Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00130: Permutations —descent tops⟶ Binary words
Images
[.,.] => [1] =>
[.,[.,.]] => [2,1] => 1
[[.,.],.] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => 11
[.,[[.,.],.]] => [2,3,1] => 01
[[.,.],[.,.]] => [1,3,2] => 01
[[.,[.,.]],.] => [2,1,3] => 10
[[[.,.],.],.] => [1,2,3] => 00
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 111
[.,[.,[[.,.],.]]] => [3,4,2,1] => 101
[.,[[.,.],[.,.]]] => [2,4,3,1] => 011
[.,[[.,[.,.]],.]] => [3,2,4,1] => 011
[.,[[[.,.],.],.]] => [2,3,4,1] => 001
[[.,.],[.,[.,.]]] => [1,4,3,2] => 011
[[.,.],[[.,.],.]] => [1,3,4,2] => 001
[[.,[.,.]],[.,.]] => [2,1,4,3] => 101
[[[.,.],.],[.,.]] => [1,2,4,3] => 001
[[.,[.,[.,.]]],.] => [3,2,1,4] => 110
[[.,[[.,.],.]],.] => [2,3,1,4] => 010
[[[.,.],[.,.]],.] => [1,3,2,4] => 010
[[[.,[.,.]],.],.] => [2,1,3,4] => 100
[[[[.,.],.],.],.] => [1,2,3,4] => 000
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 1111
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 1101
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 1011
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1011
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 1001
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 0111
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 0101
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 0111
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 0011
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 0111
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 0011
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 0011
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 0101
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 0001
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 0111
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 0101
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 0011
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 0011
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 0001
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 1011
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 1001
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 0011
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 0001
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 1101
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 0101
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 0101
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 1001
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 0001
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1110
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 1010
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 0110
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 0110
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 0010
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 0110
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 0010
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 1010
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 0010
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 1100
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 0100
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 0100
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1000
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0000
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 11101
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 11011
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 11011
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 11001
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 10111
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 10101
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 10111
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 10011
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 10111
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 10011
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 10011
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 10101
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 10001
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 01111
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 01101
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 01011
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 01011
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 01001
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 01111
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 01101
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 00111
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 00101
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 01111
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 00111
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 00111
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 01011
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 00011
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 01111
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 01011
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 00111
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 00111
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 00011
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 00111
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 00011
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 01011
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 00011
>>> Load all 2157 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 01101
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 00101
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 00101
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 01001
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 00001
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 01111
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 01101
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 01011
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 01011
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 01001
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 00111
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 00101
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 00111
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => 00011
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 00111
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 00011
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => 00011
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 00101
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => 00001
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 10111
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 10101
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 10011
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 10011
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => 10001
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 00111
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 00101
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 00011
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 00011
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 00001
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 11011
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 11001
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 01011
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => 01001
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 01011
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 01001
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 10011
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 10001
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 00011
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 00001
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 11101
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => 10101
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => 01101
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => 01101
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => 00101
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 01101
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 00101
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 10101
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 00101
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 11001
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => 01001
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 01001
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 10001
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 00001
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 11110
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 11010
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 10110
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 10110
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 10010
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 01110
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 01010
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 01110
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 00110
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 01110
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 00110
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 00110
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 01010
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 00010
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 01110
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 01010
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 00110
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 00110
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => 00010
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 10110
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 10010
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 00110
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 00010
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 11010
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => 01010
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 01010
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 10010
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 00010
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 11100
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 10100
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 01100
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 01100
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 00100
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 01100
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 00100
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 10100
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 00100
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 11000
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 01000
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 01000
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 10000
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => 111101
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => 111011
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => 111011
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => 111001
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => 110111
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => 110101
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => 110111
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => 110011
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => 110111
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => 110011
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => 110011
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => 110101
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => 110001
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => 101111
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => 101101
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => 101011
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => 101011
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => 101001
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => 101111
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => 101101
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => 100111
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => 100101
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => 101111
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => 100111
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => 100111
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => 101011
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => 100011
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => 101111
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => 101011
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => 100111
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => 100111
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => 100011
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => 100111
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => 100011
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => 101011
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => 100011
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => 101101
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => 100101
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => 100101
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => 101001
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => 100001
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => 011111
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => 011101
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => 011011
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => 011011
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => 011001
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => 010111
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => 010101
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => 010111
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => 010011
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => 010111
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => 010011
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => 010011
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => 010101
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => 010001
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => 011111
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => 011101
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => 011011
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => 011011
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => 011001
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => 001111
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => 001101
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => 001011
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => 001011
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => 001001
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => 011111
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => 011101
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => 001111
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => 001101
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => 001111
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => 001101
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => 010111
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => 010101
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => 000111
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => 000101
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => 011111
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => 010111
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => 001111
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => 001111
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => 000111
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => 001111
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => 000111
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => 010111
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => 000111
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => 011011
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => 001011
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => 001011
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => 010011
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => 000011
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => 011111
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => 011011
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => 010111
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => 010111
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => 010011
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => 001111
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => 001011
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => 001111
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => 000111
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => 001111
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => 000111
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => 000111
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => 001011
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 000011
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => 001111
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => 001011
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => 000111
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => 000111
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => 000011
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => 010111
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => 010011
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => 000111
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => 000011
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => 011011
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => 001011
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => 001011
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => 010011
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => 000011
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => 011101
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => 010101
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => 001101
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 001101
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 000101
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => 001101
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => 000101
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => 010101
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => 000101
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 011001
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 001001
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => 001001
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 010001
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 000001
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => 011111
