,.]] => [1,3,2] => 01 => 10
[[.,[.,.]],.] => [2,1,3] => 10 => 01
[[[.,.],.],.] => [1,2,3] => 00 => 11
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 111 => 000
[.,[.,[[.,.],.]]] => [3,4,2,1] => 110 => 001
[.,[[.,.],[.,.]]] => [2,4,3,1] => 101 => 010
[.,[[.,[.,.]],.]] => [3,2,4,1] => 110 => 001
[.,[[[.,.],.],.]] => [2,3,4,1] => 100 => 011
[[.,.],[.,[.,.]]] => [1,4,3,2] => 011 => 100
[[.,.],[[.,.],.]] => [1,3,4,2] => 010 => 101
[[.,[.,.]],[.,.]] => [2,1,4,3] => 101 => 010
[[[.,.],.],[.,.]] => [1,2,4,3] => 001 => 110
[[.,[.,[.,.]]],.] => [3,2,1,4] => 110 => 001
[[.,[[.,.],.]],.] => [2,3,1,4] => 100 => 011
[[[.,.],[.,.]],.] => [1,3,2,4] => 010 => 101
[[[.,[.,.]],.],.] => [2,1,3,4] => 100 => 011
[[[[.,.],.],.],.] => [1,2,3,4] => 000 => 111
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 1111 => 0000
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 1110 => 0001
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 1101 => 0010
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1110 => 0001
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 1100 => 0011
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 1011 => 0100
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 1010 => 0101
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 1101 => 0010
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 1001 => 0110
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 1110 => 0001
[.,[[.,[[.,.],.]],.]] => [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 => 0111
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 0111 => 1000
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 0110 => 1001
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 0101 => 1010
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 0110 => 1001
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 0100 => 1011
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 1011 => 0100
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 1010 => 0101
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 0011 => 1100
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 0010 => 1101
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 1101 => 0010
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 1001 => 0110
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 0101 => 1010
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 1001 => 0110
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 0001 => 1110
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1110 => 0001
[[.,[.,[[.,.],.]]],.] => [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 => 0111
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 0110 => 1001
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 0100 => 1011
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 1010 => 0101
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 0010 => 1101
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 1100 => 0011
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 1000 => 0111
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 0100 => 1011
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1000 => 0111
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0000 => 1111
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 11111 => 00000
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 11110 => 00001
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 11101 => 00010
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 11110 => 00001
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 11100 => 00011
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 11011 => 00100
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 11010 => 00101
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 11101 => 00010
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 11001 => 00110
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 11110 => 00001
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 11100 => 00011
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 11010 => 00101
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 11100 => 00011
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 11000 => 00111
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 10111 => 01000
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 10110 => 01001
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 10101 => 01010
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 10110 => 01001
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 10100 => 01011
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 11011 => 00100
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 11010 => 00101
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 10011 => 01100
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 10010 => 01101
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 11101 => 00010
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 11001 => 00110
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 10101 => 01010
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 11001 => 00110
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 10001 => 01110
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 11110 => 00001
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 11100 => 00011
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 11010 => 00101
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 11100 => 00011
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 11000 => 00111
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 10110 => 01001
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 10100 => 01011
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 11010 => 00101
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 10010 => 01101
>>> Load all 2149 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 11100 => 00011
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 11000 => 00111
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 10100 => 01011
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 11000 => 00111
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 10000 => 01111
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 01111 => 10000
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 01110 => 10001
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 01101 => 10010
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 01110 => 10001
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 01100 => 10011
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 01011 => 10100
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 01010 => 10101
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 01101 => 10010
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => 01001 => 10110
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 01110 => 10001
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 01100 => 10011
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => 01010 => 10101
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 01100 => 10011
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => 01000 => 10111
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 10111 => 01000
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 10110 => 01001
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 10101 => 01010
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 10110 => 01001
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => 10100 => 01011
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 00111 => 11000
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 00110 => 11001
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 00101 => 11010
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 00110 => 11001
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 00100 => 11011
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 11011 => 00100
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 11010 => 00101
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 10011 => 01100
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => 10010 => 01101
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 01011 => 10100
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 01010 => 10101
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 10011 => 01100
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 10010 => 01101
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 00011 => 11100
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 00010 => 11101
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 11101 => 00010
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => 11001 => 00110
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => 10101 => 01010
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => 11001 => 00110
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => 10001 => 01110
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 01101 => 10010
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 01001 => 10110
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 10101 => 01010
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 00101 => 11010
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 11001 => 00110
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => 10001 => 01110
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 01001 => 10110
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 10001 => 01110
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 00001 => 11110
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 11110 => 00001
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 11100 => 00011
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 11010 => 00101
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 11100 => 00011
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 11000 => 00111
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 10110 => 01001
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 10100 => 01011
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 11010 => 00101
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 10010 => 01101
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 11100 => 00011
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 11000 => 00111
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 10100 => 01011
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 11000 => 00111
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 10000 => 01111
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 01110 => 10001
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 01100 => 10011
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 01010 => 10101
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 01100 => 10011
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => 01000 => 10111
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 10110 => 01001
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 10100 => 01011
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 00110 => 11001
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 00100 => 11011
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 11010 => 00101
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => 10010 => 01101
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 01010 => 10101
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 10010 => 01101
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 00010 => 11101
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 11100 => 00011
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 11000 => 00111
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 10100 => 01011
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 11000 => 00111
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 10000 => 01111
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 01100 => 10011
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 01000 => 10111
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 10100 => 01011
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 00100 => 11011
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 11000 => 00111
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 10000 => 01111
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 01000 => 10111
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 10000 => 01111
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 00000 => 11111
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 111111 => 000000
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => 111110 => 000001
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => 111101 => 000010
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => 111110 => 000001
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => 111100 => 000011
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => 111011 => 000100
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => 111010 => 000101
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => 111101 => 000010
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => 111001 => 000110
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => 111110 => 000001
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => 111100 => 000011
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => 111010 => 000101
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => 111100 => 000011
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => 111000 => 000111
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => 110111 => 001000
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => 110110 => 001001
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => 110101 => 001010
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => 110110 => 001001
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => 110100 => 001011
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => 111011 => 000100
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => 111010 => 000101
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => 110011 => 001100
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => 110010 => 001101
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => 111101 => 000010
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => 111001 => 000110
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => 110101 => 001010
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => 111001 => 000110
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => 110001 => 001110
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => 111110 => 000001
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => 111100 => 000011
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => 111010 => 000101
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => 111100 => 000011
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => 111000 => 000111
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => 110110 => 001001
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => 110100 => 001011
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => 111010 => 000101
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => 110010 => 001101
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => 111100 => 000011
[.,[.,[[[.,[[.,.],.]],.],.]]] => [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 => 001111
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => 101111 => 010000
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => 101110 => 010001
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => 101101 => 010010
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => 101110 => 010001
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => 101100 => 010011
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => 101011 => 010100
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => 101010 => 010101
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => 101101 => 010010
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => 101001 => 010110
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => 101110 => 010001
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => 101100 => 010011
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => 101010 => 010101
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => 101100 => 010011
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => 101000 => 010111
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => 110111 => 001000
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => 110110 => 001001
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => 110101 => 001010
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => 110110 => 001001
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => 110100 => 001011
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => 100111 => 011000
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => 100110 => 011001
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => 100101 => 011010
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => 100110 => 011001
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => 100100 => 011011
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => 111011 => 000100
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => 111010 => 000101
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => 110011 => 001100
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => 110010 => 001101
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => 101011 => 010100
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => 101010 => 010101
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => 110011 => 001100
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => 110010 => 001101
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => 100011 => 011100
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => 100010 => 011101
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => 111101 => 000010
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => 111001 => 000110
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => 110101 => 001010
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => 111001 => 000110
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => 110001 => 001110
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => 101101 => 010010
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => 101001 => 010110
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => 110101 => 001010
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => 100101 => 011010
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => 111001 => 000110
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => 110001 => 001110
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => 101001 => 010110
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => 110001 => 001110
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => 100001 => 011110
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => 111110 => 000001
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => 111100 => 000011
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => 111010 => 000101
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => 111100 => 000011
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => 111000 => 000111
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => 110110 => 001001
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => 110100 => 001011
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => 111010 => 000101
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => 110010 => 001101
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => 111100 => 000011
[.,[[.,[[.,[[.,.],.]],.]],.]] => [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 => 001111
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => 101110 => 010001
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => 101100 => 010011
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => 101010 => 010101
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => 101100 => 010011
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => 101000 => 010111
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => 110110 => 001001
[.,[[[.,[.,.]],[[.,.],.]],.]] => [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 => 011011
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => 111010 => 000101
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => 110010 => 001101
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => 101010 => 010101
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => 110010 => 001101
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => 100010 => 011101
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => 111100 => 000011
[.,[[[.,[.,[[.,.],.]]],.],.]] => [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 => 001111
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => 101100 => 010011
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => 101000 => 010111
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => 110100 => 001011
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => 100100 => 011011
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 111000 => 000111
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 110000 => 001111
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => 101000 => 010111
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 110000 => 001111
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 100000 => 011111
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => 011111 => 100000
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => 011110 => 100001
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => 011101 => 100010
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => 011110 => 100001
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => 011100 => 100011
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => 011011 => 100100
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => 011010 => 100101
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => 011101 => 100010
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => 011001 => 100110
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => 011110 => 100001
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => 011100 => 100011
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => 011010 => 100101
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => 011100 => 100011
