Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00066: Permutations —inverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
[.,.] => [1] => [1] =>
[.,[.,.]] => [2,1] => [2,1] => 1
[[.,.],.] => [1,2] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => [3,2,1] => 11
[.,[[.,.],.]] => [2,3,1] => [3,1,2] => 01
[[.,.],[.,.]] => [1,3,2] => [1,3,2] => 01
[[.,[.,.]],.] => [2,1,3] => [2,1,3] => 10
[[[.,.],.],.] => [1,2,3] => [1,2,3] => 00
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,3,2,1] => 111
[.,[.,[[.,.],.]]] => [3,4,2,1] => [4,3,1,2] => 011
[.,[[.,.],[.,.]]] => [2,4,3,1] => [4,1,3,2] => 011
[.,[[.,[.,.]],.]] => [3,2,4,1] => [4,2,1,3] => 101
[.,[[[.,.],.],.]] => [2,3,4,1] => [4,1,2,3] => 001
[[.,.],[.,[.,.]]] => [1,4,3,2] => [1,4,3,2] => 011
[[.,.],[[.,.],.]] => [1,3,4,2] => [1,4,2,3] => 001
[[.,[.,.]],[.,.]] => [2,1,4,3] => [2,1,4,3] => 101
[[[.,.],.],[.,.]] => [1,2,4,3] => [1,2,4,3] => 001
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1,4] => 110
[[.,[[.,.],.]],.] => [2,3,1,4] => [3,1,2,4] => 010
[[[.,.],[.,.]],.] => [1,3,2,4] => [1,3,2,4] => 010
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => 100
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => 000
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,4,3,2,1] => 1111
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [5,4,3,1,2] => 0111
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [5,4,1,3,2] => 0111
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [5,4,2,1,3] => 1011
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [5,4,1,2,3] => 0011
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [5,1,4,3,2] => 0111
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [5,1,4,2,3] => 0011
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [5,2,1,4,3] => 1011
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [5,1,2,4,3] => 0011
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [5,3,2,1,4] => 1101
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [5,3,1,2,4] => 0101
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [5,1,3,2,4] => 0101
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [5,2,1,3,4] => 1001
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [5,1,2,3,4] => 0001
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [1,5,4,3,2] => 0111
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [1,5,4,2,3] => 0011
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [1,5,2,4,3] => 0011
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [1,5,3,2,4] => 0101
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [1,5,2,3,4] => 0001
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [2,1,5,4,3] => 1011
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [2,1,5,3,4] => 1001
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [1,2,5,4,3] => 0011
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [1,2,5,3,4] => 0001
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [3,2,1,5,4] => 1101
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [3,1,2,5,4] => 0101
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [1,3,2,5,4] => 0101
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [2,1,3,5,4] => 1001
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [1,2,3,5,4] => 0001
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1,5] => 1110
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [4,3,1,2,5] => 0110
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [4,1,3,2,5] => 0110
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [4,2,1,3,5] => 1010
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [4,1,2,3,5] => 0010
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [1,4,3,2,5] => 0110
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [1,4,2,3,5] => 0010
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [2,1,4,3,5] => 1010
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [1,2,4,3,5] => 0010
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4,5] => 1100
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [3,1,2,4,5] => 0100
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [1,3,2,4,5] => 0100
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => 1000
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => 0000
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [6,5,4,3,1,2] => 01111
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [6,5,4,1,3,2] => 01111
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [6,5,4,2,1,3] => 10111
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 00111
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [6,5,1,4,3,2] => 01111
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [6,5,1,4,2,3] => 00111
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [6,5,2,1,4,3] => 10111
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [6,5,1,2,4,3] => 00111
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [6,5,3,2,1,4] => 11011
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [6,5,3,1,2,4] => 01011
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [6,5,1,3,2,4] => 01011
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [6,5,2,1,3,4] => 10011
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [6,5,1,2,3,4] => 00011
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [6,1,5,4,3,2] => 01111
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [6,1,5,4,2,3] => 00111
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [6,1,5,2,4,3] => 00111
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [6,1,5,3,2,4] => 01011
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [6,1,5,2,3,4] => 00011
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [6,2,1,5,4,3] => 10111
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [6,2,1,5,3,4] => 10011
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [6,1,2,5,4,3] => 00111
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [6,1,2,5,3,4] => 00011
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [6,3,2,1,5,4] => 11011
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [6,3,1,2,5,4] => 01011
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [6,1,3,2,5,4] => 01011
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [6,2,1,3,5,4] => 10011
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [6,1,2,3,5,4] => 00011
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [6,4,3,2,1,5] => 11101
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [6,4,3,1,2,5] => 01101
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [6,4,1,3,2,5] => 01101
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [6,4,2,1,3,5] => 10101
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [6,4,1,2,3,5] => 00101
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [6,1,4,3,2,5] => 01101
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [6,1,4,2,3,5] => 00101
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [6,2,1,4,3,5] => 10101
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [6,1,2,4,3,5] => 00101
>>> Load all 1941 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [6,3,2,1,4,5] => 11001
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [6,3,1,2,4,5] => 01001
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [6,1,3,2,4,5] => 01001
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [6,2,1,3,4,5] => 10001
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 00001
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 01111
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [1,6,5,4,2,3] => 00111
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [1,6,5,2,4,3] => 00111
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [1,6,5,3,2,4] => 01011
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [1,6,5,2,3,4] => 00011
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [1,6,2,5,4,3] => 00111
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [1,6,2,5,3,4] => 00011
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [1,6,3,2,5,4] => 01011
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [1,6,2,3,5,4] => 00011
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [1,6,4,3,2,5] => 01101
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [1,6,4,2,3,5] => 00101