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => 011101
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => 011011
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => 011011
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => 011001
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => 010111
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => 010101
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => 010111
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => 010011
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => 010111
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => 010011
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => 010011
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => 010101
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => 010001
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 001111
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 001101
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 001011
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 001011
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => 001001
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 001111
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 001101
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => 000111
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => 000101
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => 001111
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => 000111
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => 000111
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => 001011
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => 000011
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => 001111
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => 001011
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => 000111
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => 000111
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => 000011
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => 000111
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => 000011
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => 001011
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => 000011
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => 001101
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => 000101
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => 000101
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => 001001
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => 000001
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => 101111
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => 101101
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => 101011
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => 101011
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => 101001
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => 100111
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => 100101
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => 100111
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => 100011
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => 100111
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => 100011
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => 100011
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => 100101
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => 100001
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => 001111
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => 001101
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => 001011
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => 001011
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => 001001
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => 000111
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => 000101
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => 000111
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => 000011
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => 000111
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => 000011
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => 000011
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => 000101
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => 000001
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => 110111
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => 110101
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => 110011
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => 110011
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => 110001
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => 010111
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => 010101
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => 010011
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => 010011
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => 010001
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => 010111
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => 010101
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => 010011
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => 010011
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => 010001
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => 100111
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => 100101
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => 100011
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => 100011
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => 100001
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => 000111
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => 000101
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => 000011
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => 000011
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => 000001
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => 111011
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => 111001
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => 101011
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => 101001
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => 011011
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => 011001
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => 011011
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => 011001
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => 001011
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => 001001
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => 011011
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => 011001
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => 001011
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => 001001
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => 101011
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => 101001
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => 001011
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => 001001
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => 110011
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => 110001
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => 010011
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => 010001
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => 010011
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => 010001
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => 100011
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => 100001
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => 000011
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => 000001
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => 111101
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => 110101
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => 101101
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => 101101
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => 100101
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => 011101
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => 010101
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => 011101
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => 001101
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => 011101
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => 001101
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => 001101
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => 010101
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => 000101
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => 011101
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => 010101
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => 001101
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => 001101
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => 000101
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => 101101
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => 100101
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => 001101
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => 000101
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => 110101
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => 010101
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => 010101
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => 100101
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => 000101
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => 111001
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => 101001
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => 011001
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => 011001
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => 001001
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => 011001
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => 001001
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => 101001
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => 001001
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => 110001
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => 010001
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => 010001
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => 100001
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 000001
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 111110
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 111010
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => 110110
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 110110
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 110010
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => 101110
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => 101010
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => 101110
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => 100110
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 101110
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 100110
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => 100110
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => 101010
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => 100010
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => 011110
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => 011010
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => 010110
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => 010110
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => 010010
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => 011110
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => 011010
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => 001110
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => 001010
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => 011110
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => 001110
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => 001110
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => 010110
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => 000110
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 011110
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => 010110
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => 001110
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => 001110
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => 000110
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => 001110
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => 000110
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => 010110
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => 000110
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => 011010
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => 001010
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => 001010
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => 010010
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 000010
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => 011110
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => 011010
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => 010110
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => 010110
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => 010010
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => 001110
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => 001010
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => 001110
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => 000110
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => 001110
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => 000110
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => 000110
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => 001010
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => 000010
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => 101110
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => 101010
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => 100110
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => 100110
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => 100010
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => 001110
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => 001010
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => 000110
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => 000110
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => 000010
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => 110110
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => 110010
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => 010110
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => 010010
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => 010110
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => 010010
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => 100110
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => 100010
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => 000110
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => 000010
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => 111010
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => 101010
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => 011010
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => 011010
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => 001010
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => 011010
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => 001010
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => 101010
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => 001010
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => 110010
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => 010010
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => 010010
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => 100010
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 000010
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 111100
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => 110100
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => 101100
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => 101100
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => 100100
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => 011100
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => 010100
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => 011100
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => 001100
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => 011100
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => 001100
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => 001100
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => 010100
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 000100
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => 011100
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => 010100
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => 001100
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => 001100
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => 000100
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => 101100
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => 100100
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => 001100
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => 000100
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => 110100
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => 010100
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => 010100
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => 100100
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => 000100
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 111000
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => 101000
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => 011000
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => 011000
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 001000
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => 011000
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => 001000
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => 101000
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => 001000
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 110000
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 010000
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 010000
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 100000
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => 1111101
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [6,8,7,5,4,3,2,1] => 1111011
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 1111011
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => 1111001
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [5,8,7,6,4,3,2,1] => 1110111
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [5,7,8,6,4,3,2,1] => 1110101
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => 1110111
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [5,6,8,7,4,3,2,1] => 1110011
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => 1110111
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => 1110011
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => 1110011
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => 1110101
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => 1110001
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => 1101111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [4,7,8,6,5,3,2,1] => 1101101