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => 011000 => 100111
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 010111 => 101000
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 010110 => 101001
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 010101 => 101010
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 010110 => 101001
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => 010100 => 101011
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 011011 => 100100
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 011010 => 100101
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => 010011 => 101100
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => 010010 => 101101
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => 011101 => 100010
[[.,.],[[.,[[.,.],.]],[.,.]]] => [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 => 101110
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => 011110 => 100001
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => 011100 => 100011
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => 011010 => 100101
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => 011100 => 100011
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => 011000 => 100111
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => 010110 => 101001
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => 010100 => 101011
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => 011010 => 100101
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => 010010 => 101101
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => 011100 => 100011
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => 011000 => 100111
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => 010100 => 101011
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => 011000 => 100111
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => 010000 => 101111
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => 101111 => 010000
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => 101110 => 010001
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => 101101 => 010010
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => 101110 => 010001
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => 101100 => 010011
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => 101011 => 010100
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => 101010 => 010101
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => 101101 => 010010
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => 101001 => 010110
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => 101110 => 010001
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => 101100 => 010011
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => 101010 => 010101
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => 101100 => 010011
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => 101000 => 010111
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => 001111 => 110000
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => 001110 => 110001
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => 001101 => 110010
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => 001110 => 110001
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => 001100 => 110011
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => 001011 => 110100
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => 001010 => 110101
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => 001101 => 110010
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => 001001 => 110110
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => 001110 => 110001
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => 001100 => 110011
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => 001010 => 110101
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => 001100 => 110011
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => 001000 => 110111
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => 110111 => 001000
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => 110110 => 001001
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => 110101 => 001010
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => 110110 => 001001
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => 110100 => 001011
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => 100111 => 011000
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => 100110 => 011001
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => 100101 => 011010
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => 100110 => 011001
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => 100100 => 011011
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => 010111 => 101000
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => 010110 => 101001
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => 010101 => 101010
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => 010110 => 101001
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => 010100 => 101011
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => 100111 => 011000
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => 100110 => 011001
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => 100101 => 011010
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => 100110 => 011001
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => 100100 => 011011
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => 000111 => 111000
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => 000110 => 111001
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => 000101 => 111010
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => 000110 => 111001
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => 000100 => 111011
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => 111011 => 000100
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => 111010 => 000101
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => 110011 => 001100
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => 110010 => 001101
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => 101011 => 010100
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => 101010 => 010101
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => 110011 => 001100
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => 110010 => 001101
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => 100011 => 011100
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => 100010 => 011101
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => 011011 => 100100
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => 011010 => 100101
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => 010011 => 101100
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => 010010 => 101101
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => 101011 => 010100
[[[.,[.,.]],[.,.]],[[.,.],.]] => [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 => 110101
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => 110011 => 001100
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => 110010 => 001101
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => 100011 => 011100
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => 100010 => 011101
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => 010011 => 101100
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => 010010 => 101101
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => 100011 => 011100
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => 100010 => 011101
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => 000011 => 111100
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => 000010 => 111101
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => 111101 => 000010
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => 111001 => 000110
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => 110101 => 001010
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => 111001 => 000110
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => 110001 => 001110
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => 101101 => 010010
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => 101001 => 010110
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => 110101 => 001010
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => 100101 => 011010
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => 111001 => 000110
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => 110001 => 001110
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => 101001 => 010110
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => 110001 => 001110
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => 100001 => 011110
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => 011101 => 100010
[[[.,.],[.,[[.,.],.]]],[.,.]] => [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 => 101110
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => 101101 => 010010
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => 101001 => 010110
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => 001101 => 110010
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => 001001 => 110110
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => 110101 => 001010
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => 100101 => 011010
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => 010101 => 101010
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => 100101 => 011010
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => 000101 => 111010
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => 111001 => 000110
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => 110001 => 001110
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => 101001 => 010110
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => 110001 => 001110
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => 100001 => 011110
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => 011001 => 100110
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => 010001 => 101110
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => 101001 => 010110
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => 001001 => 110110
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => 110001 => 001110
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => 100001 => 011110
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => 010001 => 101110
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => 100001 => 011110
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 000001 => 111110
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 111110 => 000001
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 111100 => 000011
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => 111010 => 000101
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 111100 => 000011
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 111000 => 000111
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => 110110 => 001001
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => 110100 => 001011
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => 111010 => 000101
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => 110010 => 001101
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 111100 => 000011
[[.,[.,[[.,[[.,.],.]],.]]],.] => [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 => 001111
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => 101110 => 010001
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => 101100 => 010011
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => 101010 => 010101
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => 101100 => 010011
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => 101000 => 010111
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => 110110 => 001001
[[.,[[.,[.,.]],[[.,.],.]]],.] => [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 => 011011
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => 111010 => 000101
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => 110010 => 001101
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => 101010 => 010101
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => 110010 => 001101
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => 100010 => 011101
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 111100 => 000011
[[.,[[.,[.,[[.,.],.]]],.]],.] => [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 => 001111
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => 101100 => 010011
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => 101000 => 010111
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => 110100 => 001011
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => 100100 => 011011
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => 111000 => 000111
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => 110000 => 001111
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => 101000 => 010111
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => 110000 => 001111
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 100000 => 011111
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => 011110 => 100001
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => 011100 => 100011
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => 011010 => 100101
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => 011100 => 100011
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => 011000 => 100111
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => 010110 => 101001
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => 010100 => 101011
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => 011010 => 100101
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => 010010 => 101101
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => 011100 => 100011
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => 011000 => 100111
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => 010100 => 101011
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => 011000 => 100111
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => 010000 => 101111
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => 101110 => 010001
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => 101100 => 010011
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => 101010 => 010101
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => 101100 => 010011
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => 101000 => 010111
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => 001110 => 110001
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => 001100 => 110011
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => 001010 => 110101
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => 001100 => 110011
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => 001000 => 110111
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => 110110 => 001001
[[[.,[.,[.,.]]],[[.,.],.]],.] => [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 => 011011
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => 010110 => 101001
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => 010100 => 101011
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => 100110 => 011001
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => 100100 => 011011
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => 000110 => 111001
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => 000100 => 111011
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => 111010 => 000101
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => 110010 => 001101
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => 101010 => 010101
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => 110010 => 001101
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => 100010 => 011101
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => 011010 => 100101
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => 010010 => 101101
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => 101010 => 010101
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => 001010 => 110101
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => 110010 => 001101
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => 100010 => 011101
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => 010010 => 101101
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => 100010 => 011101
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 000010 => 111101
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 111100 => 000011
[[[.,[.,[.,[[.,.],.]]]],.],.] => [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 => 001111
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => 101100 => 010011
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => 101000 => 010111
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => 110100 => 001011
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => 100100 => 011011
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => 111000 => 000111
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => 110000 => 001111
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => 101000 => 010111
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => 110000 => 001111
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 100000 => 011111
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => 011100 => 100011
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => 011000 => 100111
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => 010100 => 101011
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => 011000 => 100111
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => 010000 => 101111
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => 101100 => 010011
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => 101000 => 010111
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => 001100 => 110011
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => 001000 => 110111
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => 110100 => 001011
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => 100100 => 011011
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => 010100 => 101011
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => 100100 => 011011
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => 000100 => 111011
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 111000 => 000111
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => 110000 => 001111
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => 101000 => 010111
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => 110000 => 001111
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 100000 => 011111
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => 011000 => 100111
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => 010000 => 101111
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => 101000 => 010111
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => 001000 => 110111
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 110000 => 001111
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 100000 => 011111
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 010000 => 101111
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 100000 => 011111
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 000000 => 111111
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 1111111 => 0000000
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => 1111110 => 0000001
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [6,8,7,5,4,3,2,1] => 1111101 => 0000010
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 1111110 => 0000001
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => 1111100 => 0000011
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [5,8,7,6,4,3,2,1] => 1111011 => 0000100
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [5,7,8,6,4,3,2,1] => 1111010 => 0000101
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => 1111101 => 0000010
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [5,6,8,7,4,3,2,1] => 1111001 => 0000110
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => 1111110 => 0000001
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => 1111100 => 0000011
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => 1111010 => 0000101
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => 1111100 => 0000011
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => 1111000 => 0000111
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => 1110111 => 0001000
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [4,7,8,6,5,3,2,1] => 1110110 => 0001001
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => 1110101 => 0001010
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [4,7,6,8,5,3,2,1] => 1110110 => 0001001
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [4,6,7,8,5,3,2,1] => 1110100 => 0001011
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [5,4,7,8,6,3,2,1] => 1111010 => 0000101
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [4,5,8,7,6,3,2,1] => 1110011 => 0001100
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [4,5,7,8,6,3,2,1] => 1110010 => 0001101
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [6,5,4,8,7,3,2,1] => 1111101 => 0000010
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [5,6,4,8,7,3,2,1] => 1111001 => 0000110
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [4,6,5,8,7,3,2,1] => 1110101 => 0001010
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => 1110001 => 0001110
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 1111110 => 0000001
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => 1111100 => 0000011
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [5,7,6,4,8,3,2,1] => 1111010 => 0000101
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 1111100 => 0000011
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => 1111000 => 0000111
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1] => 1110110 => 0001001
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [4,6,7,5,8,3,2,1] => 1110100 => 0001011
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [5,4,7,6,8,3,2,1] => 1111010 => 0000101