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [1,6,2,4,3,5] => 00101
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [1,6,3,2,4,5] => 01001
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => 00001
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 10111
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [2,1,6,5,3,4] => 10011
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [2,1,6,3,5,4] => 10011
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [2,1,6,4,3,5] => 10101
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => 10001
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 00111
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [1,2,6,5,3,4] => 00011
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [1,2,6,3,5,4] => 00011
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [1,2,6,4,3,5] => 00101
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => 00001
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 11011
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [3,2,1,6,4,5] => 11001
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [3,1,2,6,5,4] => 01011
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => 01001
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 01011
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => 01001
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 10011
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => 10001
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 00011
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 00001
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 11101
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [4,3,1,2,6,5] => 01101
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [4,1,3,2,6,5] => 01101
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [4,2,1,3,6,5] => 10101
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => 00101
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 01101
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => 00101
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 10101
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 00101
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 11001
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => 01001
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 01001
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 10001
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 00001
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 11110
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [5,4,3,1,2,6] => 01110
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [5,4,1,3,2,6] => 01110
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [5,4,2,1,3,6] => 10110
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [5,4,1,2,3,6] => 00110
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [5,1,4,3,2,6] => 01110
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [5,1,4,2,3,6] => 00110
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [5,2,1,4,3,6] => 10110
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [5,1,2,4,3,6] => 00110
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [5,3,2,1,4,6] => 11010
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [5,3,1,2,4,6] => 01010
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [5,1,3,2,4,6] => 01010
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [5,2,1,3,4,6] => 10010
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => 00010
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 01110
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [1,5,4,2,3,6] => 00110
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [1,5,2,4,3,6] => 00110
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [1,5,3,2,4,6] => 01010
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => 00010
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 10110
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => 10010
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 00110
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => 00010
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 11010
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => 01010
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 01010
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 10010
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 00010
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 11100
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => 01100
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [4,1,3,2,5,6] => 01100
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [4,2,1,3,5,6] => 10100
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => 00100
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 01100
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 00100
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 10100
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 00100
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 11000
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => 01000
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 01000
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 10000
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [7,6,5,4,3,1,2] => 011111
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [7,6,5,4,1,3,2] => 011111
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [7,6,5,4,2,1,3] => 101111
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [7,6,5,4,1,2,3] => 001111
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [7,6,5,1,4,3,2] => 011111
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [7,6,5,1,4,2,3] => 001111
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [7,6,5,2,1,4,3] => 101111
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [7,6,5,1,2,4,3] => 001111
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [7,6,5,3,2,1,4] => 110111
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [7,6,5,3,1,2,4] => 010111
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [7,6,5,1,3,2,4] => 010111
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [7,6,5,2,1,3,4] => 100111
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [7,6,5,1,2,3,4] => 000111
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [7,6,1,5,4,3,2] => 011111
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [7,6,1,5,4,2,3] => 001111
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [7,6,1,5,2,4,3] => 001111
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [7,6,1,5,3,2,4] => 010111
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [7,6,1,5,2,3,4] => 000111
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [7,6,2,1,5,4,3] => 101111
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [7,6,2,1,5,3,4] => 100111
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [7,6,1,2,5,4,3] => 001111
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [7,6,1,2,5,3,4] => 000111
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [7,6,3,2,1,5,4] => 110111
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [7,6,3,1,2,5,4] => 010111
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [7,6,1,3,2,5,4] => 010111
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [7,6,2,1,3,5,4] => 100111
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [7,6,1,2,3,5,4] => 000111
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [7,6,4,3,2,1,5] => 111011
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [7,6,4,3,1,2,5] => 011011
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [7,6,4,1,3,2,5] => 011011
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [7,6,4,2,1,3,5] => 101011
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [7,6,4,1,2,3,5] => 001011
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [7,6,1,4,3,2,5] => 011011
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [7,6,1,4,2,3,5] => 001011
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [7,6,2,1,4,3,5] => 101011
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [7,6,1,2,4,3,5] => 001011
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [7,6,3,2,1,4,5] => 110011