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => 1101011
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [4,7,6,8,5,3,2,1] => 1101011
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [4,6,7,8,5,3,2,1] => 1101001
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [5,4,7,8,6,3,2,1] => 1101101
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [4,5,8,7,6,3,2,1] => 1100111
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [4,5,7,8,6,3,2,1] => 1100101
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [6,5,4,8,7,3,2,1] => 1101111
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [5,6,4,8,7,3,2,1] => 1100111
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [4,6,5,8,7,3,2,1] => 1100111
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => 1100011
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 1101111
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => 1101011
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [5,7,6,4,8,3,2,1] => 1100111
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 1100111
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => 1100011
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1] => 1100111
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [4,6,7,5,8,3,2,1] => 1100011
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [5,4,7,6,8,3,2,1] => 1101011
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [4,5,7,6,8,3,2,1] => 1100011
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => 1101101
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => 1100101
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [4,6,5,7,8,3,2,1] => 1100101
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => 1101001
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => 1100001
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [3,8,7,6,5,4,2,1] => 1011111
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [3,7,8,6,5,4,2,1] => 1011101
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [3,6,8,7,5,4,2,1] => 1011011
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [3,7,6,8,5,4,2,1] => 1011011
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => 1010111
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => 1010101
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [3,5,6,8,7,4,2,1] => 1010011
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [3,7,6,5,8,4,2,1] => 1010111
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [3,6,7,5,8,4,2,1] => 1010011
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [3,5,7,6,8,4,2,1] => 1010011
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [3,5,6,7,8,4,2,1] => 1010001
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => 1011111
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [4,3,7,8,6,5,2,1] => 1011101
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [4,3,6,7,8,5,2,1] => 1011001
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [3,4,8,7,6,5,2,1] => 1001111
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => 1001001
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [5,4,3,8,7,6,2,1] => 1011111
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [5,4,3,7,8,6,2,1] => 1011101
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [4,5,3,7,8,6,2,1] => 1001101
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [3,5,4,7,8,6,2,1] => 1001101
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [4,3,5,7,8,6,2,1] => 1010101
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [3,4,5,8,7,6,2,1] => 1000111
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [3,4,5,7,8,6,2,1] => 1000101
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [6,5,4,3,8,7,2,1] => 1011111
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [5,6,4,3,8,7,2,1] => 1010111
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [4,5,6,3,8,7,2,1] => 1000111
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [3,6,5,4,8,7,2,1] => 1001111
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => 1010111
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [5,4,3,6,8,7,2,1] => 1011011
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [4,5,3,6,8,7,2,1] => 1001011
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [4,3,5,6,8,7,2,1] => 1010011
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [3,4,5,6,8,7,2,1] => 1000011
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => 1011111
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => 1011011
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [5,7,6,4,3,8,2,1] => 1010111
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [6,5,7,4,3,8,2,1] => 1010111
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => 1010011
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [4,7,6,5,3,8,2,1] => 1001111
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [5,4,7,6,3,8,2,1] => 1001111
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => 1001111
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => 1001011
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => 1000011
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [3,7,6,5,4,8,2,1] => 1001111
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [3,5,7,6,4,8,2,1] => 1000111
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [3,5,6,7,4,8,2,1] => 1000011
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [4,3,7,6,5,8,2,1] => 1010111
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [3,4,7,6,5,8,2,1] => 1000111
[.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [3,4,6,7,5,8,2,1] => 1000011
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [4,5,3,7,6,8,2,1] => 1001011
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [3,5,4,7,6,8,2,1] => 1001011
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [4,3,5,7,6,8,2,1] => 1010011
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [3,4,5,7,6,8,2,1] => 1000011
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => 1011101
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => 1000101
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [3,6,5,4,7,8,2,1] => 1001101
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [3,5,6,4,7,8,2,1] => 1000101
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [4,3,6,5,7,8,2,1] => 1010101
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [3,4,6,5,7,8,2,1] => 1000101
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => 1011001
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [3,5,4,6,7,8,2,1] => 1001001
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => 1010001
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => 1000001
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => 0111111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [2,7,8,6,5,4,3,1] => 0111101
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => 0111011
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [2,7,6,8,5,4,3,1] => 0111011
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [2,6,7,8,5,4,3,1] => 0111001
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [2,5,8,7,6,4,3,1] => 0110111
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [2,6,7,5,8,4,3,1] => 0110011
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [2,6,5,7,8,4,3,1] => 0110101
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [2,5,6,7,8,4,3,1] => 0110001
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [2,4,8,7,6,5,3,1] => 0101111
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [2,4,7,8,6,5,3,1] => 0101101
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => 0101011
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [2,4,6,7,8,5,3,1] => 0101001
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [2,5,4,8,7,6,3,1] => 0101111
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [2,5,4,7,8,6,3,1] => 0101101
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [2,4,5,7,8,6,3,1] => 0100101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [2,6,5,4,8,7,3,1] => 0101111
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [2,5,6,4,8,7,3,1] => 0100111
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [2,4,6,5,8,7,3,1] => 0100111
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [2,4,5,6,8,7,3,1] => 0100011
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [2,7,6,5,4,8,3,1] => 0101111
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [2,6,7,5,4,8,3,1] => 0101011
[.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [2,5,6,7,4,8,3,1] => 0100011
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [2,4,7,6,5,8,3,1] => 0100111
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [2,4,6,7,5,8,3,1] => 0100011
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [2,5,4,7,6,8,3,1] => 0101011
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [2,6,5,4,7,8,3,1] => 0101101
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [2,5,6,4,7,8,3,1] => 0100101
[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [2,4,6,5,7,8,3,1] => 0100101
[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [2,5,4,6,7,8,3,1] => 0101001
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [2,4,5,6,7,8,3,1] => 0100001
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => 0111111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [3,2,7,8,6,5,4,1] => 0111101
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [3,2,6,8,7,5,4,1] => 0111011
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [3,2,5,7,8,6,4,1] => 0110101
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [3,2,6,5,8,7,4,1] => 0110111
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [3,2,5,7,6,8,4,1] => 0110011
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [3,2,5,6,7,8,4,1] => 0110001
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => 0011111
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [2,3,6,7,8,5,4,1] => 0011001
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [2,3,5,8,7,6,4,1] => 0010111
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [2,3,5,7,8,6,4,1] => 0010101
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [2,3,6,5,8,7,4,1] => 0010111
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => 0010011
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [2,3,7,6,5,8,4,1] => 0010111
[.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [2,3,5,7,6,8,4,1] => 0010011
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [2,3,5,6,7,8,4,1] => 0010001
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => 0111111
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [4,3,2,7,8,6,5,1] => 0111101
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [4,3,2,6,8,7,5,1] => 0111011
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => 0011111
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [3,4,2,7,8,6,5,1] => 0011101
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [2,4,3,8,7,6,5,1] => 0011111
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [2,4,3,6,8,7,5,1] => 0011011
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [2,4,3,6,7,8,5,1] => 0011001
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [3,2,4,8,7,6,5,1] => 0101111
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [3,2,4,7,8,6,5,1] => 0101101
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => 0001111
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [2,3,4,7,8,6,5,1] => 0001101
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [2,3,4,6,8,7,5,1] => 0001011
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [2,3,4,7,6,8,5,1] => 0001011
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [2,3,4,6,7,8,5,1] => 0001001
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [5,4,3,2,8,7,6,1] => 0111111
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [5,4,3,2,7,8,6,1] => 0111101
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [4,5,3,2,8,7,6,1] => 0101111
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [3,5,4,2,7,8,6,1] => 0011101
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [4,3,5,2,8,7,6,1] => 0011111
[.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [3,4,5,2,7,8,6,1] => 0001101
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => 0011111
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [2,5,4,3,7,8,6,1] => 0011101
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [2,4,5,3,8,7,6,1] => 0001111
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [2,4,5,3,7,8,6,1] => 0001101
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [3,2,5,4,7,8,6,1] => 0101101
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [2,3,5,4,8,7,6,1] => 0001111
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [2,3,5,4,7,8,6,1] => 0001101
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [4,3,2,5,8,7,6,1] => 0110111
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [4,3,2,5,7,8,6,1] => 0110101
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [3,4,2,5,8,7,6,1] => 0010111
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [3,4,2,5,7,8,6,1] => 0010101
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [2,4,3,5,8,7,6,1] => 0010111
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [3,2,4,5,7,8,6,1] => 0100101
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [2,3,4,5,8,7,6,1] => 0000111
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [2,3,4,5,7,8,6,1] => 0000101
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [6,5,4,3,2,8,7,1] => 0111111
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [4,6,5,3,2,8,7,1] => 0101111
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [5,4,6,3,2,8,7,1] => 0101111
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [4,5,6,3,2,8,7,1] => 0100111
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [3,6,5,4,2,8,7,1] => 0011111
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [3,5,6,4,2,8,7,1] => 0010111
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [4,3,6,5,2,8,7,1] => 0011111
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [5,4,3,6,2,8,7,1] => 0011111
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => 0001111
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [3,5,4,6,2,8,7,1] => 0001111
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [3,4,5,6,2,8,7,1] => 0000111
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [2,6,5,4,3,8,7,1] => 0011111
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [2,4,6,5,3,8,7,1] => 0001111
[.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [2,4,5,6,3,8,7,1] => 0000111
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => 0101111
[.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [2,3,5,6,4,8,7,1] => 0000111
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [4,3,2,6,5,8,7,1] => 0110111
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [3,4,2,6,5,8,7,1] => 0010111
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => 0010111
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [3,2,4,6,5,8,7,1] => 0100111
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [2,3,4,6,5,8,7,1] => 0000111
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [5,4,3,2,6,8,7,1] => 0111011
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [4,5,3,2,6,8,7,1] => 0101011
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [2,5,4,3,6,8,7,1] => 0011011
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [2,4,5,3,6,8,7,1] => 0001011
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [3,2,5,4,6,8,7,1] => 0101011
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [4,3,2,5,6,8,7,1] => 0110011
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [3,4,2,5,6,8,7,1] => 0010011
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => 0010011
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [3,2,4,5,6,8,7,1] => 0100011
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => 0000011
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 0111111
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => 0111011
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [5,7,6,4,3,2,8,1] => 0110111
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 0110111
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => 0110011
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [4,7,6,5,3,2,8,1] => 0101111
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [4,6,7,5,3,2,8,1] => 0101011
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1] => 0101111
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [4,6,5,7,3,2,8,1] => 0100111
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => 0100011
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [3,5,7,6,4,2,8,1] => 0010111
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [3,5,6,7,4,2,8,1] => 0010011
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [4,3,7,6,5,2,8,1] => 0011111
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [4,3,6,7,5,2,8,1] => 0011011
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [3,4,7,6,5,2,8,1] => 0001111
[.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [3,4,6,7,5,2,8,1] => 0001011
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [5,4,3,7,6,2,8,1] => 0011111
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [4,5,3,7,6,2,8,1] => 0001111
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [3,5,4,7,6,2,8,1] => 0001111
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [3,4,5,7,6,2,8,1] => 0000111
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 0011111
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [4,6,5,3,7,2,8,1] => 0001111
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 0001111
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => 0000111
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [3,6,5,4,7,2,8,1] => 0001111
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => 0000111
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => 0010111
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [3,4,6,5,7,2,8,1] => 0000111
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => 0011011
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => 0001011
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [3,5,4,6,7,2,8,1] => 0001011
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [4,3,5,6,7,2,8,1] => 0010011
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => 0000011
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1] => 0011111
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [2,6,5,7,4,3,8,1] => 0010111
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [2,5,6,7,4,3,8,1] => 0010011
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [2,4,6,7,5,3,8,1] => 0001011
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [2,5,4,7,6,3,8,1] => 0001111
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => 0000111
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [2,5,4,6,7,3,8,1] => 0001011
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [2,4,5,6,7,3,8,1] => 0000011
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [3,2,7,6,5,4,8,1] => 0101111
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [3,2,6,7,5,4,8,1] => 0101011
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [3,2,5,7,6,4,8,1] => 0100111
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => 0100111
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [3,2,5,6,7,4,8,1] => 0100011
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [2,3,7,6,5,4,8,1] => 0001111
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [2,3,5,7,6,4,8,1] => 0000111
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [2,3,5,6,7,4,8,1] => 0000011
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1] => 0110111
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [4,3,2,6,7,5,8,1] => 0110011