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [4,5,7,6,8,3,2,1] => 1110010 => 0001101
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => 1111100 => 0000011
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => 1111000 => 0000111
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [4,6,5,7,8,3,2,1] => 1110100 => 0001011
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => 1111000 => 0000111
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => 1110000 => 0001111
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [3,8,7,6,5,4,2,1] => 1101111 => 0010000
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [3,7,8,6,5,4,2,1] => 1101110 => 0010001
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [3,6,8,7,5,4,2,1] => 1101101 => 0010010
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [3,7,6,8,5,4,2,1] => 1101110 => 0010001
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => 1101011 => 0010100
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => 1101010 => 0010101
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [3,5,6,8,7,4,2,1] => 1101001 => 0010110
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [3,7,6,5,8,4,2,1] => 1101110 => 0010001
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [3,6,7,5,8,4,2,1] => 1101100 => 0010011
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [3,5,7,6,8,4,2,1] => 1101010 => 0010101
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [3,5,6,7,8,4,2,1] => 1101000 => 0010111
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => 1110111 => 0001000
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [4,3,7,8,6,5,2,1] => 1110110 => 0001001
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [4,3,6,7,8,5,2,1] => 1110100 => 0001011
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [3,4,8,7,6,5,2,1] => 1100111 => 0011000
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => 1100100 => 0011011
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [5,4,3,8,7,6,2,1] => 1111011 => 0000100
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [5,4,3,7,8,6,2,1] => 1111010 => 0000101
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [4,5,3,7,8,6,2,1] => 1110010 => 0001101
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [3,5,4,7,8,6,2,1] => 1101010 => 0010101
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [4,3,5,7,8,6,2,1] => 1110010 => 0001101
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [3,4,5,8,7,6,2,1] => 1100011 => 0011100
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [3,4,5,7,8,6,2,1] => 1100010 => 0011101
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [6,5,4,3,8,7,2,1] => 1111101 => 0000010
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [5,6,4,3,8,7,2,1] => 1111001 => 0000110
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [4,5,6,3,8,7,2,1] => 1110001 => 0001110
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [3,6,5,4,8,7,2,1] => 1101101 => 0010010
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => 1110101 => 0001010
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [5,4,3,6,8,7,2,1] => 1111001 => 0000110
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [4,5,3,6,8,7,2,1] => 1110001 => 0001110
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [4,3,5,6,8,7,2,1] => 1110001 => 0001110
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [3,4,5,6,8,7,2,1] => 1100001 => 0011110
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => 1111110 => 0000001
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => 1111100 => 0000011
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [5,7,6,4,3,8,2,1] => 1111010 => 0000101
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [6,5,7,4,3,8,2,1] => 1111100 => 0000011
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => 1111000 => 0000111
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [4,7,6,5,3,8,2,1] => 1110110 => 0001001
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [5,4,7,6,3,8,2,1] => 1111010 => 0000101
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => 1111100 => 0000011
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => 1111000 => 0000111
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => 1110000 => 0001111
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [3,7,6,5,4,8,2,1] => 1101110 => 0010001
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [3,5,7,6,4,8,2,1] => 1101010 => 0010101
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [3,5,6,7,4,8,2,1] => 1101000 => 0010111
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [4,3,7,6,5,8,2,1] => 1110110 => 0001001
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [3,4,7,6,5,8,2,1] => 1100110 => 0011001
[.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [3,4,6,7,5,8,2,1] => 1100100 => 0011011
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [4,5,3,7,6,8,2,1] => 1110010 => 0001101
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [3,5,4,7,6,8,2,1] => 1101010 => 0010101
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [4,3,5,7,6,8,2,1] => 1110010 => 0001101
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [3,4,5,7,6,8,2,1] => 1100010 => 0011101
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => 1111100 => 0000011
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => 1110000 => 0001111
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [3,6,5,4,7,8,2,1] => 1101100 => 0010011
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [3,5,6,4,7,8,2,1] => 1101000 => 0010111
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [4,3,6,5,7,8,2,1] => 1110100 => 0001011
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [3,4,6,5,7,8,2,1] => 1100100 => 0011011
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => 1111000 => 0000111
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [3,5,4,6,7,8,2,1] => 1101000 => 0010111
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => 1110000 => 0001111
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => 1100000 => 0011111
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => 1011111 => 0100000
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [2,7,8,6,5,4,3,1] => 1011110 => 0100001
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => 1011101 => 0100010
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [2,7,6,8,5,4,3,1] => 1011110 => 0100001
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [2,6,7,8,5,4,3,1] => 1011100 => 0100011
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [2,5,8,7,6,4,3,1] => 1011011 => 0100100
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [2,6,7,5,8,4,3,1] => 1011100 => 0100011
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [2,6,5,7,8,4,3,1] => 1011100 => 0100011
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [2,5,6,7,8,4,3,1] => 1011000 => 0100111
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [2,4,8,7,6,5,3,1] => 1010111 => 0101000
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [2,4,7,8,6,5,3,1] => 1010110 => 0101001
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => 1010101 => 0101010
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [2,4,6,7,8,5,3,1] => 1010100 => 0101011
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [2,5,4,8,7,6,3,1] => 1011011 => 0100100
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [2,5,4,7,8,6,3,1] => 1011010 => 0100101
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [2,4,5,7,8,6,3,1] => 1010010 => 0101101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [2,6,5,4,8,7,3,1] => 1011101 => 0100010
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [2,5,6,4,8,7,3,1] => 1011001 => 0100110
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [2,4,6,5,8,7,3,1] => 1010101 => 0101010
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [2,4,5,6,8,7,3,1] => 1010001 => 0101110
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [2,7,6,5,4,8,3,1] => 1011110 => 0100001
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [2,6,7,5,4,8,3,1] => 1011100 => 0100011
[.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [2,5,6,7,4,8,3,1] => 1011000 => 0100111
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [2,4,7,6,5,8,3,1] => 1010110 => 0101001
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [2,4,6,7,5,8,3,1] => 1010100 => 0101011
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [2,5,4,7,6,8,3,1] => 1011010 => 0100101
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [2,6,5,4,7,8,3,1] => 1011100 => 0100011
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [2,5,6,4,7,8,3,1] => 1011000 => 0100111
[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [2,4,6,5,7,8,3,1] => 1010100 => 0101011
[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [2,5,4,6,7,8,3,1] => 1011000 => 0100111
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [2,4,5,6,7,8,3,1] => 1010000 => 0101111
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => 1101111 => 0010000
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [3,2,6,8,7,5,4,1] => 1101101 => 0010010
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [3,2,5,7,8,6,4,1] => 1101010 => 0010101
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [3,2,6,5,8,7,4,1] => 1101101 => 0010010
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [3,2,5,7,6,8,4,1] => 1101010 => 0010101
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [3,2,5,6,7,8,4,1] => 1101000 => 0010111
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => 1001111 => 0110000
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [2,3,6,7,8,5,4,1] => 1001100 => 0110011
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [2,3,5,8,7,6,4,1] => 1001011 => 0110100
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [2,3,5,7,8,6,4,1] => 1001010 => 0110101
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [2,3,6,5,8,7,4,1] => 1001101 => 0110010
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => 1001001 => 0110110
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [2,3,7,6,5,8,4,1] => 1001110 => 0110001
[.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [2,3,5,7,6,8,4,1] => 1001010 => 0110101
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [2,3,5,6,7,8,4,1] => 1001000 => 0110111
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => 1110111 => 0001000
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [4,3,2,7,8,6,5,1] => 1110110 => 0001001
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [4,3,2,6,8,7,5,1] => 1110101 => 0001010
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => 1100111 => 0011000
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [3,4,2,7,8,6,5,1] => 1100110 => 0011001
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [2,4,3,8,7,6,5,1] => 1010111 => 0101000
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [2,4,3,6,8,7,5,1] => 1010101 => 0101010
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [2,4,3,6,7,8,5,1] => 1010100 => 0101011
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [3,2,4,8,7,6,5,1] => 1100111 => 0011000
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [3,2,4,7,8,6,5,1] => 1100110 => 0011001
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => 1000111 => 0111000
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [2,3,4,7,8,6,5,1] => 1000110 => 0111001
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [2,3,4,6,8,7,5,1] => 1000101 => 0111010
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [2,3,4,7,6,8,5,1] => 1000110 => 0111001
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [2,3,4,6,7,8,5,1] => 1000100 => 0111011
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [5,4,3,2,8,7,6,1] => 1111011 => 0000100
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [5,4,3,2,7,8,6,1] => 1111010 => 0000101
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [4,5,3,2,8,7,6,1] => 1110011 => 0001100
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [3,5,4,2,7,8,6,1] => 1101010 => 0010101
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [4,3,5,2,8,7,6,1] => 1110011 => 0001100
[.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [3,4,5,2,7,8,6,1] => 1100010 => 0011101
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => 1011011 => 0100100
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [2,5,4,3,7,8,6,1] => 1011010 => 0100101
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [2,4,5,3,8,7,6,1] => 1010011 => 0101100
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [2,4,5,3,7,8,6,1] => 1010010 => 0101101
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [3,2,5,4,7,8,6,1] => 1101010 => 0010101
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [2,3,5,4,8,7,6,1] => 1001011 => 0110100
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [2,3,5,4,7,8,6,1] => 1001010 => 0110101
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [4,3,2,5,8,7,6,1] => 1110011 => 0001100
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [4,3,2,5,7,8,6,1] => 1110010 => 0001101
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [3,4,2,5,8,7,6,1] => 1100011 => 0011100
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [3,4,2,5,7,8,6,1] => 1100010 => 0011101
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [2,4,3,5,8,7,6,1] => 1010011 => 0101100
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [3,2,4,5,7,8,6,1] => 1100010 => 0011101
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [2,3,4,5,8,7,6,1] => 1000011 => 0111100
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [2,3,4,5,7,8,6,1] => 1000010 => 0111101
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [6,5,4,3,2,8,7,1] => 1111101 => 0000010
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [4,6,5,3,2,8,7,1] => 1110101 => 0001010
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [5,4,6,3,2,8,7,1] => 1111001 => 0000110
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [4,5,6,3,2,8,7,1] => 1110001 => 0001110
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [3,6,5,4,2,8,7,1] => 1101101 => 0010010
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [3,5,6,4,2,8,7,1] => 1101001 => 0010110
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [4,3,6,5,2,8,7,1] => 1110101 => 0001010
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [5,4,3,6,2,8,7,1] => 1111001 => 0000110
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => 1110001 => 0001110
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [3,5,4,6,2,8,7,1] => 1101001 => 0010110
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [3,4,5,6,2,8,7,1] => 1100001 => 0011110
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [2,6,5,4,3,8,7,1] => 1011101 => 0100010
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [2,4,6,5,3,8,7,1] => 1010101 => 0101010
[.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [2,4,5,6,3,8,7,1] => 1010001 => 0101110
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => 1101101 => 0010010
[.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [2,3,5,6,4,8,7,1] => 1001001 => 0110110
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [4,3,2,6,5,8,7,1] => 1110101 => 0001010
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [3,4,2,6,5,8,7,1] => 1100101 => 0011010
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => 1010101 => 0101010
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [3,2,4,6,5,8,7,1] => 1100101 => 0011010
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [2,3,4,6,5,8,7,1] => 1000101 => 0111010
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [5,4,3,2,6,8,7,1] => 1111001 => 0000110
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [4,5,3,2,6,8,7,1] => 1110001 => 0001110
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [2,5,4,3,6,8,7,1] => 1011001 => 0100110
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [2,4,5,3,6,8,7,1] => 1010001 => 0101110
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [3,2,5,4,6,8,7,1] => 1101001 => 0010110
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [4,3,2,5,6,8,7,1] => 1110001 => 0001110
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [3,4,2,5,6,8,7,1] => 1100001 => 0011110
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => 1010001 => 0101110
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [3,2,4,5,6,8,7,1] => 1100001 => 0011110
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => 1000001 => 0111110
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 1111110 => 0000001
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => 1111100 => 0000011
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [5,7,6,4,3,2,8,1] => 1111010 => 0000101
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 1111100 => 0000011
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => 1111000 => 0000111
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [4,7,6,5,3,2,8,1] => 1110110 => 0001001
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [4,6,7,5,3,2,8,1] => 1110100 => 0001011
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1] => 1111100 => 0000011
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [4,6,5,7,3,2,8,1] => 1110100 => 0001011
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => 1110000 => 0001111
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [3,5,7,6,4,2,8,1] => 1101010 => 0010101
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [3,5,6,7,4,2,8,1] => 1101000 => 0010111
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [4,3,7,6,5,2,8,1] => 1110110 => 0001001
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [4,3,6,7,5,2,8,1] => 1110100 => 0001011
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [3,4,7,6,5,2,8,1] => 1100110 => 0011001
[.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [3,4,6,7,5,2,8,1] => 1100100 => 0011011
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [5,4,3,7,6,2,8,1] => 1111010 => 0000101
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [4,5,3,7,6,2,8,1] => 1110010 => 0001101
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [3,5,4,7,6,2,8,1] => 1101010 => 0010101
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [3,4,5,7,6,2,8,1] => 1100010 => 0011101
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 1111100 => 0000011
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [4,6,5,3,7,2,8,1] => 1110100 => 0001011
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 1111000 => 0000111
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => 1110000 => 0001111
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [3,6,5,4,7,2,8,1] => 1101100 => 0010011
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => 1101000 => 0010111
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => 1110100 => 0001011
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [3,4,6,5,7,2,8,1] => 1100100 => 0011011
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => 1111000 => 0000111
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => 1110000 => 0001111
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [3,5,4,6,7,2,8,1] => 1101000 => 0010111
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [4,3,5,6,7,2,8,1] => 1110000 => 0001111
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => 1100000 => 0011111
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1] => 1011110 => 0100001
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [2,6,5,7,4,3,8,1] => 1011100 => 0100011
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [2,5,6,7,4,3,8,1] => 1011000 => 0100111
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [2,4,6,7,5,3,8,1] => 1010100 => 0101011
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [2,5,4,7,6,3,8,1] => 1011010 => 0100101
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => 1010100 => 0101011
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [2,5,4,6,7,3,8,1] => 1011000 => 0100111
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [2,4,5,6,7,3,8,1] => 1010000 => 0101111
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [3,2,7,6,5,4,8,1] => 1101110 => 0010001
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [3,2,6,7,5,4,8,1] => 1101100 => 0010011
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [3,2,5,7,6,4,8,1] => 1101010 => 0010101
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => 1101100 => 0010011
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [3,2,5,6,7,4,8,1] => 1101000 => 0010111
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [2,3,7,6,5,4,8,1] => 1001110 => 0110001
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [2,3,5,7,6,4,8,1] => 1001010 => 0110101
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [2,3,5,6,7,4,8,1] => 1001000 => 0110111
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1] => 1110110 => 0001001
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [4,3,2,6,7,5,8,1] => 1110100 => 0001011
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [3,4,2,7,6,5,8,1] => 1100110 => 0011001
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [3,4,2,6,7,5,8,1] => 1100100 => 0011011
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [2,4,3,7,6,5,8,1] => 1010110 => 0101001
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [2,4,3,6,7,5,8,1] => 1010100 => 0101011
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [3,2,4,7,6,5,8,1] => 1100110 => 0011001
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [2,3,4,7,6,5,8,1] => 1000110 => 0111001
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [2,3,4,6,7,5,8,1] => 1000100 => 0111011
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [5,4,3,2,7,6,8,1] => 1111010 => 0000101
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [3,5,4,2,7,6,8,1] => 1101010 => 0010101
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => 1110010 => 0001101
[.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [3,4,5,2,7,6,8,1] => 1100010 => 0011101
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [2,5,4,3,7,6,8,1] => 1011010 => 0100101
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => 1101010 => 0010101
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [2,3,5,4,7,6,8,1] => 1001010 => 0110101
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [4,3,2,5,7,6,8,1] => 1110010 => 0001101
[.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [3,4,2,5,7,6,8,1] => 1100010 => 0011101
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [2,4,3,5,7,6,8,1] => 1010010 => 0101101