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [7,6,3,1,2,4,5] => 010011
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [7,6,1,3,2,4,5] => 010011
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [7,6,2,1,3,4,5] => 100011
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [7,6,1,2,3,4,5] => 000011
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [7,1,6,5,4,3,2] => 011111
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [7,1,6,5,4,2,3] => 001111
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [7,1,6,5,2,4,3] => 001111
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [7,1,6,5,3,2,4] => 010111
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [7,1,6,5,2,3,4] => 000111
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [7,1,6,2,5,4,3] => 001111
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [7,1,6,2,5,3,4] => 000111
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [7,1,6,3,2,5,4] => 010111
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [7,1,6,2,3,5,4] => 000111
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [7,1,6,4,3,2,5] => 011011
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [7,1,6,4,2,3,5] => 001011
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [7,1,6,2,4,3,5] => 001011
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [7,1,6,3,2,4,5] => 010011
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [7,1,6,2,3,4,5] => 000011
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [7,2,1,6,5,4,3] => 101111
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [7,2,1,6,5,3,4] => 100111
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [7,2,1,6,3,5,4] => 100111
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [7,2,1,6,4,3,5] => 101011
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [7,2,1,6,3,4,5] => 100011
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [7,1,2,6,5,4,3] => 001111
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [7,1,2,6,5,3,4] => 000111
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [7,1,2,6,3,5,4] => 000111
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [7,1,2,6,4,3,5] => 001011
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [7,1,2,6,3,4,5] => 000011
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [7,3,2,1,6,5,4] => 110111
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => [7,3,2,1,6,4,5] => 110011
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [7,3,1,2,6,5,4] => 010111
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [7,3,1,2,6,4,5] => 010011
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [7,1,3,2,6,5,4] => 010111
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [7,1,3,2,6,4,5] => 010011
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [7,2,1,3,6,5,4] => 100111
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [7,2,1,3,6,4,5] => 100011
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [7,1,2,3,6,5,4] => 000111
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [7,1,2,3,6,4,5] => 000011
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [7,4,3,2,1,6,5] => 111011
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [7,4,3,1,2,6,5] => 011011
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [7,4,1,3,2,6,5] => 011011
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => [7,4,2,1,3,6,5] => 101011
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [7,4,1,2,3,6,5] => 001011
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [7,1,4,3,2,6,5] => 011011
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [7,1,4,2,3,6,5] => 001011
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [7,2,1,4,3,6,5] => 101011
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [7,1,2,4,3,6,5] => 001011
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [7,3,2,1,4,6,5] => 110011
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [7,3,1,2,4,6,5] => 010011
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [7,1,3,2,4,6,5] => 010011
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [7,2,1,3,4,6,5] => 100011
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [7,1,2,3,4,6,5] => 000011
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [7,5,4,3,2,1,6] => 111101
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [7,5,4,3,1,2,6] => 011101
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [7,5,4,1,3,2,6] => 011101
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [7,5,4,2,1,3,6] => 101101
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [7,5,4,1,2,3,6] => 001101
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => [7,5,1,4,3,2,6] => 011101
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [7,5,1,4,2,3,6] => 001101
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [7,5,2,1,4,3,6] => 101101
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [7,5,1,2,4,3,6] => 001101
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [7,5,3,2,1,4,6] => 110101
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [7,5,3,1,2,4,6] => 010101
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [7,5,1,3,2,4,6] => 010101
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [7,5,2,1,3,4,6] => 100101
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [7,5,1,2,3,4,6] => 000101
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [7,1,5,4,3,2,6] => 011101
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [7,1,5,4,2,3,6] => 001101
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [7,1,5,2,4,3,6] => 001101
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [7,1,5,3,2,4,6] => 010101
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [7,1,5,2,3,4,6] => 000101
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [7,2,1,5,4,3,6] => 101101
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [7,2,1,5,3,4,6] => 100101
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [7,1,2,5,4,3,6] => 001101
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [7,1,2,5,3,4,6] => 000101
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => [7,3,2,1,5,4,6] => 110101
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [7,3,1,2,5,4,6] => 010101
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [7,1,3,2,5,4,6] => 010101
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [7,2,1,3,5,4,6] => 100101
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [7,1,2,3,5,4,6] => 000101
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [7,4,3,2,1,5,6] => 111001
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [7,4,3,1,2,5,6] => 011001
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [7,4,1,3,2,5,6] => 011001
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [7,4,2,1,3,5,6] => 101001
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [7,4,1,2,3,5,6] => 001001
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [7,1,4,3,2,5,6] => 011001
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [7,1,4,2,3,5,6] => 001001
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [7,2,1,4,3,5,6] => 101001
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [7,1,2,4,3,5,6] => 001001
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [7,3,2,1,4,5,6] => 110001
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [7,3,1,2,4,5,6] => 010001
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [7,1,3,2,4,5,6] => 010001
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [7,2,1,3,4,5,6] => 100001
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => 000001
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 011111
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [1,7,6,5,4,2,3] => 001111
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [1,7,6,5,2,4,3] => 001111
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [1,7,6,5,3,2,4] => 010111
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [1,7,6,5,2,3,4] => 000111
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [1,7,6,2,5,4,3] => 001111
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [1,7,6,2,5,3,4] => 000111
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [1,7,6,3,2,5,4] => 010111
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [1,7,6,2,3,5,4] => 000111
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [1,7,6,4,3,2,5] => 011011