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [3,4,2,7,6,5,8,1] => 0010111
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [3,4,2,6,7,5,8,1] => 0010011
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [2,4,3,7,6,5,8,1] => 0010111
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [2,4,3,6,7,5,8,1] => 0010011
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [3,2,4,7,6,5,8,1] => 0100111
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [2,3,4,7,6,5,8,1] => 0000111
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [2,3,4,6,7,5,8,1] => 0000011
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [5,4,3,2,7,6,8,1] => 0111011
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [3,5,4,2,7,6,8,1] => 0011011
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => 0011011
[.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [3,4,5,2,7,6,8,1] => 0001011
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [2,5,4,3,7,6,8,1] => 0011011
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => 0101011
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [2,3,5,4,7,6,8,1] => 0001011
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [4,3,2,5,7,6,8,1] => 0110011
[.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [3,4,2,5,7,6,8,1] => 0010011
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [2,4,3,5,7,6,8,1] => 0010011
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1] => 0100011
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => 0000011
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => 0111101
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => 0101101
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => 0100101
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [3,6,5,4,2,7,8,1] => 0011101
[.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [3,5,6,4,2,7,8,1] => 0010101
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [3,4,6,5,2,7,8,1] => 0001101
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => 0011101
[.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [3,5,4,6,2,7,8,1] => 0001101
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => 0010101
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => 0000101
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [2,6,5,4,3,7,8,1] => 0011101
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [2,5,6,4,3,7,8,1] => 0010101
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [2,4,6,5,3,7,8,1] => 0001101
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [2,5,4,6,3,7,8,1] => 0001101
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [2,4,5,6,3,7,8,1] => 0000101
[.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [3,2,5,6,4,7,8,1] => 0100101
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [2,3,6,5,4,7,8,1] => 0001101
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [2,3,5,6,4,7,8,1] => 0000101
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [4,3,2,6,5,7,8,1] => 0110101
[.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [3,4,2,6,5,7,8,1] => 0010101
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [2,4,3,6,5,7,8,1] => 0010101
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [2,3,4,6,5,7,8,1] => 0000101
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => 0111001
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [4,5,3,2,6,7,8,1] => 0101001
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [3,5,4,2,6,7,8,1] => 0011001
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => 0011001
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 0001001
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1] => 0011001
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [2,4,5,3,6,7,8,1] => 0001001
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [3,2,5,4,6,7,8,1] => 0101001
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1] => 0001001
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 0110001
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 0010001
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [2,4,3,5,6,7,8,1] => 0010001
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 0100001
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 0000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => 0111111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => 0111101
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => 0111011
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => 0111011
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => 0111001
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => 0110111
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,6,5,8,7,4,3,2] => 0110111
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => 0110111
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => 0110011
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,5,7,6,8,4,3,2] => 0110011
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,6,5,7,8,4,3,2] => 0110101
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => 0110001
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => 0101111
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => 0101101
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => 0101011
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,4,6,7,8,5,3,2] => 0101001
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,5,4,7,8,6,3,2] => 0101101
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,4,5,8,7,6,3,2] => 0100111
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,4,5,7,8,6,3,2] => 0100101
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,6,5,4,8,7,3,2] => 0101111
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,4,6,5,8,7,3,2] => 0100111
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,5,4,6,8,7,3,2] => 0101011
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => 0101111
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,4,7,6,5,8,3,2] => 0100111
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,4,6,7,5,8,3,2] => 0100011
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,6,5,4,7,8,3,2] => 0101101
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,5,6,4,7,8,3,2] => 0100101
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,5,4,6,7,8,3,2] => 0101001
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,4,5,6,7,8,3,2] => 0100001
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => 0011111
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,3,7,8,6,5,4,2] => 0011101
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,3,6,8,7,5,4,2] => 0011011
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,3,6,7,8,5,4,2] => 0011001
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,3,5,8,7,6,4,2] => 0010111
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => 0010101
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,3,5,6,8,7,4,2] => 0010011
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,3,6,7,5,8,4,2] => 0010011
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,3,5,7,6,8,4,2] => 0010011
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => 0010101
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => 0010001
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => 0011111
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => 0011101
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,4,3,6,8,7,5,2] => 0011011
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,4,3,7,6,8,5,2] => 0011011
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,4,3,6,7,8,5,2] => 0011001
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => 0001111
[[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,3,4,7,6,8,5,2] => 0001011
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,3,4,6,7,8,5,2] => 0001001
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,5,4,3,8,7,6,2] => 0011111
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,4,5,3,8,7,6,2] => 0001111
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,4,5,3,7,8,6,2] => 0001101
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,3,5,4,8,7,6,2] => 0001111
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,3,5,4,7,8,6,2] => 0001101
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,4,3,5,8,7,6,2] => 0010111
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,4,3,5,7,8,6,2] => 0010101
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,3,4,5,8,7,6,2] => 0000111
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => 0000101
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => 0011111
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => 0010111
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,4,6,5,3,8,7,2] => 0001111
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,4,5,6,3,8,7,2] => 0000111
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,3,6,5,4,8,7,2] => 0001111
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => 0010111
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,5,4,3,6,8,7,2] => 0011011
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,4,5,3,6,8,7,2] => 0001011
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => 0000011
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => 0011111
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,6,7,5,4,3,8,2] => 0011011
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,6,5,7,4,3,8,2] => 0010111
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,5,6,7,4,3,8,2] => 0010011
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => 0001011
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => 0000111
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,4,6,5,7,3,8,2] => 0000111
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => 0001011
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => 0000011
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,3,5,7,6,4,8,2] => 0000111
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,3,6,5,7,4,8,2] => 0000111
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,3,5,6,7,4,8,2] => 0000011
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,4,3,6,7,5,8,2] => 0010011
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,3,4,7,6,5,8,2] => 0000111
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,3,4,6,7,5,8,2] => 0000011
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,3,5,4,7,6,8,2] => 0001011
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,3,4,5,7,6,8,2] => 0000011
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,6,5,4,3,7,8,2] => 0011101
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,5,4,6,3,7,8,2] => 0001101
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,3,5,6,4,7,8,2] => 0000101
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,4,3,6,5,7,8,2] => 0010101
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,3,4,6,5,7,8,2] => 0000101
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,5,4,3,6,7,8,2] => 0011001
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => 0001001
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,3,5,4,6,7,8,2] => 0001001
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => 0010001
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => 0000001
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => 1011111
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [2,1,7,8,6,5,4,3] => 1011101
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [2,1,6,8,7,5,4,3] => 1011011
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => 1011011
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => 1011001
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [2,1,5,8,7,6,4,3] => 1010111
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => 1010101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [2,1,6,5,8,7,4,3] => 1010111
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [2,1,5,6,8,7,4,3] => 1010011
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [2,1,7,6,5,8,4,3] => 1010111
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => 1010011
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [2,1,5,7,6,8,4,3] => 1010011
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => 1010101
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => 1010001
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => 1001111
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [2,1,4,7,8,6,5,3] => 1001101
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => 1001011
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [2,1,4,7,6,8,5,3] => 1001011
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [2,1,4,6,7,8,5,3] => 1001001
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [2,1,5,4,8,7,6,3] => 1001111
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [2,1,5,4,7,8,6,3] => 1001101
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => 1000111
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [2,1,4,5,7,8,6,3] => 1000101
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [2,1,6,5,4,8,7,3] => 1001111
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [2,1,5,6,4,8,7,3] => 1000111
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => 1000111
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [2,1,5,4,6,8,7,3] => 1001011
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [2,1,4,5,6,8,7,3] => 1000011
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [2,1,7,6,5,4,8,3] => 1001111
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [2,1,6,7,5,4,8,3] => 1001011
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [2,1,5,7,6,4,8,3] => 1000111
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => 1000111
[[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [2,1,5,6,7,4,8,3] => 1000011
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [2,1,4,7,6,5,8,3] => 1000111
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [2,1,4,6,7,5,8,3] => 1000011
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => 1001011
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [2,1,5,6,4,7,8,3] => 1000101
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [2,1,5,4,6,7,8,3] => 1001001
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => 1000001
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => 0011111
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => 0011101
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,2,7,6,8,5,4,3] => 0011011
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => 0011001
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,2,5,8,7,6,4,3] => 0010111
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,2,6,5,8,7,4,3] => 0010111
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,2,5,6,8,7,4,3] => 0010011
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => 0010111
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,2,5,7,6,8,4,3] => 0010011
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,2,6,5,7,8,4,3] => 0010101
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,2,5,6,7,8,4,3] => 0010001
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => 0001111
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,2,4,7,8,6,5,3] => 0001101
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,2,4,6,8,7,5,3] => 0001011
[[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,2,4,7,6,8,5,3] => 0001011
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => 0001001
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,2,5,4,8,7,6,3] => 0001111
[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,2,5,4,7,8,6,3] => 0001101
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,2,4,5,8,7,6,3] => 0000111
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,2,4,5,7,8,6,3] => 0000101
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,2,6,5,4,8,7,3] => 0001111
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,2,4,6,5,8,7,3] => 0000111
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,2,5,4,6,8,7,3] => 0001011
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,2,4,5,6,8,7,3] => 0000011
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,2,7,6,5,4,8,3] => 0001111
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,2,5,7,6,4,8,3] => 0000111
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => 0000011
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,2,4,7,6,5,8,3] => 0000111
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,2,5,4,7,6,8,3] => 0001011
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,2,6,5,4,7,8,3] => 0001101
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,2,5,6,4,7,8,3] => 0000101
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,2,4,6,5,7,8,3] => 0000101
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => 0001001
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => 0000001
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => 1101111
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [3,2,1,7,8,6,5,4] => 1101101
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [3,2,1,6,8,7,5,4] => 1101011
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [3,2,1,7,6,8,5,4] => 1101011
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => 1101001
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => 1100111
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => 1100101
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => 1100111
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => 1100011
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => 1100111
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => 1100011
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [3,2,1,5,7,6,8,4] => 1100011
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [3,2,1,6,5,7,8,4] => 1100101
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => 1100001
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => 0101111
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [2,3,1,7,8,6,5,4] => 0101101
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [2,3,1,6,8,7,5,4] => 0101011
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [2,3,1,7,6,8,5,4] => 0101011
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [2,3,1,6,7,8,5,4] => 0101001
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [2,3,1,5,7,8,6,4] => 0100101
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [2,3,1,6,5,8,7,4] => 0100111
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [2,3,1,7,6,5,8,4] => 0100111
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [2,3,1,6,7,5,8,4] => 0100011
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [2,3,1,5,7,6,8,4] => 0100011
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [2,3,1,5,6,7,8,4] => 0100001
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => 0101111
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => 0101011
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,3,2,7,6,8,5,4] => 0101011
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,3,2,6,7,8,5,4] => 0101001
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,3,2,5,8,7,6,4] => 0100111
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,3,2,5,7,8,6,4] => 0100101
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,3,2,6,5,8,7,4] => 0100111
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,3,2,5,6,8,7,4] => 0100011
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,3,2,7,6,5,8,4] => 0100111
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,3,2,6,7,5,8,4] => 0100011
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,3,2,5,7,6,8,4] => 0100011
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,3,2,6,5,7,8,4] => 0100101
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,3,2,5,6,7,8,4] => 0100001