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1] => 1100010 => 0011101
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => 1000010 => 0111101
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => 1111100 => 0000011
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => 1111000 => 0000111
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => 1110000 => 0001111
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [3,6,5,4,2,7,8,1] => 1101100 => 0010011
[.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [3,5,6,4,2,7,8,1] => 1101000 => 0010111
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [3,4,6,5,2,7,8,1] => 1100100 => 0011011
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => 1111000 => 0000111
[.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [3,5,4,6,2,7,8,1] => 1101000 => 0010111
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => 1110000 => 0001111
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => 1100000 => 0011111
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [2,6,5,4,3,7,8,1] => 1011100 => 0100011
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [2,5,6,4,3,7,8,1] => 1011000 => 0100111
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [2,4,6,5,3,7,8,1] => 1010100 => 0101011
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [2,5,4,6,3,7,8,1] => 1011000 => 0100111
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [2,4,5,6,3,7,8,1] => 1010000 => 0101111
[.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [3,2,5,6,4,7,8,1] => 1101000 => 0010111
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [2,3,6,5,4,7,8,1] => 1001100 => 0110011
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [2,3,5,6,4,7,8,1] => 1001000 => 0110111
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [4,3,2,6,5,7,8,1] => 1110100 => 0001011
[.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [3,4,2,6,5,7,8,1] => 1100100 => 0011011
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [2,4,3,6,5,7,8,1] => 1010100 => 0101011
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [2,3,4,6,5,7,8,1] => 1000100 => 0111011
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => 1111000 => 0000111
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [4,5,3,2,6,7,8,1] => 1110000 => 0001111
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [3,5,4,2,6,7,8,1] => 1101000 => 0010111
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => 1110000 => 0001111
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 1100000 => 0011111
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1] => 1011000 => 0100111
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [2,4,5,3,6,7,8,1] => 1010000 => 0101111
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [3,2,5,4,6,7,8,1] => 1101000 => 0010111
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1] => 1001000 => 0110111
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 1110000 => 0001111
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 1100000 => 0011111
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [2,4,3,5,6,7,8,1] => 1010000 => 0101111
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 1100000 => 0011111
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 1000000 => 0111111
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => 0111111 => 1000000
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => 0111110 => 1000001
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => 0111101 => 1000010
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => 0111110 => 1000001
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => 0111100 => 1000011
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => 0111011 => 1000100
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,6,5,8,7,4,3,2] => 0111101 => 1000010
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => 0111110 => 1000001
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => 0111100 => 1000011
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,5,7,6,8,4,3,2] => 0111010 => 1000101
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,6,5,7,8,4,3,2] => 0111100 => 1000011
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => 0111000 => 1000111
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => 0110111 => 1001000
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => 0110110 => 1001001
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => 0110101 => 1001010
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,4,6,7,8,5,3,2] => 0110100 => 1001011
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,5,4,7,8,6,3,2] => 0111010 => 1000101
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,4,5,8,7,6,3,2] => 0110011 => 1001100
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,4,5,7,8,6,3,2] => 0110010 => 1001101
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,6,5,4,8,7,3,2] => 0111101 => 1000010
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,4,6,5,8,7,3,2] => 0110101 => 1001010
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,5,4,6,8,7,3,2] => 0111001 => 1000110
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => 0111110 => 1000001
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,4,7,6,5,8,3,2] => 0110110 => 1001001
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,4,6,7,5,8,3,2] => 0110100 => 1001011
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,6,5,4,7,8,3,2] => 0111100 => 1000011
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,5,6,4,7,8,3,2] => 0111000 => 1000111
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,5,4,6,7,8,3,2] => 0111000 => 1000111
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,4,5,6,7,8,3,2] => 0110000 => 1001111
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => 0101111 => 1010000
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,3,7,8,6,5,4,2] => 0101110 => 1010001
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,3,6,8,7,5,4,2] => 0101101 => 1010010
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,3,6,7,8,5,4,2] => 0101100 => 1010011
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,3,5,8,7,6,4,2] => 0101011 => 1010100
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => 0101010 => 1010101
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,3,5,6,8,7,4,2] => 0101001 => 1010110
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,3,5,7,6,8,4,2] => 0101010 => 1010101
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => 0101100 => 1010011
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => 0101000 => 1010111
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => 0110111 => 1001000
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => 0110110 => 1001001
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,4,3,6,8,7,5,2] => 0110101 => 1001010
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,4,3,7,6,8,5,2] => 0110110 => 1001001
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,4,3,6,7,8,5,2] => 0110100 => 1001011
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => 0100111 => 1011000
[[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,3,4,7,6,8,5,2] => 0100110 => 1011001
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,3,4,6,7,8,5,2] => 0100100 => 1011011
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,5,4,3,8,7,6,2] => 0111011 => 1000100
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,4,5,3,8,7,6,2] => 0110011 => 1001100
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,3,5,4,8,7,6,2] => 0101011 => 1010100
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,3,5,4,7,8,6,2] => 0101010 => 1010101
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,4,3,5,8,7,6,2] => 0110011 => 1001100
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,4,3,5,7,8,6,2] => 0110010 => 1001101
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,3,4,5,8,7,6,2] => 0100011 => 1011100
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => 0100010 => 1011101
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => 0111101 => 1000010
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => 0111001 => 1000110
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,4,6,5,3,8,7,2] => 0110101 => 1001010
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,4,5,6,3,8,7,2] => 0110001 => 1001110
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,3,6,5,4,8,7,2] => 0101101 => 1010010
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => 0110101 => 1001010
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,5,4,3,6,8,7,2] => 0111001 => 1000110
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,4,5,3,6,8,7,2] => 0110001 => 1001110
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => 0100001 => 1011110
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => 0111110 => 1000001
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,6,7,5,4,3,8,2] => 0111100 => 1000011
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,6,5,7,4,3,8,2] => 0111100 => 1000011
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,5,6,7,4,3,8,2] => 0111000 => 1000111
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => 0110100 => 1001011
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => 0111000 => 1000111
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,4,6,5,7,3,8,2] => 0110100 => 1001011
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => 0111000 => 1000111
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => 0110000 => 1001111
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,3,5,7,6,4,8,2] => 0101010 => 1010101
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,3,6,5,7,4,8,2] => 0101100 => 1010011
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,3,5,6,7,4,8,2] => 0101000 => 1010111
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,4,3,6,7,5,8,2] => 0110100 => 1001011
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,3,4,7,6,5,8,2] => 0100110 => 1011001
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,3,4,6,7,5,8,2] => 0100100 => 1011011
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,3,5,4,7,6,8,2] => 0101010 => 1010101
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,3,4,5,7,6,8,2] => 0100010 => 1011101
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,6,5,4,3,7,8,2] => 0111100 => 1000011
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,5,4,6,3,7,8,2] => 0111000 => 1000111
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,3,5,6,4,7,8,2] => 0101000 => 1010111
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,4,3,6,5,7,8,2] => 0110100 => 1001011
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,3,4,6,5,7,8,2] => 0100100 => 1011011
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,5,4,3,6,7,8,2] => 0111000 => 1000111
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => 0110000 => 1001111
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,3,5,4,6,7,8,2] => 0101000 => 1010111
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => 0110000 => 1001111
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => 0100000 => 1011111
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => 1011111 => 0100000
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [2,1,7,8,6,5,4,3] => 1011110 => 0100001
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [2,1,6,8,7,5,4,3] => 1011101 => 0100010
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => 1011110 => 0100001
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => 1011100 => 0100011
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [2,1,5,8,7,6,4,3] => 1011011 => 0100100
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => 1011010 => 0100101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [2,1,6,5,8,7,4,3] => 1011101 => 0100010
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [2,1,5,6,8,7,4,3] => 1011001 => 0100110
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [2,1,7,6,5,8,4,3] => 1011110 => 0100001
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => 1011100 => 0100011
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [2,1,5,7,6,8,4,3] => 1011010 => 0100101
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => 1011100 => 0100011
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => 1011000 => 0100111
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => 1010111 => 0101000
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [2,1,4,7,8,6,5,3] => 1010110 => 0101001
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => 1010101 => 0101010
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [2,1,4,7,6,8,5,3] => 1010110 => 0101001
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [2,1,4,6,7,8,5,3] => 1010100 => 0101011
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [2,1,5,4,8,7,6,3] => 1011011 => 0100100
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [2,1,5,4,7,8,6,3] => 1011010 => 0100101
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => 1010011 => 0101100
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [2,1,4,5,7,8,6,3] => 1010010 => 0101101
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [2,1,6,5,4,8,7,3] => 1011101 => 0100010
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [2,1,5,6,4,8,7,3] => 1011001 => 0100110
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => 1010101 => 0101010
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [2,1,5,4,6,8,7,3] => 1011001 => 0100110
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [2,1,4,5,6,8,7,3] => 1010001 => 0101110
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [2,1,7,6,5,4,8,3] => 1011110 => 0100001
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [2,1,6,7,5,4,8,3] => 1011100 => 0100011
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [2,1,5,7,6,4,8,3] => 1011010 => 0100101
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => 1011100 => 0100011
[[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [2,1,5,6,7,4,8,3] => 1011000 => 0100111
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [2,1,4,7,6,5,8,3] => 1010110 => 0101001
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [2,1,4,6,7,5,8,3] => 1010100 => 0101011
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => 1011010 => 0100101
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [2,1,5,6,4,7,8,3] => 1011000 => 0100111
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [2,1,5,4,6,7,8,3] => 1011000 => 0100111
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => 1010000 => 0101111
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => 0011111 => 1100000
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => 0011110 => 1100001
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,2,7,6,8,5,4,3] => 0011110 => 1100001
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => 0011100 => 1100011
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,2,5,8,7,6,4,3] => 0011011 => 1100100
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,2,6,5,8,7,4,3] => 0011101 => 1100010
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,2,5,6,8,7,4,3] => 0011001 => 1100110
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => 0011110 => 1100001
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,2,5,7,6,8,4,3] => 0011010 => 1100101
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,2,6,5,7,8,4,3] => 0011100 => 1100011
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,2,5,6,7,8,4,3] => 0011000 => 1100111
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => 0010111 => 1101000
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,2,4,7,8,6,5,3] => 0010110 => 1101001
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,2,4,6,8,7,5,3] => 0010101 => 1101010
[[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,2,4,7,6,8,5,3] => 0010110 => 1101001
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => 0010100 => 1101011
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,2,5,4,8,7,6,3] => 0011011 => 1100100
[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,2,5,4,7,8,6,3] => 0011010 => 1100101
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,2,4,5,8,7,6,3] => 0010011 => 1101100
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,2,4,5,7,8,6,3] => 0010010 => 1101101
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,2,6,5,4,8,7,3] => 0011101 => 1100010
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,2,4,6,5,8,7,3] => 0010101 => 1101010
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,2,5,4,6,8,7,3] => 0011001 => 1100110
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,2,4,5,6,8,7,3] => 0010001 => 1101110
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,2,7,6,5,4,8,3] => 0011110 => 1100001
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,2,5,7,6,4,8,3] => 0011010 => 1100101
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => 0011000 => 1100111
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,2,4,7,6,5,8,3] => 0010110 => 1101001
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,2,5,4,7,6,8,3] => 0011010 => 1100101
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,2,6,5,4,7,8,3] => 0011100 => 1100011
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,2,5,6,4,7,8,3] => 0011000 => 1100111
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,2,4,6,5,7,8,3] => 0010100 => 1101011
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => 0011000 => 1100111
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => 0010000 => 1101111
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => 1101111 => 0010000
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [3,2,1,7,8,6,5,4] => 1101110 => 0010001
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [3,2,1,6,8,7,5,4] => 1101101 => 0010010
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [3,2,1,7,6,8,5,4] => 1101110 => 0010001
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => 1101100 => 0010011
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => 1101011 => 0010100
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => 1101010 => 0010101
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => 1101101 => 0010010
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => 1101001 => 0010110
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => 1101110 => 0010001
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => 1101100 => 0010011
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [3,2,1,5,7,6,8,4] => 1101010 => 0010101
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [3,2,1,6,5,7,8,4] => 1101100 => 0010011
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => 1101000 => 0010111
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => 1001111 => 0110000
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [2,3,1,7,8,6,5,4] => 1001110 => 0110001
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [2,3,1,6,8,7,5,4] => 1001101 => 0110010
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [2,3,1,7,6,8,5,4] => 1001110 => 0110001
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [2,3,1,6,7,8,5,4] => 1001100 => 0110011
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [2,3,1,6,5,8,7,4] => 1001101 => 0110010
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [2,3,1,7,6,5,8,4] => 1001110 => 0110001
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [2,3,1,6,7,5,8,4] => 1001100 => 0110011
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [2,3,1,5,7,6,8,4] => 1001010 => 0110101
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [2,3,1,5,6,7,8,4] => 1001000 => 0110111
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => 0101111 => 1010000
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => 0101101 => 1010010
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,3,2,7,6,8,5,4] => 0101110 => 1010001
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,3,2,6,7,8,5,4] => 0101100 => 1010011
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,3,2,5,8,7,6,4] => 0101011 => 1010100
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,3,2,5,7,8,6,4] => 0101010 => 1010101
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,3,2,6,5,8,7,4] => 0101101 => 1010010
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,3,2,5,6,8,7,4] => 0101001 => 1010110
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,3,2,7,6,5,8,4] => 0101110 => 1010001
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,3,2,6,7,5,8,4] => 0101100 => 1010011
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,3,2,5,7,6,8,4] => 0101010 => 1010101
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,3,2,6,5,7,8,4] => 0101100 => 1010011
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,3,2,5,6,7,8,4] => 0101000 => 1010111
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => 1001111 => 0110000
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [2,1,3,7,8,6,5,4] => 1001110 => 0110001
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [2,1,3,6,8,7,5,4] => 1001101 => 0110010
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [2,1,3,6,7,8,5,4] => 1001100 => 0110011
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [2,1,3,6,5,8,7,4] => 1001101 => 0110010
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [2,1,3,5,7,6,8,4] => 1001010 => 0110101
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [2,1,3,5,6,7,8,4] => 1001000 => 0110111
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => 0001111 => 1110000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => 0001110 => 1110001
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => 0001101 => 1110010
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => 0001110 => 1110001
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => 0001100 => 1110011
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => 0001011 => 1110100
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => 0001010 => 1110101
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => 0001101 => 1110010
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => 0001001 => 1110110
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => 0001110 => 1110001
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => 0001100 => 1110011
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => 0001010 => 1110101
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => 0001100 => 1110011
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => 0001000 => 1110111