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [1,7,6,4,2,3,5] => 001011
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [1,7,6,2,4,3,5] => 001011
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [1,7,6,3,2,4,5] => 010011
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [1,7,6,2,3,4,5] => 000011
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [1,7,2,6,5,4,3] => 001111
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [1,7,2,6,5,3,4] => 000111
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [1,7,2,6,3,5,4] => 000111
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [1,7,2,6,4,3,5] => 001011
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [1,7,2,6,3,4,5] => 000011
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [1,7,3,2,6,5,4] => 010111
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [1,7,3,2,6,4,5] => 010011
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [1,7,2,3,6,5,4] => 000111
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [1,7,2,3,6,4,5] => 000011
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [1,7,4,3,2,6,5] => 011011
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [1,7,4,2,3,6,5] => 001011
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [1,7,2,4,3,6,5] => 001011
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [1,7,3,2,4,6,5] => 010011
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [1,7,2,3,4,6,5] => 000011
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [1,7,5,4,3,2,6] => 011101
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [1,7,5,4,2,3,6] => 001101
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [1,7,5,2,4,3,6] => 001101
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [1,7,5,3,2,4,6] => 010101
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [1,7,5,2,3,4,6] => 000101
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [1,7,2,5,4,3,6] => 001101
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [1,7,2,5,3,4,6] => 000101
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [1,7,3,2,5,4,6] => 010101
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [1,7,2,3,5,4,6] => 000101
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [1,7,4,3,2,5,6] => 011001
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [1,7,4,2,3,5,6] => 001001
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [1,7,2,4,3,5,6] => 001001
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [1,7,3,2,4,5,6] => 010001
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => 000001
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 101111
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [2,1,7,6,5,3,4] => 100111
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [2,1,7,6,3,5,4] => 100111
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [2,1,7,6,4,3,5] => 101011
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [2,1,7,6,3,4,5] => 100011
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [2,1,7,3,6,5,4] => 100111
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [2,1,7,3,6,4,5] => 100011
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [2,1,7,4,3,6,5] => 101011
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [2,1,7,3,4,6,5] => 100011
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [2,1,7,5,4,3,6] => 101101
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [2,1,7,5,3,4,6] => 100101
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [2,1,7,3,5,4,6] => 100101
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [2,1,7,4,3,5,6] => 101001
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => 100001
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 001111
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [1,2,7,6,5,3,4] => 000111
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [1,2,7,6,3,5,4] => 000111
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [1,2,7,6,4,3,5] => 001011
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [1,2,7,6,3,4,5] => 000011
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [1,2,7,3,6,5,4] => 000111
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [1,2,7,3,6,4,5] => 000011
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [1,2,7,4,3,6,5] => 001011
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [1,2,7,3,4,6,5] => 000011
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [1,2,7,5,4,3,6] => 001101
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [1,2,7,5,3,4,6] => 000101
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [1,2,7,3,5,4,6] => 000101
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [1,2,7,4,3,5,6] => 001001
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => 000001
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => 110111
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [3,2,1,7,6,4,5] => 110011
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [3,2,1,7,4,6,5] => 110011
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [3,2,1,7,5,4,6] => 110101
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [3,2,1,7,4,5,6] => 110001
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [3,1,2,7,6,5,4] => 010111
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [3,1,2,7,6,4,5] => 010011
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [3,1,2,7,4,6,5] => 010011
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [3,1,2,7,5,4,6] => 010101
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => 010001
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => 010111
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [1,3,2,7,6,4,5] => 010011
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [1,3,2,7,4,6,5] => 010011
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [1,3,2,7,5,4,6] => 010101
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => 010001
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => 100111
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [2,1,3,7,6,4,5] => 100011
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [2,1,3,7,4,6,5] => 100011
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [2,1,3,7,5,4,6] => 100101
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => 100001
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => 000111
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [1,2,3,7,6,4,5] => 000011
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [1,2,3,7,4,6,5] => 000011
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [1,2,3,7,5,4,6] => 000101
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => 000001
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => 111011
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [4,3,2,1,7,5,6] => 111001
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [4,3,1,2,7,6,5] => 011011
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [4,3,1,2,7,5,6] => 011001
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [4,1,3,2,7,6,5] => 011011
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [4,1,3,2,7,5,6] => 011001
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [4,2,1,3,7,6,5] => 101011
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [4,2,1,3,7,5,6] => 101001
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [4,1,2,3,7,6,5] => 001011
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => 001001
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => 011011
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [1,4,3,2,7,5,6] => 011001
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [1,4,2,3,7,6,5] => 001011
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => 001001
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [2,1,4,3,7,6,5] => 101011
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6] => 101001
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => 001011
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => 001001
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => 110011
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [3,2,1,4,7,5,6] => 110001
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [3,1,2,4,7,6,5] => 010011
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => 010001
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => 010011