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => 1001111
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [2,1,3,7,8,6,5,4] => 1001101
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [2,1,3,6,8,7,5,4] => 1001011
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [2,1,3,6,7,8,5,4] => 1001001
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [2,1,3,6,5,8,7,4] => 1000111
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [2,1,3,5,7,6,8,4] => 1000011
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [2,1,3,5,6,7,8,4] => 1000001
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => 0001111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => 0001101
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => 0001011
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => 0001011
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => 0001001
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => 0000111
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => 0000101
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => 0000111
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => 0000011
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => 0000111
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => 0000011
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => 0000011
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => 0000101
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => 0000001
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => 1110111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => 1110101
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => 1110011
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => 1110011
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => 1110001
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => 1010111
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => 1010101
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => 1010011
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => 1010011
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [3,4,2,1,6,7,8,5] => 1010001
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => 0110111
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [2,4,3,1,7,8,6,5] => 0110101
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => 0110011
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => 0110011
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [2,4,3,1,6,7,8,5] => 0110001
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => 0110111
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => 0110101
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => 0110011
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => 0110011
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [3,2,4,1,6,7,8,5] => 0110001
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => 0010111
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [2,3,4,1,7,8,6,5] => 0010101
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [2,3,4,1,6,8,7,5] => 0010011
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => 0010011
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => 0010001
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => 0110111
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,4,3,2,6,8,7,5] => 0110011
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => 0110011
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => 0110001
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => 0010111
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,3,4,2,7,8,6,5] => 0010101
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,3,4,2,6,8,7,5] => 0010011
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => 0010011
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,3,4,2,6,7,8,5] => 0010001
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => 1010111
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => 1010101
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => 1010011
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => 1010011
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => 1010001
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => 0010111
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,2,4,3,7,8,6,5] => 0010101
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => 0010011
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => 0010011
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => 0010001
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => 1100111
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [3,2,1,4,7,8,6,5] => 1100101
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [3,2,1,4,6,8,7,5] => 1100011
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [3,2,1,4,7,6,8,5] => 1100011
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [3,2,1,4,6,7,8,5] => 1100001
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => 0100111
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [2,3,1,4,7,8,6,5] => 0100101
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => 0100011
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [2,3,1,4,6,7,8,5] => 0100001
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => 0100111
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,3,2,4,6,8,7,5] => 0100011
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => 0100011
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,3,2,4,6,7,8,5] => 0100001
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => 1000111
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [2,1,3,4,7,8,6,5] => 1000101
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => 1000011
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => 1000001
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => 0000111
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => 0000101
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => 0000011
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => 0000011
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => 0000001
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => 1111011
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => 1111001
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [4,5,3,2,1,8,7,6] => 1101011
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [3,5,4,2,1,8,7,6] => 1011011
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [3,5,4,2,1,7,8,6] => 1011001
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [4,3,5,2,1,8,7,6] => 1011011
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [3,4,5,2,1,8,7,6] => 1001011
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [3,4,5,2,1,7,8,6] => 1001001
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [2,5,4,3,1,8,7,6] => 0111011
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [2,5,4,3,1,7,8,6] => 0111001
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [2,4,5,3,1,8,7,6] => 0101011
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [2,4,5,3,1,7,8,6] => 0101001
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => 0111011
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [3,2,5,4,1,7,8,6] => 0111001
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [2,3,5,4,1,8,7,6] => 0011011
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => 0111011
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [4,3,2,5,1,7,8,6] => 0111001
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => 0011011
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [3,4,2,5,1,7,8,6] => 0011001
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [2,4,3,5,1,8,7,6] => 0011011
[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [2,4,3,5,1,7,8,6] => 0011001
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [3,2,4,5,1,8,7,6] => 0101011
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [2,3,4,5,1,8,7,6] => 0001011
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => 0001001
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => 0111011
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,5,4,3,2,7,8,6] => 0111001
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,4,5,3,2,8,7,6] => 0101011
[[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,4,5,3,2,7,8,6] => 0101001
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,3,5,4,2,7,8,6] => 0011001
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,4,3,5,2,8,7,6] => 0011011
[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,4,3,5,2,7,8,6] => 0011001
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,3,4,5,2,8,7,6] => 0001011
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,3,4,5,2,7,8,6] => 0001001
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [2,1,5,4,3,8,7,6] => 1011011
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [2,1,4,5,3,8,7,6] => 1001011
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => 0011011
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,2,5,4,3,7,8,6] => 0011001
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => 0001011
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,2,4,5,3,7,8,6] => 0001001
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => 0101011
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,3,2,5,4,7,8,6] => 0101001
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [2,1,3,5,4,8,7,6] => 1001011
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [2,1,3,5,4,7,8,6] => 1001001
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => 0001011
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,2,3,5,4,7,8,6] => 0001001
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => 1110011
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => 1110001
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [3,4,2,1,5,8,7,6] => 1010011
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [2,4,3,1,5,8,7,6] => 0110011
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => 0110011
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => 0110001
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [2,3,4,1,5,8,7,6] => 0010011
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [2,3,4,1,5,7,8,6] => 0010001
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => 0110011
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,4,3,2,5,7,8,6] => 0110001
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,3,4,2,5,8,7,6] => 0010011
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,3,4,2,5,7,8,6] => 0010001
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [2,1,4,3,5,8,7,6] => 1010011
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [2,1,4,3,5,7,8,6] => 1010001
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,2,4,3,5,8,7,6] => 0010011
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,2,4,3,5,7,8,6] => 0010001
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => 1100011
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [3,2,1,4,5,7,8,6] => 1100001
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => 0100001
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,3,2,4,5,8,7,6] => 0100011
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,3,2,4,5,7,8,6] => 0100001
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [2,1,3,4,5,8,7,6] => 1000011
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [2,1,3,4,5,7,8,6] => 1000001
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => 0000011
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => 0000001
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => 1111101
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [5,6,4,3,2,1,8,7] => 1110101
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [4,6,5,3,2,1,8,7] => 1101101
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [5,4,6,3,2,1,8,7] => 1101101
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => 1100101
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [3,6,5,4,2,1,8,7] => 1011101
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => 1010101
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [4,3,6,5,2,1,8,7] => 1011101
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [3,4,6,5,2,1,8,7] => 1001101
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [5,4,3,6,2,1,8,7] => 1011101
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [4,5,3,6,2,1,8,7] => 1001101
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [4,3,5,6,2,1,8,7] => 1010101
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [3,4,5,6,2,1,8,7] => 1000101
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [2,6,5,4,3,1,8,7] => 0111101
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [2,5,6,4,3,1,8,7] => 0110101
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [2,4,6,5,3,1,8,7] => 0101101
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [3,2,6,5,4,1,8,7] => 0111101
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [3,2,5,6,4,1,8,7] => 0110101
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [2,3,6,5,4,1,8,7] => 0011101
[[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [2,3,5,6,4,1,8,7] => 0010101
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [4,3,2,6,5,1,8,7] => 0111101
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [3,4,2,6,5,1,8,7] => 0011101
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => 0011101
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [5,4,3,2,6,1,8,7] => 0111101
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [4,5,3,2,6,1,8,7] => 0101101
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [3,5,4,2,6,1,8,7] => 0011101
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => 0011101
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [3,4,5,2,6,1,8,7] => 0001101
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [2,5,4,3,6,1,8,7] => 0011101
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [2,4,5,3,6,1,8,7] => 0001101
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => 0101101
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [4,3,2,5,6,1,8,7] => 0110101
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [3,4,2,5,6,1,8,7] => 0010101
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [2,4,3,5,6,1,8,7] => 0010101
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => 0000101
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => 0111101
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => 0110101
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,5,4,6,3,2,8,7] => 0101101
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,3,6,5,4,2,8,7] => 0011101
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,3,4,5,6,2,8,7] => 0000101
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => 1011101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => 1010101
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => 1001101
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => 1001101
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => 1000101
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,2,4,5,6,3,8,7] => 0000101
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [3,2,1,6,5,4,8,7] => 1101101
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [2,3,1,6,5,4,8,7] => 0101101
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,3,2,6,5,4,8,7] => 0101101
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,3,2,5,6,4,8,7] => 0100101
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [2,1,3,6,5,4,8,7] => 1001101
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [2,1,3,5,6,4,8,7] => 1000101
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,2,3,6,5,4,8,7] => 0001101
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,2,3,5,6,4,8,7] => 0000101
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => 1110101
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => 1010101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => 0110101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => 0110101
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => 0010101
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => 0010101
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => 1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => 0010101
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [2,3,1,4,6,5,8,7] => 0100101
[[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,3,2,4,6,5,8,7] => 0100101
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [2,1,3,4,6,5,8,7] => 1000101
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => 0000101
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => 1111001
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [4,5,3,2,1,6,8,7] => 1101001
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => [3,5,4,2,1,6,8,7] => 1011001
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [4,3,5,2,1,6,8,7] => 1011001
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [3,4,5,2,1,6,8,7] => 1001001
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [2,5,4,3,1,6,8,7] => 0111001
[[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [2,4,5,3,1,6,8,7] => 0101001
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [3,2,5,4,1,6,8,7] => 0111001
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [2,3,5,4,1,6,8,7] => 0011001
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [2,4,3,5,1,6,8,7] => 0011001
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [2,3,4,5,1,6,8,7] => 0001001
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,4,5,3,2,6,8,7] => 0101001
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,3,5,4,2,6,8,7] => 0011001
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,3,4,5,2,6,8,7] => 0001001
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => 1011001
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => 1001001
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,2,5,4,3,6,8,7] => 0011001
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [2,1,3,5,4,6,8,7] => 1001001
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => 0001001
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => 1110001
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [3,4,2,1,5,6,8,7] => 1010001
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => 0110001
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [2,3,4,1,5,6,8,7] => 0010001
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,4,3,2,5,6,8,7] => 0110001
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,3,4,2,5,6,8,7] => 0010001
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [2,1,4,3,5,6,8,7] => 1010001
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => 0010001
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [3,2,1,4,5,6,8,7] => 1100001
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [2,3,1,4,5,6,8,7] => 0100001
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => 0100001
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => 1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => 0000001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 1111110
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 1111010
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => 1110110
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 1110110
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 1110010
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => 1101110
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [4,6,7,5,3,2,1,8] => 1101010
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [5,4,7,6,3,2,1,8] => 1101110
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [4,5,7,6,3,2,1,8] => 1100110
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 1101110
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => 1100110