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => 1110111 => 0001000
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => 1110110 => 0001001
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => 1110101 => 0001010
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => 1110110 => 0001001
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => 1110100 => 0001011
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => 1100111 => 0011000
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => 1100110 => 0011001
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => 1100101 => 0011010
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => 1100110 => 0011001
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [3,4,2,1,6,7,8,5] => 1100100 => 0011011
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => 1010111 => 0101000
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [2,4,3,1,7,8,6,5] => 1010110 => 0101001
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => 1010101 => 0101010
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => 1010110 => 0101001
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [2,4,3,1,6,7,8,5] => 1010100 => 0101011
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => 1100111 => 0011000
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => 1100110 => 0011001
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => 1100101 => 0011010
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => 1100110 => 0011001
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [3,2,4,1,6,7,8,5] => 1100100 => 0011011
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => 1000111 => 0111000
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [2,3,4,1,7,8,6,5] => 1000110 => 0111001
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [2,3,4,1,6,8,7,5] => 1000101 => 0111010
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => 1000110 => 0111001
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => 1000100 => 0111011
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => 0110111 => 1001000
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,4,3,2,6,8,7,5] => 0110101 => 1001010
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => 0110110 => 1001001
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => 0110100 => 1001011
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => 0100111 => 1011000
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,3,4,2,7,8,6,5] => 0100110 => 1011001
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,3,4,2,6,8,7,5] => 0100101 => 1011010
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => 0100110 => 1011001
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,3,4,2,6,7,8,5] => 0100100 => 1011011
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => 1010111 => 0101000
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => 1010110 => 0101001
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => 1010101 => 0101010
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => 1010110 => 0101001
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => 1010100 => 0101011
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => 0010111 => 1101000
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,2,4,3,7,8,6,5] => 0010110 => 1101001
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => 0010101 => 1101010
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => 0010110 => 1101001
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => 0010100 => 1101011
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => 1100111 => 0011000
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [3,2,1,4,7,8,6,5] => 1100110 => 0011001
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [3,2,1,4,6,8,7,5] => 1100101 => 0011010
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [3,2,1,4,7,6,8,5] => 1100110 => 0011001
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [3,2,1,4,6,7,8,5] => 1100100 => 0011011
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => 1000111 => 0111000
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [2,3,1,4,7,8,6,5] => 1000110 => 0111001
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => 1000110 => 0111001
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [2,3,1,4,6,7,8,5] => 1000100 => 0111011
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => 0100111 => 1011000
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,3,2,4,6,8,7,5] => 0100101 => 1011010
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => 0100110 => 1011001
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,3,2,4,6,7,8,5] => 0100100 => 1011011
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => 1000111 => 0111000
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [2,1,3,4,7,8,6,5] => 1000110 => 0111001
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => 1000110 => 0111001
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => 1000100 => 0111011
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => 0000111 => 1111000
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => 0000110 => 1111001
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => 0000101 => 1111010
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => 0000110 => 1111001
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => 0000100 => 1111011
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => 1111011 => 0000100
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => 1111010 => 0000101
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [4,5,3,2,1,8,7,6] => 1110011 => 0001100
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [3,5,4,2,1,8,7,6] => 1101011 => 0010100
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [3,5,4,2,1,7,8,6] => 1101010 => 0010101
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [4,3,5,2,1,8,7,6] => 1110011 => 0001100
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [3,4,5,2,1,8,7,6] => 1100011 => 0011100
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [3,4,5,2,1,7,8,6] => 1100010 => 0011101
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [2,5,4,3,1,8,7,6] => 1011011 => 0100100
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [2,5,4,3,1,7,8,6] => 1011010 => 0100101
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [2,4,5,3,1,8,7,6] => 1010011 => 0101100
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [2,4,5,3,1,7,8,6] => 1010010 => 0101101
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => 1101011 => 0010100
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [3,2,5,4,1,7,8,6] => 1101010 => 0010101
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [2,3,5,4,1,8,7,6] => 1001011 => 0110100
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => 1110011 => 0001100
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [4,3,2,5,1,7,8,6] => 1110010 => 0001101
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => 1100011 => 0011100
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [3,4,2,5,1,7,8,6] => 1100010 => 0011101
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [2,4,3,5,1,8,7,6] => 1010011 => 0101100
[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [2,4,3,5,1,7,8,6] => 1010010 => 0101101
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [3,2,4,5,1,8,7,6] => 1100011 => 0011100
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [2,3,4,5,1,8,7,6] => 1000011 => 0111100
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => 1000010 => 0111101
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => 0111011 => 1000100
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,5,4,3,2,7,8,6] => 0111010 => 1000101
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,4,5,3,2,8,7,6] => 0110011 => 1001100
[[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,4,5,3,2,7,8,6] => 0110010 => 1001101
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,3,5,4,2,7,8,6] => 0101010 => 1010101
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,4,3,5,2,8,7,6] => 0110011 => 1001100
[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,4,3,5,2,7,8,6] => 0110010 => 1001101
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,3,4,5,2,8,7,6] => 0100011 => 1011100
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,3,4,5,2,7,8,6] => 0100010 => 1011101
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [2,1,5,4,3,8,7,6] => 1011011 => 0100100
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [2,1,4,5,3,8,7,6] => 1010011 => 0101100
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => 0011011 => 1100100
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,2,5,4,3,7,8,6] => 0011010 => 1100101
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => 0010011 => 1101100
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,2,4,5,3,7,8,6] => 0010010 => 1101101
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => 0101011 => 1010100
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,3,2,5,4,7,8,6] => 0101010 => 1010101
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [2,1,3,5,4,8,7,6] => 1001011 => 0110100
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [2,1,3,5,4,7,8,6] => 1001010 => 0110101
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => 0001011 => 1110100
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,2,3,5,4,7,8,6] => 0001010 => 1110101
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => 1110011 => 0001100
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => 1110010 => 0001101
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [3,4,2,1,5,8,7,6] => 1100011 => 0011100
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [2,4,3,1,5,8,7,6] => 1010011 => 0101100
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => 1100011 => 0011100
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => 1100010 => 0011101
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [2,3,4,1,5,8,7,6] => 1000011 => 0111100
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [2,3,4,1,5,7,8,6] => 1000010 => 0111101
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => 0110011 => 1001100
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,4,3,2,5,7,8,6] => 0110010 => 1001101
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,3,4,2,5,8,7,6] => 0100011 => 1011100
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,3,4,2,5,7,8,6] => 0100010 => 1011101
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [2,1,4,3,5,8,7,6] => 1010011 => 0101100
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [2,1,4,3,5,7,8,6] => 1010010 => 0101101
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,2,4,3,5,8,7,6] => 0010011 => 1101100
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,2,4,3,5,7,8,6] => 0010010 => 1101101
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => 1100011 => 0011100
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [3,2,1,4,5,7,8,6] => 1100010 => 0011101
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => 1000010 => 0111101
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,3,2,4,5,8,7,6] => 0100011 => 1011100
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,3,2,4,5,7,8,6] => 0100010 => 1011101
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [2,1,3,4,5,8,7,6] => 1000011 => 0111100
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [2,1,3,4,5,7,8,6] => 1000010 => 0111101
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => 0000011 => 1111100
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => 0000010 => 1111101
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => 1111101 => 0000010
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [5,6,4,3,2,1,8,7] => 1111001 => 0000110
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [4,6,5,3,2,1,8,7] => 1110101 => 0001010
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [5,4,6,3,2,1,8,7] => 1111001 => 0000110
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => 1110001 => 0001110
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [3,6,5,4,2,1,8,7] => 1101101 => 0010010
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => 1101001 => 0010110
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [4,3,6,5,2,1,8,7] => 1110101 => 0001010
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [3,4,6,5,2,1,8,7] => 1100101 => 0011010
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [5,4,3,6,2,1,8,7] => 1111001 => 0000110
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [4,5,3,6,2,1,8,7] => 1110001 => 0001110
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [4,3,5,6,2,1,8,7] => 1110001 => 0001110
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [3,4,5,6,2,1,8,7] => 1100001 => 0011110
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [2,6,5,4,3,1,8,7] => 1011101 => 0100010
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [2,5,6,4,3,1,8,7] => 1011001 => 0100110
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [2,4,6,5,3,1,8,7] => 1010101 => 0101010
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [3,2,6,5,4,1,8,7] => 1101101 => 0010010
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [3,2,5,6,4,1,8,7] => 1101001 => 0010110
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [2,3,6,5,4,1,8,7] => 1001101 => 0110010
[[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [2,3,5,6,4,1,8,7] => 1001001 => 0110110
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [4,3,2,6,5,1,8,7] => 1110101 => 0001010
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [3,4,2,6,5,1,8,7] => 1100101 => 0011010
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => 1010101 => 0101010
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [5,4,3,2,6,1,8,7] => 1111001 => 0000110
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [4,5,3,2,6,1,8,7] => 1110001 => 0001110
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [3,5,4,2,6,1,8,7] => 1101001 => 0010110
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => 1110001 => 0001110
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [3,4,5,2,6,1,8,7] => 1100001 => 0011110
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [2,5,4,3,6,1,8,7] => 1011001 => 0100110
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [2,4,5,3,6,1,8,7] => 1010001 => 0101110
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => 1101001 => 0010110
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [4,3,2,5,6,1,8,7] => 1110001 => 0001110
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [3,4,2,5,6,1,8,7] => 1100001 => 0011110
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [2,4,3,5,6,1,8,7] => 1010001 => 0101110
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => 1000001 => 0111110
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => 0111101 => 1000010
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => 0111001 => 1000110
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,5,4,6,3,2,8,7] => 0111001 => 1000110
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,3,6,5,4,2,8,7] => 0101101 => 1010010
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,3,4,5,6,2,8,7] => 0100001 => 1011110
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => 1011101 => 0100010
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => 1011001 => 0100110
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => 1010101 => 0101010
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => 1011001 => 0100110
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => 1010001 => 0101110
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,2,4,5,6,3,8,7] => 0010001 => 1101110
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [3,2,1,6,5,4,8,7] => 1101101 => 0010010
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [2,3,1,6,5,4,8,7] => 1001101 => 0110010
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,3,2,6,5,4,8,7] => 0101101 => 1010010
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,3,2,5,6,4,8,7] => 0101001 => 1010110
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [2,1,3,6,5,4,8,7] => 1001101 => 0110010
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [2,1,3,5,6,4,8,7] => 1001001 => 0110110
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,2,3,6,5,4,8,7] => 0001101 => 1110010
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,2,3,5,6,4,8,7] => 0001001 => 1110110
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => 1110101 => 0001010
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => 1100101 => 0011010
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => 1010101 => 0101010
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => 1100101 => 0011010
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => 1000101 => 0111010
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => 0100101 => 1011010
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => 1010101 => 0101010
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => 0010101 => 1101010
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [2,3,1,4,6,5,8,7] => 1000101 => 0111010
[[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,3,2,4,6,5,8,7] => 0100101 => 1011010
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [2,1,3,4,6,5,8,7] => 1000101 => 0111010
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => 0000101 => 1111010
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => 1111001 => 0000110
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [4,5,3,2,1,6,8,7] => 1110001 => 0001110
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => [3,5,4,2,1,6,8,7] => 1101001 => 0010110
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [4,3,5,2,1,6,8,7] => 1110001 => 0001110
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [3,4,5,2,1,6,8,7] => 1100001 => 0011110
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [2,5,4,3,1,6,8,7] => 1011001 => 0100110
[[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [2,4,5,3,1,6,8,7] => 1010001 => 0101110
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [3,2,5,4,1,6,8,7] => 1101001 => 0010110
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [2,3,5,4,1,6,8,7] => 1001001 => 0110110
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [2,4,3,5,1,6,8,7] => 1010001 => 0101110
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [2,3,4,5,1,6,8,7] => 1000001 => 0111110
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,4,5,3,2,6,8,7] => 0110001 => 1001110
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,3,5,4,2,6,8,7] => 0101001 => 1010110
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,3,4,5,2,6,8,7] => 0100001 => 1011110
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => 1011001 => 0100110
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => 1010001 => 0101110
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,2,5,4,3,6,8,7] => 0011001 => 1100110
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [2,1,3,5,4,6,8,7] => 1001001 => 0110110
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => 0001001 => 1110110
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => 1110001 => 0001110
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [3,4,2,1,5,6,8,7] => 1100001 => 0011110
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => 1100001 => 0011110
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [2,3,4,1,5,6,8,7] => 1000001 => 0111110
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,4,3,2,5,6,8,7] => 0110001 => 1001110
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,3,4,2,5,6,8,7] => 0100001 => 1011110
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [2,1,4,3,5,6,8,7] => 1010001 => 0101110
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => 0010001 => 1101110
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [3,2,1,4,5,6,8,7] => 1100001 => 0011110
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [2,3,1,4,5,6,8,7] => 1000001 => 0111110
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => 0100001 => 1011110
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => 1000001 => 0111110
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => 0000001 => 1111110
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 1111110 => 0000001
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 1111100 => 0000011
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => 1111010 => 0000101
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 1111100 => 0000011
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 1111000 => 0000111
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => 1110110 => 0001001
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [4,6,7,5,3,2,1,8] => 1110100 => 0001011
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [5,4,7,6,3,2,1,8] => 1111010 => 0000101
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [4,5,7,6,3,2,1,8] => 1110010 => 0001101
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 1111100 => 0000011
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => 1111000 => 0000111
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [4,6,5,7,3,2,1,8] => 1110100 => 0001011
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => 1111000 => 0000111
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => 1110000 => 0001111
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [3,5,7,6,4,2,1,8] => 1101010 => 0010101
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [3,5,6,7,4,2,1,8] => 1101000 => 0010111
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [4,3,7,6,5,2,1,8] => 1110110 => 0001001
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => 1100110 => 0011001
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [5,4,3,7,6,2,1,8] => 1111010 => 0000101
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [4,5,3,7,6,2,1,8] => 1110010 => 0001101
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [3,5,4,7,6,2,1,8] => 1101010 => 0010101
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [4,3,5,7,6,2,1,8] => 1110010 => 0001101
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => 1111100 => 0000011
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => 1111000 => 0000111
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => 1111000 => 0000111
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [3,6,5,4,7,2,1,8] => 1101100 => 0010011
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [3,5,6,4,7,2,1,8] => 1101000 => 0010111
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [4,3,6,5,7,2,1,8] => 1110100 => 0001011