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => 010001
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [2,1,3,4,7,6,5] => 100011
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [2,1,3,4,7,5,6] => 100001
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => 000011
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => 000001
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 111101
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [5,4,3,1,2,7,6] => 011101
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [5,4,1,3,2,7,6] => 011101
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [5,4,2,1,3,7,6] => 101101
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [5,4,1,2,3,7,6] => 001101
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [5,1,4,3,2,7,6] => 011101
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [5,1,4,2,3,7,6] => 001101
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [5,2,1,4,3,7,6] => 101101
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [5,1,2,4,3,7,6] => 001101
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [5,3,2,1,4,7,6] => 110101
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [5,3,1,2,4,7,6] => 010101
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [5,1,3,2,4,7,6] => 010101
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [5,2,1,3,4,7,6] => 100101
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => 000101
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => 011101
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [1,5,4,2,3,7,6] => 001101
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [1,5,2,4,3,7,6] => 001101
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [1,5,3,2,4,7,6] => 010101
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => 000101
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [2,1,5,4,3,7,6] => 101101
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6] => 100101
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => 001101
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => 000101
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [3,2,1,5,4,7,6] => 110101
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => 010101
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => 010101
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => 100101
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => 000101
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => 111001
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [4,3,1,2,5,7,6] => 011001
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [4,1,3,2,5,7,6] => 011001
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [4,2,1,3,5,7,6] => 101001
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => 001001
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => 011001
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => 001001
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => 101001
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => 001001
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [3,2,1,4,5,7,6] => 110001
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => 010001
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => 010001
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => 100001
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 000001
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 111110
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [6,5,4,3,1,2,7] => 011110
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [6,5,4,1,3,2,7] => 011110
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [6,5,4,2,1,3,7] => 101110
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [6,5,4,1,2,3,7] => 001110
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [6,5,1,4,3,2,7] => 011110
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [6,5,1,4,2,3,7] => 001110
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [6,5,2,1,4,3,7] => 101110
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [6,5,1,2,4,3,7] => 001110
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [6,5,3,2,1,4,7] => 110110
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [6,5,3,1,2,4,7] => 010110
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [6,5,1,3,2,4,7] => 010110
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [6,5,2,1,3,4,7] => 100110
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [6,5,1,2,3,4,7] => 000110
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [6,1,5,4,3,2,7] => 011110
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [6,1,5,4,2,3,7] => 001110
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [6,1,5,2,4,3,7] => 001110
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [6,1,5,3,2,4,7] => 010110
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [6,1,5,2,3,4,7] => 000110
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [6,2,1,5,4,3,7] => 101110
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [6,2,1,5,3,4,7] => 100110
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [6,1,2,5,4,3,7] => 001110
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [6,1,2,5,3,4,7] => 000110
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [6,3,2,1,5,4,7] => 110110
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [6,3,1,2,5,4,7] => 010110
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [6,1,3,2,5,4,7] => 010110
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [6,2,1,3,5,4,7] => 100110
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [6,1,2,3,5,4,7] => 000110
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [6,4,3,2,1,5,7] => 111010
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [6,4,3,1,2,5,7] => 011010
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [6,4,1,3,2,5,7] => 011010
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [6,4,2,1,3,5,7] => 101010
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [6,4,1,2,3,5,7] => 001010
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [6,1,4,3,2,5,7] => 011010
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [6,1,4,2,3,5,7] => 001010
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [6,2,1,4,3,5,7] => 101010
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [6,1,2,4,3,5,7] => 001010
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [6,3,2,1,4,5,7] => 110010
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [6,3,1,2,4,5,7] => 010010
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [6,1,3,2,4,5,7] => 010010
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [6,2,1,3,4,5,7] => 100010
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => 000010
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => 011110
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [1,6,5,4,2,3,7] => 001110
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [1,6,5,2,4,3,7] => 001110
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [1,6,5,3,2,4,7] => 010110
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [1,6,5,2,3,4,7] => 000110
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [1,6,2,5,4,3,7] => 001110
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [1,6,2,5,3,4,7] => 000110
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [1,6,3,2,5,4,7] => 010110
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [1,6,2,3,5,4,7] => 000110
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [1,6,4,3,2,5,7] => 011010
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [1,6,4,2,3,5,7] => 001010
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [1,6,2,4,3,5,7] => 001010
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [1,6,3,2,4,5,7] => 010010
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => 000010
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => 101110
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [2,1,6,5,3,4,7] => 100110
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [2,1,6,3,5,4,7] => 100110
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [2,1,6,4,3,5,7] => 101010
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => 100010
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => 001110