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [4,6,5,7,3,2,1,8] => 1100110
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => 1101010
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => 1100010
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [3,5,7,6,4,2,1,8] => 1010110
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [3,5,6,7,4,2,1,8] => 1010010
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [4,3,7,6,5,2,1,8] => 1011110
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => 1001110
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [5,4,3,7,6,2,1,8] => 1011110
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [4,5,3,7,6,2,1,8] => 1001110
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [3,5,4,7,6,2,1,8] => 1001110
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [4,3,5,7,6,2,1,8] => 1010110
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => 1011110
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => 1010110
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => 1001110
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [3,6,5,4,7,2,1,8] => 1001110
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [3,5,6,4,7,2,1,8] => 1000110
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [4,3,6,5,7,2,1,8] => 1010110
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => 1011010
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => 1000010
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => 0111110
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [2,6,7,5,4,3,1,8] => 0111010
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [2,5,7,6,4,3,1,8] => 0110110
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [2,5,6,7,4,3,1,8] => 0110010
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => 0101010
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [2,5,4,7,6,3,1,8] => 0101110
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [2,5,6,4,7,3,1,8] => 0100110
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [2,5,4,6,7,3,1,8] => 0101010
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [2,4,5,6,7,3,1,8] => 0100010
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => 0111110
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [3,2,6,7,5,4,1,8] => 0111010
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [3,2,5,7,6,4,1,8] => 0110110
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [3,2,6,5,7,4,1,8] => 0110110
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [3,2,5,6,7,4,1,8] => 0110010
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [2,3,7,6,5,4,1,8] => 0011110
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [2,3,6,7,5,4,1,8] => 0011010
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [2,3,5,7,6,4,1,8] => 0010110
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [2,3,6,5,7,4,1,8] => 0010110
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [2,3,5,6,7,4,1,8] => 0010010
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [4,3,2,6,7,5,1,8] => 0111010
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [3,4,2,7,6,5,1,8] => 0011110
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [3,4,2,6,7,5,1,8] => 0011010
[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [3,2,4,6,7,5,1,8] => 0101010
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [2,3,4,7,6,5,1,8] => 0001110
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [2,3,4,6,7,5,1,8] => 0001010
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => 0111110
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [4,5,3,2,7,6,1,8] => 0101110
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [3,5,4,2,7,6,1,8] => 0011110
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [4,3,5,2,7,6,1,8] => 0011110
[[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [3,4,5,2,7,6,1,8] => 0001110
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => 0101110
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [4,3,2,5,7,6,1,8] => 0110110
[[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [3,4,2,5,7,6,1,8] => 0010110
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => 0000110
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => 0111110
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => 0110110
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => 0101110
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [3,6,5,4,2,7,1,8] => 0011110
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [3,5,6,4,2,7,1,8] => 0010110
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [3,4,6,5,2,7,1,8] => 0001110
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => 0011110
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => 0001110
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => 0001110
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => 0010110
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => 0000110
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [2,5,4,6,3,7,1,8] => 0001110
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [3,2,6,5,4,7,1,8] => 0101110
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [2,3,5,6,4,7,1,8] => 0000110
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [4,3,2,6,5,7,1,8] => 0110110
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [3,4,2,6,5,7,1,8] => 0010110
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [2,4,3,6,5,7,1,8] => 0010110
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => 0000110
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => 0111010
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [3,5,4,2,6,7,1,8] => 0011010
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => 0001010
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [2,5,4,3,6,7,1,8] => 0011010
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [2,4,5,3,6,7,1,8] => 0001010
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [2,3,5,4,6,7,1,8] => 0001010
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => 0110010
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => 0010010
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => 0100010
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 0000010
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => 0111110
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => 0111010
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,6,5,7,4,3,2,8] => 0110110
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,5,6,7,4,3,2,8] => 0110010
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,4,7,6,5,3,2,8] => 0101110
[[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,4,6,7,5,3,2,8] => 0101010
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,5,4,7,6,3,2,8] => 0101110
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,5,6,4,7,3,2,8] => 0100110
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,4,6,5,7,3,2,8] => 0100110
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,5,4,6,7,3,2,8] => 0101010
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => 0100010
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,3,7,6,5,4,2,8] => 0011110
[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,3,6,7,5,4,2,8] => 0011010
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,3,5,7,6,4,2,8] => 0010110
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,3,6,5,7,4,2,8] => 0010110
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,3,5,6,7,4,2,8] => 0010010
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => 0001010
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,3,5,4,7,6,2,8] => 0001110
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,4,3,5,7,6,2,8] => 0010110
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,3,4,5,7,6,2,8] => 0000110
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,5,4,6,3,7,2,8] => 0001110
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,4,5,6,3,7,2,8] => 0000110
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,3,6,5,4,7,2,8] => 0001110
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => 0000110
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,4,3,6,5,7,2,8] => 0010110
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,3,4,6,5,7,2,8] => 0000110
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,5,4,3,6,7,2,8] => 0011010
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,4,5,3,6,7,2,8] => 0001010
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,3,5,4,6,7,2,8] => 0001010
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,3,4,5,6,7,2,8] => 0000010
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [2,1,7,6,5,4,3,8] => 1011110
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [2,1,6,7,5,4,3,8] => 1011010
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [2,1,5,6,7,4,3,8] => 1010010
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [2,1,4,6,7,5,3,8] => 1001010
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [2,1,5,4,6,7,3,8] => 1001010
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [2,1,4,5,6,7,3,8] => 1000010
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8] => 0011110
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,2,6,7,5,4,3,8] => 0011010
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,2,5,7,6,4,3,8] => 0010110
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,2,5,6,7,4,3,8] => 0010010
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,2,4,6,7,5,3,8] => 0001010
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,2,5,6,4,7,3,8] => 0000110
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,2,5,4,6,7,3,8] => 0001010
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,2,4,5,6,7,3,8] => 0000010
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => 1101110
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [3,2,1,6,7,5,4,8] => 1101010
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [3,2,1,5,7,6,4,8] => 1100110
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [3,2,1,6,5,7,4,8] => 1100110
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [3,2,1,5,6,7,4,8] => 1100010
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [2,3,1,6,7,5,4,8] => 0101010
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [2,3,1,6,5,7,4,8] => 0100110
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => 0100010
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,3,2,7,6,5,4,8] => 0101110
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,3,2,6,7,5,4,8] => 0101010
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,3,2,5,7,6,4,8] => 0100110
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,3,2,6,5,7,4,8] => 0100110
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,3,2,5,6,7,4,8] => 0100010
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [2,1,3,6,7,5,4,8] => 1001010
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => 0001110
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => 0001010
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,2,3,5,7,6,4,8] => 0000110
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,2,3,6,5,7,4,8] => 0000110
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => 0000010
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => 1110110
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => 1110010
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8] => 0110110
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => 0110010
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8] => 0010110
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [2,3,4,1,6,7,5,8] => 0010010
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => 0110110
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,4,3,2,6,7,5,8] => 0110010
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => 0010010
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [2,1,4,3,6,7,5,8] => 1010010
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,2,4,3,6,7,5,8] => 0010010
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => 1100110
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => 0100010
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8] => 0100110
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [2,1,3,4,6,7,5,8] => 1000010
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => 0000110
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => 0000010
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8] => 1111010
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [4,5,3,2,1,7,6,8] => 1101010
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [3,5,4,2,1,7,6,8] => 1011010
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [3,4,5,2,1,7,6,8] => 1001010
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [2,5,4,3,1,7,6,8] => 0111010
[[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [2,4,5,3,1,7,6,8] => 0101010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [3,2,5,4,1,7,6,8] => 0111010
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [2,3,5,4,1,7,6,8] => 0011010
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [3,4,2,5,1,7,6,8] => 0011010
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8] => 0011010
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [2,3,4,5,1,7,6,8] => 0001010
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => 0111010
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,4,5,3,2,7,6,8] => 0101010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => 0011010
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,4,3,5,2,7,6,8] => 0011010
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => 0001010
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [2,1,5,4,3,7,6,8] => 1011010
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,2,4,5,3,7,6,8] => 0001010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => 1101010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => 0101010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => 0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => 0001010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => 1110010
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => 0110010
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [2,3,4,1,5,7,6,8] => 0010010
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => 0110010
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,3,4,2,5,7,6,8] => 0010010
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => 0010010
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [3,2,1,4,5,7,6,8] => 1100010
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8] => 0100010
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => 0100010
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => 1000010
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => 0000010
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 1111100
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => 1110100
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => 1101100
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => 1100100
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [3,6,5,4,2,1,7,8] => 1011100
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [4,3,6,5,2,1,7,8] => 1011100
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => 1011100
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => 1000100
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [2,4,6,5,3,1,7,8] => 0101100
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [2,4,5,6,3,1,7,8] => 0100100
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [2,3,6,5,4,1,7,8] => 0011100
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [2,3,5,6,4,1,7,8] => 0010100
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [4,3,2,6,5,1,7,8] => 0111100
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [2,4,3,6,5,1,7,8] => 0011100
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => 0001100
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => 0111100
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => 0101100
[[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [3,5,4,2,6,1,7,8] => 0011100
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => 0011100
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => 0001100
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => 0001100
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => 0110100
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => 0010100
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => 0100100
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 0000100
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => 0111100
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,5,6,4,3,2,7,8] => 0110100
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,4,6,5,3,2,7,8] => 0101100
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,5,4,6,3,2,7,8] => 0101100
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,4,5,6,3,2,7,8] => 0100100
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => 0010100
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,4,3,6,5,2,7,8] => 0011100
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,5,4,3,6,2,7,8] => 0011100
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,4,5,3,6,2,7,8] => 0001100
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,3,5,4,6,2,7,8] => 0001100
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,4,3,5,6,2,7,8] => 0010100
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => 0000100
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [2,1,5,6,4,3,7,8] => 1010100
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [2,1,4,6,5,3,7,8] => 1001100
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => 0011100
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => 0010100
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,2,4,6,5,3,7,8] => 0001100
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => 0000100
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [3,2,1,6,5,4,7,8] => 1101100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [3,2,1,5,6,4,7,8] => 1100100
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [2,3,1,6,5,4,7,8] => 0101100
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [2,3,1,5,6,4,7,8] => 0100100
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => 0101100
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,3,2,5,6,4,7,8] => 0100100
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => 0001100
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,2,3,5,6,4,7,8] => 0000100
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => 1110100
[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [2,4,3,1,6,5,7,8] => 0110100
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => 0110100
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [2,3,4,1,6,5,7,8] => 0010100
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => 1010100
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => 0010100
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => 0100100
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => 1000100
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => 0000100
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 1111000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => 1101000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [3,5,4,2,1,6,7,8] => 1011000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => 1011000
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => 1001000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [2,5,4,3,1,6,7,8] => 0111000
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => 0101000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [3,2,5,4,1,6,7,8] => 0111000