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => 1111000 => 0000111
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => 1100000 => 0011111
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => 1011110 => 0100001
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [2,6,7,5,4,3,1,8] => 1011100 => 0100011
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [2,5,7,6,4,3,1,8] => 1011010 => 0100101
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [2,5,6,7,4,3,1,8] => 1011000 => 0100111
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => 1010100 => 0101011
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [2,5,4,7,6,3,1,8] => 1011010 => 0100101
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [2,5,6,4,7,3,1,8] => 1011000 => 0100111
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [2,5,4,6,7,3,1,8] => 1011000 => 0100111
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [2,4,5,6,7,3,1,8] => 1010000 => 0101111
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => 1101110 => 0010001
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [3,2,6,7,5,4,1,8] => 1101100 => 0010011
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [3,2,5,7,6,4,1,8] => 1101010 => 0010101
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [3,2,6,5,7,4,1,8] => 1101100 => 0010011
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [3,2,5,6,7,4,1,8] => 1101000 => 0010111
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [2,3,7,6,5,4,1,8] => 1001110 => 0110001
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [2,3,6,7,5,4,1,8] => 1001100 => 0110011
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [2,3,5,7,6,4,1,8] => 1001010 => 0110101
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [2,3,6,5,7,4,1,8] => 1001100 => 0110011
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [2,3,5,6,7,4,1,8] => 1001000 => 0110111
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [4,3,2,6,7,5,1,8] => 1110100 => 0001011
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [3,4,2,7,6,5,1,8] => 1100110 => 0011001
[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [3,2,4,6,7,5,1,8] => 1100100 => 0011011
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [2,3,4,7,6,5,1,8] => 1000110 => 0111001
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [2,3,4,6,7,5,1,8] => 1000100 => 0111011
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => 1111010 => 0000101
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [4,5,3,2,7,6,1,8] => 1110010 => 0001101
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [3,5,4,2,7,6,1,8] => 1101010 => 0010101
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [4,3,5,2,7,6,1,8] => 1110010 => 0001101
[[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [3,4,5,2,7,6,1,8] => 1100010 => 0011101
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => 1101010 => 0010101
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [4,3,2,5,7,6,1,8] => 1110010 => 0001101
[[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [3,4,2,5,7,6,1,8] => 1100010 => 0011101
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => 1000010 => 0111101
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => 1111100 => 0000011
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => 1111000 => 0000111
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => 1111000 => 0000111
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [3,6,5,4,2,7,1,8] => 1101100 => 0010011
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [3,4,6,5,2,7,1,8] => 1100100 => 0011011
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => 1111000 => 0000111
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => 1110000 => 0001111
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => 1101000 => 0010111
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => 1110000 => 0001111
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => 1100000 => 0011111
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [2,5,4,6,3,7,1,8] => 1011000 => 0100111
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [3,2,6,5,4,7,1,8] => 1101100 => 0010011
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [2,3,5,6,4,7,1,8] => 1001000 => 0110111
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [4,3,2,6,5,7,1,8] => 1110100 => 0001011
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [3,4,2,6,5,7,1,8] => 1100100 => 0011011
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [2,4,3,6,5,7,1,8] => 1010100 => 0101011
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => 1000100 => 0111011
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => 1111000 => 0000111
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [3,5,4,2,6,7,1,8] => 1101000 => 0010111
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => 1100000 => 0011111
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [2,5,4,3,6,7,1,8] => 1011000 => 0100111
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [2,4,5,3,6,7,1,8] => 1010000 => 0101111
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [2,3,5,4,6,7,1,8] => 1001000 => 0110111
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => 1110000 => 0001111
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => 1100000 => 0011111
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => 1100000 => 0011111
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 1000000 => 0111111
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => 0111110 => 1000001
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => 0111100 => 1000011
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,6,5,7,4,3,2,8] => 0111100 => 1000011
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,5,6,7,4,3,2,8] => 0111000 => 1000111
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,4,7,6,5,3,2,8] => 0110110 => 1001001
[[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,4,6,7,5,3,2,8] => 0110100 => 1001011
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,5,4,7,6,3,2,8] => 0111010 => 1000101
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,5,6,4,7,3,2,8] => 0111000 => 1000111
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,4,6,5,7,3,2,8] => 0110100 => 1001011
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,5,4,6,7,3,2,8] => 0111000 => 1000111
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => 0110000 => 1001111
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,3,7,6,5,4,2,8] => 0101110 => 1010001
[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,3,6,7,5,4,2,8] => 0101100 => 1010011
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,3,5,7,6,4,2,8] => 0101010 => 1010101
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,3,6,5,7,4,2,8] => 0101100 => 1010011
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,3,5,6,7,4,2,8] => 0101000 => 1010111
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => 0100100 => 1011011
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,3,5,4,7,6,2,8] => 0101010 => 1010101
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,4,3,5,7,6,2,8] => 0110010 => 1001101
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,3,4,5,7,6,2,8] => 0100010 => 1011101
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,5,4,6,3,7,2,8] => 0111000 => 1000111
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,4,5,6,3,7,2,8] => 0110000 => 1001111
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,3,6,5,4,7,2,8] => 0101100 => 1010011
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => 0101000 => 1010111
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,4,3,6,5,7,2,8] => 0110100 => 1001011
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,3,4,6,5,7,2,8] => 0100100 => 1011011
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,5,4,3,6,7,2,8] => 0111000 => 1000111
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,4,5,3,6,7,2,8] => 0110000 => 1001111
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,3,5,4,6,7,2,8] => 0101000 => 1010111
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,3,4,5,6,7,2,8] => 0100000 => 1011111
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [2,1,7,6,5,4,3,8] => 1011110 => 0100001
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [2,1,6,7,5,4,3,8] => 1011100 => 0100011
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [2,1,5,6,7,4,3,8] => 1011000 => 0100111
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [2,1,4,6,7,5,3,8] => 1010100 => 0101011
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [2,1,5,4,6,7,3,8] => 1011000 => 0100111
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [2,1,4,5,6,7,3,8] => 1010000 => 0101111
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8] => 0011110 => 1100001
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,2,6,7,5,4,3,8] => 0011100 => 1100011
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,2,5,7,6,4,3,8] => 0011010 => 1100101
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,2,5,6,7,4,3,8] => 0011000 => 1100111
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,2,4,6,7,5,3,8] => 0010100 => 1101011
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,2,5,6,4,7,3,8] => 0011000 => 1100111
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,2,5,4,6,7,3,8] => 0011000 => 1100111
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,2,4,5,6,7,3,8] => 0010000 => 1101111
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => 1101110 => 0010001
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [3,2,1,6,7,5,4,8] => 1101100 => 0010011
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [3,2,1,5,7,6,4,8] => 1101010 => 0010101
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [3,2,1,6,5,7,4,8] => 1101100 => 0010011
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [3,2,1,5,6,7,4,8] => 1101000 => 0010111
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [2,3,1,6,7,5,4,8] => 1001100 => 0110011
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [2,3,1,6,5,7,4,8] => 1001100 => 0110011
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => 1001000 => 0110111
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,3,2,7,6,5,4,8] => 0101110 => 1010001
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,3,2,6,7,5,4,8] => 0101100 => 1010011
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,3,2,5,7,6,4,8] => 0101010 => 1010101
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,3,2,6,5,7,4,8] => 0101100 => 1010011
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,3,2,5,6,7,4,8] => 0101000 => 1010111
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [2,1,3,6,7,5,4,8] => 1001100 => 0110011
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => 0001110 => 1110001
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => 0001100 => 1110011
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,2,3,5,7,6,4,8] => 0001010 => 1110101
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,2,3,6,5,7,4,8] => 0001100 => 1110011
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => 0001000 => 1110111
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => 1110110 => 0001001
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => 1110100 => 0001011
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8] => 1100110 => 0011001
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => 1100100 => 0011011
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8] => 1000110 => 0111001
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [2,3,4,1,6,7,5,8] => 1000100 => 0111011
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => 0110110 => 1001001
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,4,3,2,6,7,5,8] => 0110100 => 1001011
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => 0100100 => 1011011
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [2,1,4,3,6,7,5,8] => 1010100 => 0101011
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,2,4,3,6,7,5,8] => 0010100 => 1101011
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => 1100110 => 0011001
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => 1000100 => 0111011
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8] => 0100110 => 1011001
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [2,1,3,4,6,7,5,8] => 1000100 => 0111011
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => 0000110 => 1111001
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => 0000100 => 1111011
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8] => 1111010 => 0000101
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [4,5,3,2,1,7,6,8] => 1110010 => 0001101
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [3,5,4,2,1,7,6,8] => 1101010 => 0010101
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [3,4,5,2,1,7,6,8] => 1100010 => 0011101
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [2,5,4,3,1,7,6,8] => 1011010 => 0100101
[[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [2,4,5,3,1,7,6,8] => 1010010 => 0101101
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [3,2,5,4,1,7,6,8] => 1101010 => 0010101
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [2,3,5,4,1,7,6,8] => 1001010 => 0110101
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [3,4,2,5,1,7,6,8] => 1100010 => 0011101
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8] => 1010010 => 0101101
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [2,3,4,5,1,7,6,8] => 1000010 => 0111101
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => 0111010 => 1000101
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,4,5,3,2,7,6,8] => 0110010 => 1001101
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => 0101010 => 1010101
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,4,3,5,2,7,6,8] => 0110010 => 1001101
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => 0100010 => 1011101
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [2,1,5,4,3,7,6,8] => 1011010 => 0100101
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,2,4,5,3,7,6,8] => 0010010 => 1101101
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => 1101010 => 0010101
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => 1001010 => 0110101
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => 0101010 => 1010101
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => 0001010 => 1110101
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => 1110010 => 0001101
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => 1100010 => 0011101
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [2,3,4,1,5,7,6,8] => 1000010 => 0111101
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => 0110010 => 1001101
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,3,4,2,5,7,6,8] => 0100010 => 1011101
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => 0010010 => 1101101
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [3,2,1,4,5,7,6,8] => 1100010 => 0011101
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8] => 1000010 => 0111101
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => 0100010 => 1011101
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => 1000010 => 0111101
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => 0000010 => 1111101
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 1111100 => 0000011
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => 1111000 => 0000111
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => 1111000 => 0000111
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => 1110000 => 0001111
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [3,6,5,4,2,1,7,8] => 1101100 => 0010011
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [4,3,6,5,2,1,7,8] => 1110100 => 0001011
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => 1111000 => 0000111
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => 1100000 => 0011111
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [2,4,6,5,3,1,7,8] => 1010100 => 0101011
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [2,4,5,6,3,1,7,8] => 1010000 => 0101111
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [2,3,6,5,4,1,7,8] => 1001100 => 0110011
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [2,3,5,6,4,1,7,8] => 1001000 => 0110111
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [4,3,2,6,5,1,7,8] => 1110100 => 0001011
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [2,4,3,6,5,1,7,8] => 1010100 => 0101011
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => 1000100 => 0111011
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => 1111000 => 0000111
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => 1110000 => 0001111
[[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [3,5,4,2,6,1,7,8] => 1101000 => 0010111
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => 1110000 => 0001111
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => 1100000 => 0011111
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => 1001000 => 0110111
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => 1110000 => 0001111
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => 1100000 => 0011111
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => 1100000 => 0011111
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 1000000 => 0111111
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => 0111100 => 1000011
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,5,6,4,3,2,7,8] => 0111000 => 1000111
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,4,6,5,3,2,7,8] => 0110100 => 1001011
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,5,4,6,3,2,7,8] => 0111000 => 1000111
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,4,5,6,3,2,7,8] => 0110000 => 1001111
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => 0101000 => 1010111
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,4,3,6,5,2,7,8] => 0110100 => 1001011
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,5,4,3,6,2,7,8] => 0111000 => 1000111
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,4,5,3,6,2,7,8] => 0110000 => 1001111
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,3,5,4,6,2,7,8] => 0101000 => 1010111
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,4,3,5,6,2,7,8] => 0110000 => 1001111
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => 0100000 => 1011111
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [2,1,5,6,4,3,7,8] => 1011000 => 0100111
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [2,1,4,6,5,3,7,8] => 1010100 => 0101011
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => 0011100 => 1100011
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => 0011000 => 1100111
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,2,4,6,5,3,7,8] => 0010100 => 1101011
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => 0010000 => 1101111
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [3,2,1,6,5,4,7,8] => 1101100 => 0010011
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [3,2,1,5,6,4,7,8] => 1101000 => 0010111
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [2,3,1,6,5,4,7,8] => 1001100 => 0110011
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [2,3,1,5,6,4,7,8] => 1001000 => 0110111
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => 0101100 => 1010011
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,3,2,5,6,4,7,8] => 0101000 => 1010111
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => 0001100 => 1110011
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,2,3,5,6,4,7,8] => 0001000 => 1110111
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => 1110100 => 0001011
[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [2,4,3,1,6,5,7,8] => 1010100 => 0101011
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => 1100100 => 0011011
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [2,3,4,1,6,5,7,8] => 1000100 => 0111011
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => 1010100 => 0101011
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => 0010100 => 1101011
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => 0100100 => 1011011
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => 1000100 => 0111011
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => 0000100 => 1111011
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 1111000 => 0000111
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => 1110000 => 0001111
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [3,5,4,2,1,6,7,8] => 1101000 => 0010111
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => 1110000 => 0001111
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => 1100000 => 0011111
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [2,5,4,3,1,6,7,8] => 1011000 => 0100111
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => 1010000 => 0101111
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [3,2,5,4,1,6,7,8] => 1101000 => 0010111
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [2,3,5,4,1,6,7,8] => 1001000 => 0110111
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => 1110000 => 0001111
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => 1100000 => 0011111
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => 1010000 => 0101111
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => 1100000 => 0011111
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 1000000 => 0111111
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => 0111000 => 1000111
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,4,5,3,2,6,7,8] => 0110000 => 1001111
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,3,5,4,2,6,7,8] => 0101000 => 1010111
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => 0100000 => 1011111
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8] => 1011000 => 0100111
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => 1010000 => 0101111
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => 0011000 => 1100111
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [3,2,1,5,4,6,7,8] => 1101000 => 0010111
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [2,3,1,5,4,6,7,8] => 1001000 => 0110111
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => 0101000 => 1010111
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8] => 1001000 => 0110111
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => 0001000 => 1110111