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [1,2,6,5,3,4,7] => 000110
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [1,2,6,3,5,4,7] => 000110
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [1,2,6,4,3,5,7] => 001010
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => 000010
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => 110110
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [3,2,1,6,4,5,7] => 110010
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [3,1,2,6,5,4,7] => 010110
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => 010010
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => 010110
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => 010010
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4,7] => 100110
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7] => 100010
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => 000110
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => 000010
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => 111010
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [4,3,1,2,6,5,7] => 011010
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [4,1,3,2,6,5,7] => 011010
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [4,2,1,3,6,5,7] => 101010
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => 001010
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => 011010
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => 001010
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => 101010
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => 001010
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5,7] => 110010
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => 010010
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 010010
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => 100010
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 000010
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 111100
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [5,4,3,1,2,6,7] => 011100
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [5,4,1,3,2,6,7] => 011100
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [5,4,2,1,3,6,7] => 101100
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [5,4,1,2,3,6,7] => 001100
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [5,1,4,3,2,6,7] => 011100
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [5,1,4,2,3,6,7] => 001100
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [5,2,1,4,3,6,7] => 101100
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [5,1,2,4,3,6,7] => 001100
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [5,3,2,1,4,6,7] => 110100
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [5,3,1,2,4,6,7] => 010100
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [5,1,3,2,4,6,7] => 010100
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [5,2,1,3,4,6,7] => 100100
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => 000100
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => 011100
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [1,5,4,2,3,6,7] => 001100
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [1,5,2,4,3,6,7] => 001100
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [1,5,3,2,4,6,7] => 010100
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => 000100
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6,7] => 101100
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7] => 100100
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 001100
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => 000100
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6,7] => 110100
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => 010100
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => 010100
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => 100100
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 000100
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 111000
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [4,3,1,2,5,6,7] => 011000
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [4,1,3,2,5,6,7] => 011000
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [4,2,1,3,5,6,7] => 101000
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => 001000
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => 011000
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => 001000
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => 101000
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 001000
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 110000
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => 010000
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 010000
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 100000
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [8,7,6,5,4,3,1,2] => 0111111
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [6,8,7,5,4,3,2,1] => [8,7,6,5,4,1,3,2] => 0111111
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [8,7,6,5,4,2,1,3] => 1011111
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [8,7,6,5,4,1,2,3] => 0011111
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [5,8,7,6,4,3,2,1] => [8,7,6,5,1,4,3,2] => 0111111
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [5,7,8,6,4,3,2,1] => [8,7,6,5,1,4,2,3] => 0011111
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => [8,7,6,5,2,1,4,3] => 1011111
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [5,6,8,7,4,3,2,1] => [8,7,6,5,1,2,4,3] => 0011111
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [8,7,6,5,3,2,1,4] => 1101111
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => [8,7,6,5,3,1,2,4] => 0101111
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => [8,7,6,5,1,3,2,4] => 0101111
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [8,7,6,5,2,1,3,4] => 1001111
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [8,7,6,5,1,2,3,4] => 0001111
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => [8,7,6,1,5,4,3,2] => 0111111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [4,7,8,6,5,3,2,1] => [8,7,6,1,5,4,2,3] => 0011111
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => [8,7,6,1,5,2,4,3] => 0011111
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [4,7,6,8,5,3,2,1] => [8,7,6,1,5,3,2,4] => 0101111
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [4,6,7,8,5,3,2,1] => [8,7,6,1,5,2,3,4] => 0001111
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [5,4,7,8,6,3,2,1] => [8,7,6,2,1,5,3,4] => 1001111
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [4,5,8,7,6,3,2,1] => [8,7,6,1,2,5,4,3] => 0011111
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [4,5,7,8,6,3,2,1] => [8,7,6,1,2,5,3,4] => 0001111
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [6,5,4,8,7,3,2,1] => [8,7,6,3,2,1,5,4] => 1101111
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [4,6,5,8,7,3,2,1] => [8,7,6,1,3,2,5,4] => 0101111
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => [8,7,6,1,2,3,5,4] => 0001111
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [8,7,6,4,3,2,1,5] => 1110111
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => [8,7,6,4,3,1,2,5] => 0110111
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [5,7,6,4,8,3,2,1] => [8,7,6,4,1,3,2,5] => 0110111
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [8,7,6,4,2,1,3,5] => 1010111
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => [8,7,6,4,1,2,3,5] => 0010111
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1] => [8,7,6,1,4,3,2,5] => 0110111
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [4,6,7,5,8,3,2,1] => [8,7,6,1,4,2,3,5] => 0010111
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [5,4,7,6,8,3,2,1] => [8,7,6,2,1,4,3,5] => 1010111
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [4,5,7,6,8,3,2,1] => [8,7,6,1,2,4,3,5] => 0010111
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => [8,7,6,3,2,1,4,5] => 1100111
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => [8,7,6,3,1,2,4,5] => 0100111
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [4,6,5,7,8,3,2,1] => [8,7,6,1,3,2,4,5] => 0100111
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => [8,7,6,2,1,3,4,5] => 1000111