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [2,3,5,4,1,6,7,8] => 0011000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => 0111000
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => 0011000
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => 0011000
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => 0101000
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 0001000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => 0111000
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,4,5,3,2,6,7,8] => 0101000
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,3,5,4,2,6,7,8] => 0011000
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => 0001000
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8] => 1011000
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => 1001000
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => 0011000
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [3,2,1,5,4,6,7,8] => 1101000
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [2,3,1,5,4,6,7,8] => 0101000
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => 0101000
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8] => 1001000
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => 0001000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 1110000
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => 1010000
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => 0110000
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => 0110000
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => 0010000
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => 0110000
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => 0010000
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => 1010000
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => 0010000
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 1100000
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => 0100000
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => 0100000
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 1000000
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => 11111101
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => 11111001
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => 11110001
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => 11100001
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => 11000001
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => 10000001
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => 111111101
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [7,9,8,6,5,4,3,2,1] => 11111011
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => 111111001
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => 111110001
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => 111100001
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => 111000001
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [3,5,6,7,8,9,4,2,1] => 10100001
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => 110000001
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [2,4,5,6,7,8,9,3,1] => 01000001
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => 100000001
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,2] => 00000001
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 000000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => 11111011
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => 11110111
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => 11101111
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => 11011111
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => 10111111
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => 01111111
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 11111110
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => 111111011
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [6,8,7,9,5,4,3,2,1] => 11110011
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => 111110111
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [5,8,7,6,9,4,3,2,1] => 11100111
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => 111101111
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [4,8,7,6,5,9,3,2,1] => 11001111
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => 111011111
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [3,8,7,6,5,4,9,2,1] => 10011111
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => 110111111
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [2,8,7,6,5,4,3,9,1] => 00111111
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => 101111111
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,8,7,6,5,4,3,2,9] => 01111110
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => 011111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 111111110
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,3,5,7,9,10,8,6,4,2] => 001010101
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [1,6,7,5,8,4,9,3,10,2] => 000001111
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => 000011110
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,10,9,1] => 001010111
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,1,4,6,5,3,8,10,9,7] => 100110011
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,1,4,6,5,3,8,7,10,9] => 100110101
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,9,8,1,10] => 010101110
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => 101010101
[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,10,9,12,11,1] => 00101010111
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3,8,7,10,12,11,9] => 10011010011
[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,10,9,7,12,11] => 10011001101
[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [2,1,4,6,5,3,8,7,10,9,12,11] => 10011010101
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,9,8,11,10,1,12] => 01010101110
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => 10101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => 00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => 000000001
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,9,8] => 10000001
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 01000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,8,10,9] => 100000001
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,3,2,4,5,6,7,9,8] => 01000001
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [2,3,1,4,5,6,7,9,8] => 01000001
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [2,4,3,5,6,7,8,9,1] => 00100001
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 00100001
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 010000001
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000001
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => 00000001
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,7,8,9,6] => 00000001
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,6,7,8,9,5] => 00000001
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,5,6,7,8,9,4] => 00000001
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,3] => 00000001
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => 00000011
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,7,9,10,8] => 000000001
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,5,8,7,9,6] => 00000011
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,6,8,9,10,7] => 000000001
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,4,7,6,8,9,5] => 00000101
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,5,7,8,9,10,6] => 000000001
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [1,2,3,6,5,7,8,9,4] => 00001001
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,4,6,7,8,9,10,5] => 000000001
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [1,2,5,4,6,7,8,9,3] => 00010001
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,3,5,6,7,8,9,10,4] => 000000001
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,4,3,5,6,7,8,9,2] => 00100001
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,10,3] => 000000001
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,10,2] => 000000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => 01111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 11111010
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => 01111101
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => 011111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 111111010
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 11110110
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,8,7,9,6,5,4,3,2] => 01111011
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,9,10,8,7,6,5,4,3,2] => 011111101
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => 000011111
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [5,4,7,6,8,3,9,2,10,1] => 000101111
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [4,3,7,6,8,5,9,2,10,1] => 001001111
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [5,4,6,3,8,7,9,2,10,1] => 000110111
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [4,3,6,5,8,7,9,2,10,1] => 001010111
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [3,2,7,6,8,5,9,4,10,1] => 010001111
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [3,2,6,5,8,7,9,4,10,1] => 010010111
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [4,3,5,2,8,7,9,6,10,1] => 001100111
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [3,2,5,4,8,7,9,6,10,1] => 010100111
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [5,4,6,3,7,2,9,8,10,1] => 000111011
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [4,3,6,5,7,2,9,8,10,1] => 001011011
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [3,2,6,5,7,4,9,8,10,1] => 010011011
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [4,3,5,2,7,6,9,8,10,1] => 001101011
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,10,1] => 010101011
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [2,1,7,6,8,5,9,4,10,3] => 100001111
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [2,1,6,5,8,7,9,4,10,3] => 100010111
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [2,1,5,4,8,7,9,6,10,3] => 100100111
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [2,1,6,5,7,4,9,8,10,3] => 100011011
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [2,1,5,4,7,6,9,8,10,3] => 100101011
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [3,2,4,1,8,7,9,6,10,5] => 011000111
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [3,2,4,1,7,6,9,8,10,5] => 011001011
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,4,3,8,7,9,6,10,5] => 101000111
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,4,3,7,6,9,8,10,5] => 101001011
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [4,3,5,2,6,1,9,8,10,7] => 001110011
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [3,2,5,4,6,1,9,8,10,7] => 010110011
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [2,1,5,4,6,3,9,8,10,7] => 100110011
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [3,2,4,1,6,5,9,8,10,7] => 011010011
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,6,5,9,8,10,7] => 101010011
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [5,4,6,3,7,2,8,1,10,9] => 000111101
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [4,3,6,5,7,2,8,1,10,9] => 001011101
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [3,2,6,5,7,4,8,1,10,9] => 010011101
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [4,3,5,2,7,6,8,1,10,9] => 001101101
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,7,6,8,1,10,9] => 010101101
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [2,1,6,5,7,4,8,3,10,9] => 100011101
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [2,1,5,4,7,6,8,3,10,9] => 100101101
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [3,2,4,1,7,6,8,5,10,9] => 011001101
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,4,3,7,6,8,5,10,9] => 101001101
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [4,3,5,2,6,1,8,7,10,9] => 001110101
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => [3,2,5,4,6,1,8,7,10,9] => 010110101
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [2,1,5,4,6,3,8,7,10,9] => 100110101
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7,10,9] => 011010101
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [7,6,8,5,9,4,10,3,11,2,12,1] => 00000111111
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]] => [6,5,8,7,9,4,10,3,11,2,12,1] => 00001011111
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]] => [5,4,8,7,9,6,10,3,11,2,12,1] => 00010011111
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]] => [6,5,7,4,9,8,10,3,11,2,12,1] => 00001101111
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]] => [5,4,7,6,9,8,10,3,11,2,12,1] => 00010101111
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]] => [4,3,8,7,9,6,10,5,11,2,12,1] => 00100011111
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]] => [4,3,7,6,9,8,10,5,11,2,12,1] => 00100101111
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]] => [5,4,6,3,9,8,10,7,11,2,12,1] => 00011001111
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]] => [4,3,6,5,9,8,10,7,11,2,12,1] => 00101001111
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]] => [6,5,7,4,8,3,10,9,11,2,12,1] => 00001110111
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => [5,4,7,6,8,3,10,9,11,2,12,1] => 00010110111
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => [4,3,7,6,8,5,10,9,11,2,12,1] => 00100110111
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => [5,4,6,3,8,7,10,9,11,2,12,1] => 00011010111
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => [4,3,6,5,8,7,10,9,11,2,12,1] => 00101010111
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [3,2,8,7,9,6,10,5,11,4,12,1] => 01000011111
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [3,2,7,6,9,8,10,5,11,4,12,1] => 01000101111
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [3,2,6,5,9,8,10,7,11,4,12,1] => 01001001111
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [3,2,7,6,8,5,10,9,11,4,12,1] => 01000110111
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [3,2,6,5,8,7,10,9,11,4,12,1] => 01001010111
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => [4,3,5,2,9,8,10,7,11,6,12,1] => 00110001111
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]] => [4,3,5,2,8,7,10,9,11,6,12,1] => 00110010111
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [3,2,5,4,9,8,10,7,11,6,12,1] => 01010001111
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [3,2,5,4,8,7,10,9,11,6,12,1] => 01010010111
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => [5,4,6,3,7,2,10,9,11,8,12,1] => 00011100111
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]] => [4,3,6,5,7,2,10,9,11,8,12,1] => 00101100111
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,10,9,11,8,12,1] => 01001100111
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]] => [4,3,5,2,7,6,10,9,11,8,12,1] => 00110100111
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [3,2,5,4,7,6,10,9,11,8,12,1] => 01010100111
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => [6,5,7,4,8,3,9,2,11,10,12,1] => 00001111011
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => [5,4,7,6,8,3,9,2,11,10,12,1] => 00010111011
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => [4,3,7,6,8,5,9,2,11,10,12,1] => 00100111011
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => [5,4,6,3,8,7,9,2,11,10,12,1] => 00011011011
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => [4,3,6,5,8,7,9,2,11,10,12,1] => 00101011011
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [3,2,7,6,8,5,9,4,11,10,12,1] => 01000111011
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [3,2,6,5,8,7,9,4,11,10,12,1] => 01001011011
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,8,7,9,6,11,10,12,1] => 00110011011
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [3,2,5,4,8,7,9,6,11,10,12,1] => 01010011011
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]] => [5,4,6,3,7,2,9,8,11,10,12,1] => 00011101011
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => [4,3,6,5,7,2,9,8,11,10,12,1] => 00101101011
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [3,2,6,5,7,4,9,8,11,10,12,1] => 01001101011
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => [4,3,5,2,7,6,9,8,11,10,12,1] => 00110101011
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,11,10,12,1] => 01010101011
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [2,1,8,7,9,6,10,5,11,4,12,3] => 10000011111
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [2,1,7,6,9,8,10,5,11,4,12,3] => 10000101111
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [2,1,6,5,9,8,10,7,11,4,12,3] => 10001001111
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [2,1,7,6,8,5,10,9,11,4,12,3] => 10000110111
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [2,1,6,5,8,7,10,9,11,4,12,3] => 10001010111
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [2,1,5,4,9,8,10,7,11,6,12,3] => 10010001111
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [2,1,5,4,8,7,10,9,11,6,12,3] => 10010010111
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,10,9,11,8,12,3] => 10001100111
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [2,1,5,4,7,6,10,9,11,8,12,3] => 10010100111
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [2,1,7,6,8,5,9,4,11,10,12,3] => 10000111011
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [2,1,6,5,8,7,9,4,11,10,12,3] => 10001011011
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [2,1,5,4,8,7,9,6,11,10,12,3] => 10010011011
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [2,1,6,5,7,4,9,8,11,10,12,3] => 10001101011
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [2,1,5,4,7,6,9,8,11,10,12,3] => 10010101011
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [3,2,4,1,9,8,10,7,11,6,12,5] => 01100001111
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [3,2,4,1,8,7,10,9,11,6,12,5] => 01100010111
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,4,1,7,6,10,9,11,8,12,5] => 01100100111
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [3,2,4,1,8,7,9,6,11,10,12,5] => 01100011011
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,4,1,7,6,9,8,11,10,12,5] => 01100101011
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [2,1,4,3,9,8,10,7,11,6,12,5] => 10100001111
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [2,1,4,3,8,7,10,9,11,6,12,5] => 10100010111
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [2,1,4,3,7,6,10,9,11,8,12,5] => 10100100111
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [2,1,4,3,8,7,9,6,11,10,12,5] => 10100011011
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [2,1,4,3,7,6,9,8,11,10,12,5] => 10100101011
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1,10,9,11,8,12,7] => 00111000111
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => [4,3,5,2,6,1,9,8,11,10,12,7] => 00111001011
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [3,2,5,4,6,1,10,9,11,8,12,7] => 01011000111
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1,9,8,11,10,12,7] => 01011001011
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [2,1,5,4,6,3,10,9,11,8,12,7] => 10011000111
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,6,3,9,8,11,10,12,7] => 10011001011
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [3,2,4,1,6,5,10,9,11,8,12,7] => 01101000111
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [3,2,4,1,6,5,9,8,11,10,12,7] => 01101001011
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,4,3,6,5,10,9,11,8,12,7] => 10101000111
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,4,3,6,5,9,8,11,10,12,7] => 10101001011