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 1110000 => 0001111
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => 1100000 => 0011111
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => 1010000 => 0101111
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => 1100000 => 0011111
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => 1000000 => 0111111
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => 0110000 => 1001111
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => 0100000 => 1011111
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => 1010000 => 0101111
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => 0010000 => 1101111
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 1100000 => 0011111
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => 1000000 => 0111111
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => 0100000 => 1011111
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 1000000 => 0111111
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 0000000 => 1111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 11111111 => 00000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => 11111110 => 00000001
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => 11111100 => 00000011
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => 11111000 => 00000111
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => 11110000 => 00001111
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => 11100000 => 00011111
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => 11000000 => 00111111
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 10000000 => 01111111
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 00000000 => 11111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 000000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => 111111110 => 000000001
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [7,9,8,6,5,4,3,2,1] => 11111101 => 00000010
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => 111111100 => 000000011
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => 111111000 => 000000111
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => 111110000 => 000001111
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => 111100000 => 000011111
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [3,5,6,7,8,9,4,2,1] => 11010000 => 00101111
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => 111000000 => 000111111
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [2,4,5,6,7,8,9,3,1] => 10100000 => 01011111
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => 110000000 => 001111111
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,2] => 01000000 => 10111111
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 100000000 => 011111111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 111111111
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => 11111110 => 00000001
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => 11111110 => 00000001
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => 11111110 => 00000001
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => 11111110 => 00000001
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => 11111110 => 00000001
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => 11111110 => 00000001
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 11111110 => 00000001
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => 111111110 => 000000001
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [6,8,7,9,5,4,3,2,1] => 11111010 => 00000101
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => 111111110 => 000000001
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [5,8,7,6,9,4,3,2,1] => 11110110 => 00001001
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => 111111110 => 000000001
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [4,8,7,6,5,9,3,2,1] => 11101110 => 00010001
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => 111111110 => 000000001
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [3,8,7,6,5,4,9,2,1] => 11011110 => 00100001
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => 111111110 => 000000001
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [2,8,7,6,5,4,3,9,1] => 10111110 => 01000001
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => 111111110 => 000000001
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,8,7,6,5,4,3,2,9] => 01111110 => 10000001
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => 111111110 => 000000001
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 111111110 => 000000001
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,3,5,7,9,10,8,6,4,2] => 010101010 => 101010101
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [1,6,7,5,8,4,9,3,10,2] => 011110000 => 100001111
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => 111100000 => 000011111
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,10,9,1] => 101010101 => 010101010
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,1,4,6,5,3,8,10,9,7] => 101010101 => 010101010
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,1,4,6,5,3,8,7,10,9] => 101010101 => 010101010
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,9,8,1,10] => 110101010 => 001010101
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => 101010101 => 010101010
[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,10,9,12,11,1] => 10101010101 => 01010101010
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3,8,7,10,12,11,9] => 10101010101 => 01010101010
[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,10,9,7,12,11] => 10101010101 => 01010101010
[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [2,1,4,6,5,3,8,7,10,9,12,11] => 10101010101 => 01010101010
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,9,8,11,10,1,12] => 11010101010 => 00101010101
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => 10101010101 => 01010101010
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => 00000001 => 11111110
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => 000000001 => 111111110
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,9,8] => 10000001 => 01111110
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 11000000 => 00111111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001 => 1111111110
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,8,10,9] => 100000001 => 011111110
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,3,2,4,5,6,7,9,8] => 01000001 => 10111110
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [2,3,1,4,5,6,7,9,8] => 10000001 => 01111110
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [2,4,3,5,6,7,8,9,1] => 10100000 => 01011111
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 11000000 => 00111111
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 110000000 => 001111111
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 1000000000 => 0111111111
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => 00000010 => 11111101
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,7,8,9,6] => 00000100 => 11111011
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,6,7,8,9,5] => 00001000 => 11110111
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,5,6,7,8,9,4] => 00010000 => 11101111
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,3] => 00100000 => 11011111
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => 00000011 => 11111100
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,7,9,10,8] => 000000010 => 111111101
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,5,8,7,9,6] => 00000110 => 11111001
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,6,8,9,10,7] => 000000100 => 111111011
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,4,7,6,8,9,5] => 00001100 => 11110011
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,5,7,8,9,10,6] => 000001000 => 111110111
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [1,2,3,6,5,7,8,9,4] => 00011000 => 11100111
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,4,6,7,8,9,10,5] => 000010000 => 111101111
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [1,2,5,4,6,7,8,9,3] => 00110000 => 11001111
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,3,5,6,7,8,9,10,4] => 000100000 => 111011111
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,4,3,5,6,7,8,9,2] => 01100000 => 10011111
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,10,3] => 001000000 => 110111111
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,10,2] => 010000000 => 101111111
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => 01111111 => 10000000
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 11111100 => 00000011
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => 01111110 => 10000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 100000000
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110 => 0000000001
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 111111100 => 000000011
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 11111100 => 00000011
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,8,7,9,6,5,4,3,2] => 01111110 => 10000001
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,9,10,8,7,6,5,4,3,2] => 011111110 => 100000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 1000000000
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => 111110000 => 000001111
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [5,4,7,6,8,3,9,2,10,1] => 111101000 => 000010111
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [4,3,7,6,8,5,9,2,10,1] => 111011000 => 000100111
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [5,4,6,3,8,7,9,2,10,1] => 111100100 => 000011011
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [4,3,6,5,8,7,9,2,10,1] => 111010100 => 000101011
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [3,2,7,6,8,5,9,4,10,1] => 110111000 => 001000111
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [3,2,6,5,8,7,9,4,10,1] => 110110100 => 001001011
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [4,3,5,2,8,7,9,6,10,1] => 111001100 => 000110011
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [3,2,5,4,8,7,9,6,10,1] => 110101100 => 001010011
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [5,4,6,3,7,2,9,8,10,1] => 111100010 => 000011101
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [4,3,6,5,7,2,9,8,10,1] => 111010010 => 000101101
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [3,2,6,5,7,4,9,8,10,1] => 110110010 => 001001101
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [4,3,5,2,7,6,9,8,10,1] => 111001010 => 000110101
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,10,1] => 110101010 => 001010101
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [2,1,7,6,8,5,9,4,10,3] => 101111000 => 010000111
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [2,1,6,5,8,7,9,4,10,3] => 101110100 => 010001011
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [2,1,5,4,8,7,9,6,10,3] => 101101100 => 010010011
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [2,1,6,5,7,4,9,8,10,3] => 101110010 => 010001101
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [2,1,5,4,7,6,9,8,10,3] => 101101010 => 010010101
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [3,2,4,1,8,7,9,6,10,5] => 110011100 => 001100011
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [3,2,4,1,7,6,9,8,10,5] => 110011010 => 001100101
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,4,3,8,7,9,6,10,5] => 101011100 => 010100011
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,4,3,7,6,9,8,10,5] => 101011010 => 010100101
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [4,3,5,2,6,1,9,8,10,7] => 111000110 => 000111001
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [3,2,5,4,6,1,9,8,10,7] => 110100110 => 001011001
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [2,1,5,4,6,3,9,8,10,7] => 101100110 => 010011001
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [3,2,4,1,6,5,9,8,10,7] => 110010110 => 001101001
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,6,5,9,8,10,7] => 101010110 => 010101001
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [5,4,6,3,7,2,8,1,10,9] => 111100001 => 000011110
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [4,3,6,5,7,2,8,1,10,9] => 111010001 => 000101110
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [3,2,6,5,7,4,8,1,10,9] => 110110001 => 001001110
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [4,3,5,2,7,6,8,1,10,9] => 111001001 => 000110110
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,7,6,8,1,10,9] => 110101001 => 001010110
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [2,1,6,5,7,4,8,3,10,9] => 101110001 => 010001110
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [2,1,5,4,7,6,8,3,10,9] => 101101001 => 010010110
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [3,2,4,1,7,6,8,5,10,9] => 110011001 => 001100110
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,4,3,7,6,8,5,10,9] => 101011001 => 010100110
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [4,3,5,2,6,1,8,7,10,9] => 111000101 => 000111010
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => [3,2,5,4,6,1,8,7,10,9] => 110100101 => 001011010
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [2,1,5,4,6,3,8,7,10,9] => 101100101 => 010011010
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7,10,9] => 110010101 => 001101010
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [7,6,8,5,9,4,10,3,11,2,12,1] => 11111100000 => 00000011111
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]] => [6,5,8,7,9,4,10,3,11,2,12,1] => 11111010000 => 00000101111
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]] => [5,4,8,7,9,6,10,3,11,2,12,1] => 11110110000 => 00001001111
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]] => [6,5,7,4,9,8,10,3,11,2,12,1] => 11111001000 => 00000110111
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]] => [5,4,7,6,9,8,10,3,11,2,12,1] => 11110101000 => 00001010111
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]] => [4,3,8,7,9,6,10,5,11,2,12,1] => 11101110000 => 00010001111
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]] => [4,3,7,6,9,8,10,5,11,2,12,1] => 11101101000 => 00010010111
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]] => [5,4,6,3,9,8,10,7,11,2,12,1] => 11110011000 => 00001100111
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]] => [4,3,6,5,9,8,10,7,11,2,12,1] => 11101011000 => 00010100111
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]] => [6,5,7,4,8,3,10,9,11,2,12,1] => 11111000100 => 00000111011
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => [5,4,7,6,8,3,10,9,11,2,12,1] => 11110100100 => 00001011011
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => [4,3,7,6,8,5,10,9,11,2,12,1] => 11101100100 => 00010011011
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => [5,4,6,3,8,7,10,9,11,2,12,1] => 11110010100 => 00001101011
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => [4,3,6,5,8,7,10,9,11,2,12,1] => 11101010100 => 00010101011
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [3,2,8,7,9,6,10,5,11,4,12,1] => 11011110000 => 00100001111
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [3,2,7,6,9,8,10,5,11,4,12,1] => 11011101000 => 00100010111
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [3,2,6,5,9,8,10,7,11,4,12,1] => 11011011000 => 00100100111
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [3,2,7,6,8,5,10,9,11,4,12,1] => 11011100100 => 00100011011
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [3,2,6,5,8,7,10,9,11,4,12,1] => 11011010100 => 00100101011
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => [4,3,5,2,9,8,10,7,11,6,12,1] => 11100111000 => 00011000111
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]] => [4,3,5,2,8,7,10,9,11,6,12,1] => 11100110100 => 00011001011
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [3,2,5,4,9,8,10,7,11,6,12,1] => 11010111000 => 00101000111
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [3,2,5,4,8,7,10,9,11,6,12,1] => 11010110100 => 00101001011
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => [5,4,6,3,7,2,10,9,11,8,12,1] => 11110001100 => 00001110011
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]] => [4,3,6,5,7,2,10,9,11,8,12,1] => 11101001100 => 00010110011
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,10,9,11,8,12,1] => 11011001100 => 00100110011
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]] => [4,3,5,2,7,6,10,9,11,8,12,1] => 11100101100 => 00011010011
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [3,2,5,4,7,6,10,9,11,8,12,1] => 11010101100 => 00101010011
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => [6,5,7,4,8,3,9,2,11,10,12,1] => 11111000010 => 00000111101
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => [5,4,7,6,8,3,9,2,11,10,12,1] => 11110100010 => 00001011101
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => [4,3,7,6,8,5,9,2,11,10,12,1] => 11101100010 => 00010011101
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => [5,4,6,3,8,7,9,2,11,10,12,1] => 11110010010 => 00001101101
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => [4,3,6,5,8,7,9,2,11,10,12,1] => 11101010010 => 00010101101
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [3,2,7,6,8,5,9,4,11,10,12,1] => 11011100010 => 00100011101
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [3,2,6,5,8,7,9,4,11,10,12,1] => 11011010010 => 00100101101
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,8,7,9,6,11,10,12,1] => 11100110010 => 00011001101
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [3,2,5,4,8,7,9,6,11,10,12,1] => 11010110010 => 00101001101
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]] => [5,4,6,3,7,2,9,8,11,10,12,1] => 11110001010 => 00001110101
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => [4,3,6,5,7,2,9,8,11,10,12,1] => 11101001010 => 00010110101
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [3,2,6,5,7,4,9,8,11,10,12,1] => 11011001010 => 00100110101
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => [4,3,5,2,7,6,9,8,11,10,12,1] => 11100101010 => 00011010101
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,11,10,12,1] => 11010101010 => 00101010101
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [2,1,8,7,9,6,10,5,11,4,12,3] => 10111110000 => 01000001111
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [2,1,7,6,9,8,10,5,11,4,12,3] => 10111101000 => 01000010111
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [2,1,6,5,9,8,10,7,11,4,12,3] => 10111011000 => 01000100111
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [2,1,7,6,8,5,10,9,11,4,12,3] => 10111100100 => 01000011011
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [2,1,6,5,8,7,10,9,11,4,12,3] => 10111010100 => 01000101011
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [2,1,5,4,9,8,10,7,11,6,12,3] => 10110111000 => 01001000111
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [2,1,5,4,8,7,10,9,11,6,12,3] => 10110110100 => 01001001011
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,10,9,11,8,12,3] => 10111001100 => 01000110011
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [2,1,5,4,7,6,10,9,11,8,12,3] => 10110101100 => 01001010011
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [2,1,7,6,8,5,9,4,11,10,12,3] => 10111100010 => 01000011101
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [2,1,6,5,8,7,9,4,11,10,12,3] => 10111010010 => 01000101101
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [2,1,5,4,8,7,9,6,11,10,12,3] => 10110110010 => 01001001101
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [2,1,6,5,7,4,9,8,11,10,12,3] => 10111001010 => 01000110101
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [2,1,5,4,7,6,9,8,11,10,12,3] => 10110101010 => 01001010101
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [3,2,4,1,9,8,10,7,11,6,12,5] => 11001111000 => 00110000111
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [3,2,4,1,8,7,10,9,11,6,12,5] => 11001110100 => 00110001011
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,4,1,7,6,10,9,11,8,12,5] => 11001101100 => 00110010011
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [3,2,4,1,8,7,9,6,11,10,12,5] => 11001110010 => 00110001101
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,4,1,7,6,9,8,11,10,12,5] => 11001101010 => 00110010101
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [2,1,4,3,9,8,10,7,11,6,12,5] => 10101111000 => 01010000111
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [2,1,4,3,8,7,10,9,11,6,12,5] => 10101110100 => 01010001011
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [2,1,4,3,7,6,10,9,11,8,12,5] => 10101101100 => 01010010011
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [2,1,4,3,8,7,9,6,11,10,12,5] => 10101110010 => 01010001101
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [2,1,4,3,7,6,9,8,11,10,12,5] => 10101101010 => 01010010101
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1,10,9,11,8,12,7] => 11100011100 => 00011100011
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => [4,3,5,2,6,1,9,8,11,10,12,7] => 11100011010 => 00011100101
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [3,2,5,4,6,1,10,9,11,8,12,7] => 11010011100 => 00101100011
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1,9,8,11,10,12,7] => 11010011010 => 00101100101
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [2,1,5,4,6,3,10,9,11,8,12,7] => 10110011100 => 01001100011
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,6,3,9,8,11,10,12,7] => 10110011010 => 01001100101
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [3,2,4,1,6,5,10,9,11,8,12,7] => 11001011100 => 00110100011
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [3,2,4,1,6,5,9,8,11,10,12,7] => 11001011010 => 00110100101
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,4,3,6,5,10,9,11,8,12,7] => 10101011100 => 01010100011
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,4,3,6,5,9,8,11,10,12,7] => 10101011010 => 01010100101
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]] => [5,4,6,3,7,2,8,1,11,10,12,9] => 11110000110 => 00001111001
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => [4,3,6,5,7,2,8,1,11,10,12,9] => 11101000110 => 00010111001
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [3,2,6,5,7,4,8,1,11,10,12,9] => 11011000110 => 00100111001