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [8,7,6,1,2,3,4,5] => 0000111
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [3,8,7,6,5,4,2,1] => [8,7,1,6,5,4,3,2] => 0111111
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [3,6,8,7,5,4,2,1] => [8,7,1,6,5,2,4,3] => 0011111
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [3,7,6,8,5,4,2,1] => [8,7,1,6,5,3,2,4] => 0101111
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [3,6,7,8,5,4,2,1] => [8,7,1,6,5,2,3,4] => 0001111
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => [8,7,1,6,2,5,4,3] => 0011111
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => [8,7,1,6,2,5,3,4] => 0001111
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [3,5,6,8,7,4,2,1] => [8,7,1,6,2,3,5,4] => 0001111
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [3,7,6,5,8,4,2,1] => [8,7,1,6,4,3,2,5] => 0110111
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [3,6,7,5,8,4,2,1] => [8,7,1,6,4,2,3,5] => 0010111
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [3,5,6,7,8,4,2,1] => [8,7,1,6,2,3,4,5] => 0000111
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => [8,7,2,1,6,5,4,3] => 1011111
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [4,3,6,7,8,5,2,1] => [8,7,2,1,6,3,4,5] => 1000111
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [3,4,8,7,6,5,2,1] => [8,7,1,2,6,5,4,3] => 0011111
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [3,4,7,8,6,5,2,1] => [8,7,1,2,6,5,3,4] => 0001111
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => [8,7,1,2,6,3,4,5] => 0000111
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [5,4,3,8,7,6,2,1] => [8,7,3,2,1,6,5,4] => 1101111
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [5,4,3,7,8,6,2,1] => [8,7,3,2,1,6,4,5] => 1100111
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [4,5,3,7,8,6,2,1] => [8,7,3,1,2,6,4,5] => 0100111
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [3,5,4,7,8,6,2,1] => [8,7,1,3,2,6,4,5] => 0100111
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [4,3,5,8,7,6,2,1] => [8,7,2,1,3,6,5,4] => 1001111
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [4,3,5,7,8,6,2,1] => [8,7,2,1,3,6,4,5] => 1000111
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [3,4,5,8,7,6,2,1] => [8,7,1,2,3,6,5,4] => 0001111
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [3,4,5,7,8,6,2,1] => [8,7,1,2,3,6,4,5] => 0000111
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [6,5,4,3,8,7,2,1] => [8,7,4,3,2,1,6,5] => 1110111
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [4,6,5,3,8,7,2,1] => [8,7,4,1,3,2,6,5] => 0110111
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [5,4,6,3,8,7,2,1] => [8,7,4,2,1,3,6,5] => 1010111
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [4,5,6,3,8,7,2,1] => [8,7,4,1,2,3,6,5] => 0010111
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [3,6,5,4,8,7,2,1] => [8,7,1,4,3,2,6,5] => 0110111
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => [8,7,2,1,4,3,6,5] => 1010111
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [3,4,6,5,8,7,2,1] => [8,7,1,2,4,3,6,5] => 0010111
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [5,4,3,6,8,7,2,1] => [8,7,3,2,1,4,6,5] => 1100111
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [4,5,3,6,8,7,2,1] => [8,7,3,1,2,4,6,5] => 0100111
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [3,5,4,6,8,7,2,1] => [8,7,1,3,2,4,6,5] => 0100111
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [4,3,5,6,8,7,2,1] => [8,7,2,1,3,4,6,5] => 1000111
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [3,4,5,6,8,7,2,1] => [8,7,1,2,3,4,6,5] => 0000111
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [8,7,5,4,3,2,1,6] => 1111011
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => [8,7,5,4,3,1,2,6] => 0111011
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [5,7,6,4,3,8,2,1] => [8,7,5,4,1,3,2,6] => 0111011
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => [8,7,5,4,1,2,3,6] => 0011011
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [4,7,6,5,3,8,2,1] => [8,7,5,1,4,3,2,6] => 0111011
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [4,6,7,5,3,8,2,1] => [8,7,5,1,4,2,3,6] => 0011011
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [4,5,7,6,3,8,2,1] => [8,7,5,1,2,4,3,6] => 0011011
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => [8,7,5,3,2,1,4,6] => 1101011
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [5,6,4,7,3,8,2,1] => [8,7,5,3,1,2,4,6] => 0101011
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [8,7,5,2,1,3,4,6] => 1001011
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => [8,7,5,1,2,3,4,6] => 0001011
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [3,6,7,5,4,8,2,1] => [8,7,1,5,4,2,3,6] => 0011011
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [3,5,6,7,4,8,2,1] => [8,7,1,5,2,3,4,6] => 0001011
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [4,3,7,6,5,8,2,1] => [8,7,2,1,5,4,3,6] => 1011011
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [4,3,6,7,5,8,2,1] => [8,7,2,1,5,3,4,6] => 1001011
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [3,4,7,6,5,8,2,1] => [8,7,1,2,5,4,3,6] => 0011011
[.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [3,4,6,7,5,8,2,1] => [8,7,1,2,5,3,4,6] => 0001011
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [5,4,3,7,6,8,2,1] => [8,7,3,2,1,5,4,6] => 1101011
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [3,5,4,7,6,8,2,1] => [8,7,1,3,2,5,4,6] => 0101011
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [4,3,5,7,6,8,2,1] => [8,7,2,1,3,5,4,6] => 1001011
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => [8,7,4,3,2,1,5,6] => 1110011
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => [5,4,6,3,7,8,2,1] => [8,7,4,2,1,3,5,6] => 1010011
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => [8,7,4,1,2,3,5,6] => 0010011
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [3,6,5,4,7,8,2,1] => [8,7,1,4,3,2,5,6] => 0110011
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [3,5,6,4,7,8,2,1] => [8,7,1,4,2,3,5,6] => 0010011
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [4,3,6,5,7,8,2,1] => [8,7,2,1,4,3,5,6] => 1010011
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [3,4,6,5,7,8,2,1] => [8,7,1,2,4,3,5,6] => 0010011
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => [8,7,3,2,1,4,5,6] => 1100011
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [3,5,4,6,7,8,2,1] => [8,7,1,3,2,4,5,6] => 0100011
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [8,7,2,1,3,4,5,6] => 1000011
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [8,7,1,2,3,4,5,6] => 0000011
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => [8,1,7,6,5,4,3,2] => 0111111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [2,7,8,6,5,4,3,1] => [8,1,7,6,5,4,2,3] => 0011111
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => [8,1,7,6,5,2,4,3] => 0011111
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [2,7,6,8,5,4,3,1] => [8,1,7,6,5,3,2,4] => 0101111
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [2,6,7,8,5,4,3,1] => [8,1,7,6,5,2,3,4] => 0001111
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [2,5,8,7,6,4,3,1] => [8,1,7,6,2,5,4,3] => 0011111
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [2,7,6,5,8,4,3,1] => [8,1,7,6,4,3,2,5] => 0110111
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [2,6,7,5,8,4,3,1] => [8,1,7,6,4,2,3,5] => 0010111
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [2,5,7,6,8,4,3,1] => [8,1,7,6,2,4,3,5] => 0010111
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [2,6,5,7,8,4,3,1] => [8,1,7,6,3,2,4,5] => 0100111
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [2,5,6,7,8,4,3,1] => [8,1,7,6,2,3,4,5] => 0000111
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [2,4,8,7,6,5,3,1] => [8,1,7,2,6,5,4,3] => 0011111
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => [8,1,7,2,6,3,5,4] => 0001111
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [2,4,7,6,8,5,3,1] => [8,1,7,2,6,4,3,5] => 0010111
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [2,4,6,7,8,5,3,1] => [8,1,7,2,6,3,4,5] => 0000111