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]] => [5,4,6,3,7,2,8,1,11,10,12,9] => 00011110011
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => [4,3,6,5,7,2,8,1,11,10,12,9] => 00101110011
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [3,2,6,5,7,4,8,1,11,10,12,9] => 01001110011
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => [4,3,5,2,7,6,8,1,11,10,12,9] => 00110110011
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [3,2,5,4,7,6,8,1,11,10,12,9] => 01010110011
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [2,1,6,5,7,4,8,3,11,10,12,9] => 10001110011
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [2,1,5,4,7,6,8,3,11,10,12,9] => 10010110011
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5,11,10,12,9] => 01100110011
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5,11,10,12,9] => 10100110011
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]] => [4,3,5,2,6,1,8,7,11,10,12,9] => 00111010011
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [3,2,5,4,6,1,8,7,11,10,12,9] => 01011010011
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3,8,7,11,10,12,9] => 10011010011
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [3,2,4,1,6,5,8,7,11,10,12,9] => 01101010011
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,6,5,8,7,11,10,12,9] => 10101010011
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => [6,5,7,4,8,3,9,2,10,1,12,11] => 00001111101
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]] => [5,4,7,6,8,3,9,2,10,1,12,11] => 00010111101
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]] => [4,3,7,6,8,5,9,2,10,1,12,11] => 00100111101
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => [5,4,6,3,8,7,9,2,10,1,12,11] => 00011011101
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]] => [4,3,6,5,8,7,9,2,10,1,12,11] => 00101011101
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [3,2,7,6,8,5,9,4,10,1,12,11] => 01000111101
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [3,2,6,5,8,7,9,4,10,1,12,11] => 01001011101
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,8,7,9,6,10,1,12,11] => 00110011101
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [3,2,5,4,8,7,9,6,10,1,12,11] => 01010011101
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => [5,4,6,3,7,2,9,8,10,1,12,11] => 00011101101
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => [4,3,6,5,7,2,9,8,10,1,12,11] => 00101101101
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [3,2,6,5,7,4,9,8,10,1,12,11] => 01001101101
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => [4,3,5,2,7,6,9,8,10,1,12,11] => 00110101101
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,7,6,9,8,10,1,12,11] => 01010101101
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [2,1,7,6,8,5,9,4,10,3,12,11] => 10000111101
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [2,1,6,5,8,7,9,4,10,3,12,11] => 10001011101
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [2,1,5,4,8,7,9,6,10,3,12,11] => 10010011101
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [2,1,6,5,7,4,9,8,10,3,12,11] => 10001101101
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [2,1,5,4,7,6,9,8,10,3,12,11] => 10010101101
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [3,2,4,1,8,7,9,6,10,5,12,11] => 01100011101
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,4,1,7,6,9,8,10,5,12,11] => 01100101101
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [2,1,4,3,8,7,9,6,10,5,12,11] => 10100011101
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [2,1,4,3,7,6,9,8,10,5,12,11] => 10100101101
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => [4,3,5,2,6,1,9,8,10,7,12,11] => 00111001101
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [3,2,5,4,6,1,9,8,10,7,12,11] => 01011001101
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,9,8,10,7,12,11] => 10011001101
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5,9,8,10,7,12,11] => 01101001101
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,4,3,6,5,9,8,10,7,12,11] => 10101001101
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]] => [5,4,6,3,7,2,8,1,10,9,12,11] => 00011110101
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]] => [4,3,6,5,7,2,8,1,10,9,12,11] => 00101110101
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [3,2,6,5,7,4,8,1,10,9,12,11] => 01001110101
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => [4,3,5,2,7,6,8,1,10,9,12,11] => 00110110101
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]] => [3,2,5,4,7,6,8,1,10,9,12,11] => 01010110101
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [2,1,6,5,7,4,8,3,10,9,12,11] => 10001110101
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => [2,1,5,4,7,6,8,3,10,9,12,11] => 10010110101
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,7,6,8,5,10,9,12,11] => 01100110101
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [2,1,4,3,7,6,8,5,10,9,12,11] => 10100110101
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => [4,3,5,2,6,1,8,7,10,9,12,11] => 00111010101
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => [3,2,5,4,6,1,8,7,10,9,12,11] => 01011010101
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [2,1,5,4,6,3,8,7,10,9,12,11] => 10011010101
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7,10,9,12,11] => 01101010101
[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,10,9,2] => 001010111
[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,10,9,12,11,2] => 00101010111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [2,1,9,8,7,6,5,4,3] => 10111111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [3,2,1,9,8,7,6,5,4] => 11011111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [4,3,2,1,9,8,7,6,5] => 11101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [5,4,3,2,1,9,8,7,6] => 11110111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [6,5,4,3,2,1,9,8,7] => 11111011
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [7,6,5,4,3,2,1,9,8] => 11111101
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,9,8,7,6,5,4,3] => 00111111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => 101111111
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [2,3,1,9,8,7,6,5,4] => 01011111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [3,2,1,10,9,8,7,6,5,4] => 110111111
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]] => [3,4,2,1,9,8,7,6,5] => 10101111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => 111011111
[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => [4,5,3,2,1,9,8,7,6] => 11010111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [5,4,3,2,1,10,9,8,7,6] => 111101111
[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => [5,6,4,3,2,1,9,8,7] => 11101011
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => 111110111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [6,7,5,4,3,2,1,9,8] => 11110101
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [7,6,5,4,3,2,1,10,9,8] => 111111011
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => 111111101
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 11111100
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 11111000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 11110000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 11100000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 11000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 10000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 111111100
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 111111000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 111110000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 111100000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 111000000
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,4,3,2,5,6,7,8,9] => 01100000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 110000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9] => 01000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 100000000
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [4,9,8,7,6,5,3,2,1] => 11011111
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [3,9,8,7,6,5,4,2,1] => 10111111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => 01111111
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [6,10,9,8,7,5,4,3,2,1] => 111101111
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,8,7,5,10,9] => 011001101
[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => [2,4,3,1,6,5,8,10,9,7] => 011010011
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7,10,9] => 011010101
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,3,6,8,7,5,10,9] => 101001101
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,5,8,10,9,7] => 101010011
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5,10,12,11,9] => 01100110011
[[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,8,7,5,10,9,12,11] => 01100110101
[[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5,8,10,9,7,12,11] => 01101001101
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,4,3,1,6,5,8,7,10,12,11,9] => 01101010011
[[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7,10,9,12,11] => 01101010101
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5,10,12,11,9] => 10100110011
[[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,1,4,3,6,8,7,5,10,9,12,11] => 10100110101
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,3,6,5,8,10,9,7,12,11] => 10101001101
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,5,8,7,10,12,11,9] => 10101010011
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,9,8,1] => 00000011
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [2,1,3,4,5,6,8,7,9] => 10000010
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [2,1,3,4,5,6,8,9,7] => 10000001
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [2,3,4,5,6,8,9,7,1] => 00000101
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,8,10,9,1] => 000000011
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [2,1,4,3,5,6,7,8,9] => 10100000
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [3,2,1,5,4,6,7,8,9] => 11010000
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [6,5,4,3,2,1,8,7,9] => 11111010
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => 00000011
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 00000010
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => 01000000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 00000100
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10] => 010000000
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [2,4,3,1,5,6,7,8,9] => 01100000
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [2,3,5,4,1,6,7,8,9] => 00110000
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [2,3,4,6,5,1,7,8,9] => 00011000
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [2,3,4,5,7,6,1,8,9] => 00001100
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [2,3,4,5,6,8,7,1,9] => 00000110
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 000000010
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9] => 00100000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,2,3,5,4,6,7,8,9] => 00010000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,6,5,7,8,9] => 00001000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,7,6,8,9] => 00000100
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,8,7,9] => 00000010
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9,10] => 010000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9,10] => 001000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,2,3,5,4,6,7,8,9,10] => 000100000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,2,3,4,6,5,7,8,9,10] => 000010000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,5,7,6,8,9,10] => 000001000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,6,8,7,9,10] => 000000100
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,9,8,10] => 000000010
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [1,3,4,5,6,7,9,8,2] => 00000011
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [7,6,5,4,3,2,9,8,1] => 01111111
[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,1] => 01100001
[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => [5,4,3,2,6,7,8,9,1] => 01110001
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => 01111001
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => [7,6,5,4,3,2,8,9,1] => 01111101
[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,10,1] => 011000001
[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]] => [5,4,3,2,6,7,8,9,10,1] => 011100001
[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]] => [6,5,4,3,2,7,8,9,10,1] => 011110001
[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]] => [7,6,5,4,3,2,8,9,10,1] => 011111001
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]] => [8,7,6,5,4,3,2,9,10,1] => 011111101
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,7,6,5,4,3,2,9,8] => 01111101
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [6,5,4,3,2,1,8,9,7] => 11111001
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,2,10,9,8,7,6,5,4,3] => 001111111
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,3,2,9,8,7,6,5,4] => 01011111
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [2,1,8,7,6,5,4,3,9] => 10111110
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,9,8,7,6,5,4,3,2,10] => 011111110
[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [2,8,7,9,6,5,4,3,1] => 01111011
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [1,3,4,5,2,6,7,8,9] => 00010000
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [1,2,4,5,3,6,7,8,9] => 00010000
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [2,1,4,5,3,6,7,8,9] => 10010000
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [1,3,2,5,4,6,7,8,9] => 01010000
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [8,7,6,5,4,3,2,10,9,1] => 011111111
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [2,1,4,5,6,7,8,9,3] => 10000001
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,3,4,5,6,7,8,2,9] => 00000010
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] => [2,1,8,9,7,6,5,4,3] => 10111101
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,7,10,9,8] => 000000011
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => 11110010
[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.] => [6,5,7,8,4,3,2,1,9] => 11101010
[[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.] => [6,5,4,7,8,3,2,1,9] => 11011010
[[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.] => [6,5,4,3,7,8,2,1,9] => 10111010
[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => [6,5,4,3,2,7,8,1,9] => 01111010
[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]] => [5,4,3,2,1,7,8,9,6] => 11110001
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => 111110010
[[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]] => [4,3,2,1,6,7,8,9,5] => 11100001
[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.] => [7,6,8,9,5,4,3,2,1,10] => 111101010
[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.] => [7,6,5,8,9,4,3,2,1,10] => 111011010
[[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.] => [7,6,5,4,8,9,3,2,1,10] => 110111010
[[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.] => [7,6,5,4,3,8,9,2,1,10] => 101111010
[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.] => [7,6,5,4,3,2,8,9,1,10] => 011111010
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,9,8,7,6] => 00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,9,8,7,6,5] => 00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,9,8,7,6,5,4] => 00011111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,7,6,9,8] => 00000101
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,6,10,9,8,7] => 000000111
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,4,6,5,9,8,7] => 00001011
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,5,10,9,8,7,6] => 000001111
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,3,5,4,9,8,7,6] => 00010111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,4,10,9,8,7,6,5] => 000011111
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,2,4,3,9,8,7,6,5] => 00101111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,3,10,9,8,7,6,5,4] => 000111111
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,6,8,7,10,9] => 000000101
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => 1111111011
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [1,9,8,10,7,6,5,4,3,2] => 011111011
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [2,8,9,7,6,5,4,3,1] => 01111101
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => 1111111101
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => 01111011
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => 10100000
[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10,11] => 0100000000
[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9,10] => 101000000
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.] => [3,4,2,5,1,6,7,8,9] => 00110000
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => 01111110
[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.] => [6,5,8,7,4,3,2,1,9] => 11101110
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => [7,6,5,8,4,3,2,1,9] => 11101110
[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.] => [6,7,5,8,4,3,2,1,9] => 11100110
[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]] => [4,3,2,1,8,9,7,6,5] => 11101101
[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [2,3,1,5,4,6,7,8,9] => 01010000
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => 11010000
[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]] => [4,3,2,1,6,7,8,9,10,5] => 111000001
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => 01000010
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [5,4,3,2,1,8,7,6,9] => 11110110
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [7,6,5,4,3,2,1,9,8,10] => 111111010
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [2,3,9,8,7,6,5,4,1] => 00111111
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [2,8,7,6,5,4,3,1,9] => 01111110
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [2,3,4,5,6,7,1,9,8] => 00000101
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,3,4,2,5,6,7,8,9] => 00100000
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => [8,7,6,5,4,3,2,9,1,10] => 011111110
[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [1,4,5,6,7,8,3,9,2] => 00000011
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010
[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]] => [2,1,3,5,6,7,8,9,4] => 10000001
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.] => [5,6,4,3,2,1,7,8,9] => 11101000
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => [5,6,4,3,2,1,7,8,9,10] => 111010000
[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.] => [6,7,5,4,3,2,1,8,9,10,11] => 1111010000
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.] => [6,7,5,4,3,2,1,8,9,10] => 111101000
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.] => [5,6,4,3,2,7,1,8,9] => 01101100
[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]] => [1,2,5,6,7,4,8,9,3] => 00000101
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => 11110100
[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]] => [5,4,3,2,1,8,9,7,6] => 11110101
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [7,6,5,4,3,2,1,9,10,8] => 111111001
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 tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
searching the database
Sorry, this map was not found in the database.