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => [4,3,5,2,7,6,8,1,11,10,12,9] => 11100100110 => 00011011001
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [3,2,5,4,7,6,8,1,11,10,12,9] => 11010100110 => 00101011001
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [2,1,6,5,7,4,8,3,11,10,12,9] => 10111000110 => 01000111001
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [2,1,5,4,7,6,8,3,11,10,12,9] => 10110100110 => 01001011001
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5,11,10,12,9] => 11001100110 => 00110011001
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5,11,10,12,9] => 10101100110 => 01010011001
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]] => [4,3,5,2,6,1,8,7,11,10,12,9] => 11100010110 => 00011101001
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [3,2,5,4,6,1,8,7,11,10,12,9] => 11010010110 => 00101101001
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3,8,7,11,10,12,9] => 10110010110 => 01001101001
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [3,2,4,1,6,5,8,7,11,10,12,9] => 11001010110 => 00110101001
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,6,5,8,7,11,10,12,9] => 10101010110 => 01010101001
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => [6,5,7,4,8,3,9,2,10,1,12,11] => 11111000001 => 00000111110
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]] => [5,4,7,6,8,3,9,2,10,1,12,11] => 11110100001 => 00001011110
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]] => [4,3,7,6,8,5,9,2,10,1,12,11] => 11101100001 => 00010011110
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => [5,4,6,3,8,7,9,2,10,1,12,11] => 11110010001 => 00001101110
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]] => [4,3,6,5,8,7,9,2,10,1,12,11] => 11101010001 => 00010101110
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [3,2,7,6,8,5,9,4,10,1,12,11] => 11011100001 => 00100011110
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [3,2,6,5,8,7,9,4,10,1,12,11] => 11011010001 => 00100101110
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,8,7,9,6,10,1,12,11] => 11100110001 => 00011001110
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [3,2,5,4,8,7,9,6,10,1,12,11] => 11010110001 => 00101001110
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => [5,4,6,3,7,2,9,8,10,1,12,11] => 11110001001 => 00001110110
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => [4,3,6,5,7,2,9,8,10,1,12,11] => 11101001001 => 00010110110
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [3,2,6,5,7,4,9,8,10,1,12,11] => 11011001001 => 00100110110
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => [4,3,5,2,7,6,9,8,10,1,12,11] => 11100101001 => 00011010110
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,7,6,9,8,10,1,12,11] => 11010101001 => 00101010110
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [2,1,7,6,8,5,9,4,10,3,12,11] => 10111100001 => 01000011110
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [2,1,6,5,8,7,9,4,10,3,12,11] => 10111010001 => 01000101110
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [2,1,5,4,8,7,9,6,10,3,12,11] => 10110110001 => 01001001110
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [2,1,6,5,7,4,9,8,10,3,12,11] => 10111001001 => 01000110110
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [2,1,5,4,7,6,9,8,10,3,12,11] => 10110101001 => 01001010110
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [3,2,4,1,8,7,9,6,10,5,12,11] => 11001110001 => 00110001110
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,4,1,7,6,9,8,10,5,12,11] => 11001101001 => 00110010110
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [2,1,4,3,8,7,9,6,10,5,12,11] => 10101110001 => 01010001110
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [2,1,4,3,7,6,9,8,10,5,12,11] => 10101101001 => 01010010110
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => [4,3,5,2,6,1,9,8,10,7,12,11] => 11100011001 => 00011100110
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [3,2,5,4,6,1,9,8,10,7,12,11] => 11010011001 => 00101100110
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,9,8,10,7,12,11] => 10110011001 => 01001100110
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5,9,8,10,7,12,11] => 11001011001 => 00110100110
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,4,3,6,5,9,8,10,7,12,11] => 10101011001 => 01010100110
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]] => [5,4,6,3,7,2,8,1,10,9,12,11] => 11110000101 => 00001111010
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]] => [4,3,6,5,7,2,8,1,10,9,12,11] => 11101000101 => 00010111010
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [3,2,6,5,7,4,8,1,10,9,12,11] => 11011000101 => 00100111010
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => [4,3,5,2,7,6,8,1,10,9,12,11] => 11100100101 => 00011011010
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]] => [3,2,5,4,7,6,8,1,10,9,12,11] => 11010100101 => 00101011010
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [2,1,6,5,7,4,8,3,10,9,12,11] => 10111000101 => 01000111010
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => [2,1,5,4,7,6,8,3,10,9,12,11] => 10110100101 => 01001011010
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,7,6,8,5,10,9,12,11] => 11001100101 => 00110011010
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [2,1,4,3,7,6,8,5,10,9,12,11] => 10101100101 => 01010011010
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => [4,3,5,2,6,1,8,7,10,9,12,11] => 11100010101 => 00011101010
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => [3,2,5,4,6,1,8,7,10,9,12,11] => 11010010101 => 00101101010
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [2,1,5,4,6,3,8,7,10,9,12,11] => 10110010101 => 01001101010
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7,10,9,12,11] => 11001010101 => 00110101010
[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,10,9,2] => 011010101 => 100101010
[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,10,9,12,11,2] => 01101010101 => 10010101010
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [2,1,9,8,7,6,5,4,3] => 10111111 => 01000000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [3,2,1,9,8,7,6,5,4] => 11011111 => 00100000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [4,3,2,1,9,8,7,6,5] => 11101111 => 00010000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [5,4,3,2,1,9,8,7,6] => 11110111 => 00001000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [6,5,4,3,2,1,9,8,7] => 11111011 => 00000100
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [7,6,5,4,3,2,1,9,8] => 11111101 => 00000010
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,9,8,7,6,5,4,3] => 00111111 => 11000000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 010000000
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [2,3,1,9,8,7,6,5,4] => 10011111 => 01100000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [3,2,1,10,9,8,7,6,5,4] => 110111111 => 001000000
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]] => [3,4,2,1,9,8,7,6,5] => 11001111 => 00110000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => 111011111 => 000100000
[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => [4,5,3,2,1,9,8,7,6] => 11100111 => 00011000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [5,4,3,2,1,10,9,8,7,6] => 111101111 => 000010000
[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => [5,6,4,3,2,1,9,8,7] => 11110011 => 00001100
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => 111110111 => 000001000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [6,7,5,4,3,2,1,9,8] => 11111001 => 00000110
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [7,6,5,4,3,2,1,10,9,8] => 111111011 => 000000100
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => 111111101 => 000000010
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 11111100 => 00000011
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 11111000 => 00000111
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 11110000 => 00001111
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 11100000 => 00011111
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 11000000 => 00111111
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 10000000 => 01111111
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 111111100 => 000000011
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 111111000 => 000000111
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 111110000 => 000001111
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 111100000 => 000011111
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 111000000 => 000111111
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,4,3,2,5,6,7,8,9] => 01100000 => 10011111
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 110000000 => 001111111
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9] => 01000000 => 10111111
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 100000000 => 011111111
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [4,9,8,7,6,5,3,2,1] => 11101111 => 00010000
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [3,9,8,7,6,5,4,2,1] => 11011111 => 00100000
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => 10111111 => 01000000
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [6,10,9,8,7,5,4,3,2,1] => 111110111 => 000001000
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,8,7,5,10,9] => 101010101 => 010101010
[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => [2,4,3,1,6,5,8,10,9,7] => 101010101 => 010101010
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7,10,9] => 101010101 => 010101010
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,3,6,8,7,5,10,9] => 101010101 => 010101010
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,5,8,10,9,7] => 101010101 => 010101010
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5,10,12,11,9] => 10101010101 => 01010101010
[[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,8,7,5,10,9,12,11] => 10101010101 => 01010101010
[[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5,8,10,9,7,12,11] => 10101010101 => 01010101010
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,4,3,1,6,5,8,7,10,12,11,9] => 10101010101 => 01010101010
[[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7,10,9,12,11] => 10101010101 => 01010101010
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5,10,12,11,9] => 10101010101 => 01010101010
[[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,1,4,3,6,8,7,5,10,9,12,11] => 10101010101 => 01010101010
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,3,6,5,8,10,9,7,12,11] => 10101010101 => 01010101010
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,5,8,7,10,12,11,9] => 10101010101 => 01010101010
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,9,8,1] => 10000001 => 01111110
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000 => 0111111111
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [2,1,3,4,5,6,8,7,9] => 10000010 => 01111101
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [2,1,3,4,5,6,8,9,7] => 10000010 => 01111101
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [2,3,4,5,6,8,9,7,1] => 10000010 => 01111101
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,8,10,9,1] => 100000001 => 011111110
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [2,1,4,3,5,6,7,8,9] => 10100000 => 01011111
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [3,2,1,5,4,6,7,8,9] => 11010000 => 00101111
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [6,5,4,3,2,1,8,7,9] => 11111010 => 00000101
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => 11000000 => 00111111
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 10000000 => 01111111
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => 10000000 => 01111111
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 10000000 => 01111111
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10] => 100000000 => 011111111
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [2,4,3,1,5,6,7,8,9] => 10100000 => 01011111
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [2,3,5,4,1,6,7,8,9] => 10010000 => 01101111
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [2,3,4,6,5,1,7,8,9] => 10001000 => 01110111
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [2,3,4,5,7,6,1,8,9] => 10000100 => 01111011
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [2,3,4,5,6,8,7,1,9] => 10000010 => 01111101
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 100000000 => 011111111
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9] => 00100000 => 11011111
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,2,3,5,4,6,7,8,9] => 00010000 => 11101111
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,6,5,7,8,9] => 00001000 => 11110111
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,7,6,8,9] => 00000100 => 11111011
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,8,7,9] => 00000010 => 11111101
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9,10] => 010000000 => 101111111
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9,10] => 001000000 => 110111111
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,2,3,5,4,6,7,8,9,10] => 000100000 => 111011111
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,2,3,4,6,5,7,8,9,10] => 000010000 => 111101111
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,5,7,6,8,9,10] => 000001000 => 111110111
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,6,8,7,9,10] => 000000100 => 111111011
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,9,8,10] => 000000010 => 111111101
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [1,3,4,5,6,7,9,8,2] => 01000001 => 10111110
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [7,6,5,4,3,2,9,8,1] => 11111101 => 00000010
[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,1] => 11100000 => 00011111
[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => [5,4,3,2,6,7,8,9,1] => 11110000 => 00001111
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => 11111000 => 00000111
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => [7,6,5,4,3,2,8,9,1] => 11111100 => 00000011
[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,10,1] => 111000000 => 000111111
[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]] => [5,4,3,2,6,7,8,9,10,1] => 111100000 => 000011111
[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]] => [6,5,4,3,2,7,8,9,10,1] => 111110000 => 000001111
[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]] => [7,6,5,4,3,2,8,9,10,1] => 111111000 => 000000111
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]] => [8,7,6,5,4,3,2,9,10,1] => 111111100 => 000000011
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,7,6,5,4,3,2,9,8] => 01111101 => 10000010
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [6,5,4,3,2,1,8,9,7] => 11111010 => 00000101
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000 => 1111111111
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,2,10,9,8,7,6,5,4,3] => 001111111 => 110000000
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,3,2,9,8,7,6,5,4] => 01011111 => 10100000
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [2,1,8,7,6,5,4,3,9] => 10111110 => 01000001
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,9,8,7,6,5,4,3,2,10] => 011111110 => 100000001
[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [2,8,7,9,6,5,4,3,1] => 10111110 => 01000001
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [1,3,4,5,2,6,7,8,9] => 01000000 => 10111111
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [1,2,4,5,3,6,7,8,9] => 00100000 => 11011111
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [2,1,4,5,3,6,7,8,9] => 10100000 => 01011111
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [1,3,2,5,4,6,7,8,9] => 01010000 => 10101111
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [8,7,6,5,4,3,2,10,9,1] => 111111101 => 000000010
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [2,1,4,5,6,7,8,9,3] => 10100000 => 01011111
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,3,4,5,6,7,8,2,9] => 01000000 => 10111111
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,7,10,9,8] => 000000011 => 111111100
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => 11111000 => 00000111
[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.] => [6,5,7,8,4,3,2,1,9] => 11111000 => 00000111
[[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.] => [6,5,4,7,8,3,2,1,9] => 11111000 => 00000111
[[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.] => [6,5,4,3,7,8,2,1,9] => 11111000 => 00000111
[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => [6,5,4,3,2,7,8,1,9] => 11111000 => 00000111
[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]] => [5,4,3,2,1,7,8,9,6] => 11110100 => 00001011
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => 111111000 => 000000111
[[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]] => [4,3,2,1,6,7,8,9,5] => 11101000 => 00010111
[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.] => [7,6,8,9,5,4,3,2,1,10] => 111111000 => 000000111
[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.] => [7,6,5,8,9,4,3,2,1,10] => 111111000 => 000000111
[[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.] => [7,6,5,4,8,9,3,2,1,10] => 111111000 => 000000111
[[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.] => [7,6,5,4,3,8,9,2,1,10] => 111111000 => 000000111
[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.] => [7,6,5,4,3,2,8,9,1,10] => 111111000 => 000000111
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,9,8,7,6] => 00000111 => 11111000
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,9,8,7,6,5] => 00001111 => 11110000
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,9,8,7,6,5,4] => 00011111 => 11100000
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,7,6,9,8] => 00000101 => 11111010
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,6,10,9,8,7] => 000000111 => 111111000
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,4,6,5,9,8,7] => 00001011 => 11110100
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,5,10,9,8,7,6] => 000001111 => 111110000
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,3,5,4,9,8,7,6] => 00010111 => 11101000
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,4,10,9,8,7,6,5] => 000011111 => 111100000
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,2,4,3,9,8,7,6,5] => 00101111 => 11010000
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,3,10,9,8,7,6,5,4] => 000111111 => 111000000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,6,8,7,10,9] => 000000101 => 111111010
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => 1111111110 => 0000000001
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [1,9,8,10,7,6,5,4,3,2] => 011111110 => 100000001
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [2,8,9,7,6,5,4,3,1] => 10111110 => 01000001
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => 1111111110 => 0000000001
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => 11111100 => 00000011
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => 11000000 => 00111111
[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10,11] => 1000000000 => 0111111111
[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9,10] => 110000000 => 001111111
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.] => [3,4,2,5,1,6,7,8,9] => 11000000 => 00111111
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => 11111100 => 00000011
[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.] => [6,5,8,7,4,3,2,1,9] => 11111010 => 00000101
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => [7,6,5,8,4,3,2,1,9] => 11111100 => 00000011
[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.] => [6,7,5,8,4,3,2,1,9] => 11111000 => 00000111
[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]] => [4,3,2,1,8,9,7,6,5] => 11101110 => 00010001
[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [2,3,1,5,4,6,7,8,9] => 10010000 => 01101111
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => 11100000 => 00011111
[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]] => [4,3,2,1,6,7,8,9,10,5] => 111010000 => 000101111
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => 11000000 => 00111111
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [5,4,3,2,1,8,7,6,9] => 11110110 => 00001001
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [7,6,5,4,3,2,1,9,8,10] => 111111010 => 000000101
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [2,3,9,8,7,6,5,4,1] => 10011111 => 01100000
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [2,8,7,6,5,4,3,1,9] => 10111110 => 01000001
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [2,3,4,5,6,7,1,9,8] => 10000001 => 01111110
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,3,4,2,5,6,7,8,9] => 01000000 => 10111111
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => [8,7,6,5,4,3,2,9,1,10] => 111111100 => 000000011
[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [1,4,5,6,7,8,3,9,2] => 01100000 => 10011111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010 => 1111111101
[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]] => [2,1,3,5,6,7,8,9,4] => 10010000 => 01101111
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.] => [5,6,4,3,2,1,7,8,9] => 11110000 => 00001111
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => [5,6,4,3,2,1,7,8,9,10] => 111100000 => 000011111
[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.] => [6,7,5,4,3,2,1,8,9,10,11] => 1111100000 => 0000011111
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.] => [6,7,5,4,3,2,1,8,9,10] => 111110000 => 000001111
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.] => [5,6,4,3,2,7,1,8,9] => 11110000 => 00001111
[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]] => [1,2,5,6,7,4,8,9,3] => 00110000 => 11001111
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => 11111000 => 00000111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [7,6,5,4,3,2,1,9,10,8] => 111111010 => 000000101
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
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
searching the database
Sorry, this map was not found in the database.