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [2,5,4,8,7,6,3,1] => [8,1,7,3,2,6,5,4] => 0101111
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [2,5,4,7,8,6,3,1] => [8,1,7,3,2,6,4,5] => 0100111
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [2,4,5,8,7,6,3,1] => [8,1,7,2,3,6,5,4] => 0001111
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [2,4,5,7,8,6,3,1] => [8,1,7,2,3,6,4,5] => 0000111
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [2,6,5,4,8,7,3,1] => [8,1,7,4,3,2,6,5] => 0110111
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [2,5,6,4,8,7,3,1] => [8,1,7,4,2,3,6,5] => 0010111
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [2,4,6,5,8,7,3,1] => [8,1,7,2,4,3,6,5] => 0010111
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [2,7,6,5,4,8,3,1] => [8,1,7,5,4,3,2,6] => 0111011
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [2,6,7,5,4,8,3,1] => [8,1,7,5,4,2,3,6] => 0011011
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [2,5,7,6,4,8,3,1] => [8,1,7,5,2,4,3,6] => 0011011
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [2,6,5,7,4,8,3,1] => [8,1,7,5,3,2,4,6] => 0101011
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [2,4,7,6,5,8,3,1] => [8,1,7,2,5,4,3,6] => 0011011
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [2,4,6,7,5,8,3,1] => [8,1,7,2,5,3,4,6] => 0001011
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [2,5,4,7,6,8,3,1] => [8,1,7,3,2,5,4,6] => 0101011
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [2,5,6,4,7,8,3,1] => [8,1,7,4,2,3,5,6] => 0010011
[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [2,4,6,5,7,8,3,1] => [8,1,7,2,4,3,5,6] => 0010011
[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [2,5,4,6,7,8,3,1] => [8,1,7,3,2,4,5,6] => 0100011
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [2,4,5,6,7,8,3,1] => [8,1,7,2,3,4,5,6] => 0000011
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => [8,2,1,7,6,5,4,3] => 1011111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [3,2,7,8,6,5,4,1] => [8,2,1,7,6,5,3,4] => 1001111
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [3,2,6,8,7,5,4,1] => [8,2,1,7,6,3,5,4] => 1001111
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [3,2,7,6,8,5,4,1] => [8,2,1,7,6,4,3,5] => 1010111
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [3,2,6,7,8,5,4,1] => [8,2,1,7,6,3,4,5] => 1000111
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [3,2,6,5,8,7,4,1] => [8,2,1,7,4,3,6,5] => 1010111
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [3,2,7,6,5,8,4,1] => [8,2,1,7,5,4,3,6] => 1011011
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [3,2,6,7,5,8,4,1] => [8,2,1,7,5,3,4,6] => 1001011
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [3,2,5,7,6,8,4,1] => [8,2,1,7,3,5,4,6] => 1001011
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [3,2,6,5,7,8,4,1] => [8,2,1,7,4,3,5,6] => 1010011
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [3,2,5,6,7,8,4,1] => [8,2,1,7,3,4,5,6] => 1000011
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => [8,1,2,7,6,5,4,3] => 0011111
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [2,3,6,8,7,5,4,1] => [8,1,2,7,6,3,5,4] => 0001111
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [2,3,6,7,8,5,4,1] => [8,1,2,7,6,3,4,5] => 0000111
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [2,3,5,8,7,6,4,1] => [8,1,2,7,3,6,5,4] => 0001111
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [2,3,5,7,8,6,4,1] => [8,1,2,7,3,6,4,5] => 0000111
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [2,3,6,5,8,7,4,1] => [8,1,2,7,4,3,6,5] => 0010111
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => [8,1,2,7,3,4,6,5] => 0000111
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [2,3,7,6,5,8,4,1] => [8,1,2,7,5,4,3,6] => 0011011
[.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [2,3,5,7,6,8,4,1] => [8,1,2,7,3,5,4,6] => 0001011
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [2,3,5,6,7,8,4,1] => [8,1,2,7,3,4,5,6] => 0000011
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => [8,3,2,1,7,6,5,4] => 1101111
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [4,3,2,7,8,6,5,1] => [8,3,2,1,7,6,4,5] => 1100111
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [4,3,2,6,8,7,5,1] => [8,3,2,1,7,4,6,5] => 1100111
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [4,3,2,6,7,8,5,1] => [8,3,2,1,7,4,5,6] => 1100011
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => [8,3,1,2,7,6,5,4] => 0101111
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [3,4,2,7,8,6,5,1] => [8,3,1,2,7,6,4,5] => 0100111
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [3,4,2,6,7,8,5,1] => [8,3,1,2,7,4,5,6] => 0100011
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [2,4,3,8,7,6,5,1] => [8,1,3,2,7,6,5,4] => 0101111
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [2,4,3,7,8,6,5,1] => [8,1,3,2,7,6,4,5] => 0100111
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [2,4,3,6,8,7,5,1] => [8,1,3,2,7,4,6,5] => 0100111
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [2,4,3,7,6,8,5,1] => [8,1,3,2,7,5,4,6] => 0101011
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [3,2,4,8,7,6,5,1] => [8,2,1,3,7,6,5,4] => 1001111
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [3,2,4,7,8,6,5,1] => [8,2,1,3,7,6,4,5] => 1000111
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [3,2,4,6,8,7,5,1] => [8,2,1,3,7,4,6,5] => 1000111
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => [8,1,2,3,7,6,5,4] => 0001111
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [2,3,4,7,6,8,5,1] => [8,1,2,3,7,5,4,6] => 0001011
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [2,3,4,6,7,8,5,1] => [8,1,2,3,7,4,5,6] => 0000011
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [5,4,3,2,8,7,6,1] => [8,4,3,2,1,7,6,5] => 1110111
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [5,4,3,2,7,8,6,1] => [8,4,3,2,1,7,5,6] => 1110011
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [4,5,3,2,8,7,6,1] => [8,4,3,1,2,7,6,5] => 0110111
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [3,5,4,2,8,7,6,1] => [8,4,1,3,2,7,6,5] => 0110111
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [4,3,5,2,8,7,6,1] => [8,4,2,1,3,7,6,5] => 1010111
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [4,3,5,2,7,8,6,1] => [8,4,2,1,3,7,5,6] => 1010011
[.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [3,4,5,2,7,8,6,1] => [8,4,1,2,3,7,5,6] => 0010011
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => [8,1,4,3,2,7,6,5] => 0110111
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [2,5,4,3,7,8,6,1] => [8,1,4,3,2,7,5,6] => 0110011
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [2,4,5,3,8,7,6,1] => [8,1,4,2,3,7,6,5] => 0010111
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [2,4,5,3,7,8,6,1] => [8,1,4,2,3,7,5,6] => 0010011
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [3,2,5,4,8,7,6,1] => [8,2,1,4,3,7,6,5] => 1010111
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [3,2,5,4,7,8,6,1] => [8,2,1,4,3,7,5,6] => 1010011
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [2,3,5,4,8,7,6,1] => [8,1,2,4,3,7,6,5] => 0010111
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [4,3,2,5,8,7,6,1] => [8,3,2,1,4,7,6,5] => 1100111
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [4,3,2,5,7,8,6,1] => [8,3,2,1,4,7,5,6] => 1100011
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [3,4,2,5,8,7,6,1] => [8,3,1,2,4,7,6,5] => 0100111
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [3,4,2,5,7,8,6,1] => [8,3,1,2,4,7,5,6] => 0100011
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [2,4,3,5,8,7,6,1] => [8,1,3,2,4,7,6,5] => 0100111
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [3,2,4,5,7,8,6,1] => [8,2,1,3,4,7,5,6] => 1000011
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [2,3,4,5,8,7,6,1] => [8,1,2,3,4,7,6,5] => 0000111
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [2,3,4,5,7,8,6,1] => [8,1,2,3,4,7,5,6] => 0000011
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [6,5,4,3,2,8,7,1] => [8,5,4,3,2,1,7,6] => 1111011
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [4,6,5,3,2,8,7,1] => [8,5,4,1,3,2,7,6] => 0111011
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [5,4,6,3,2,8,7,1] => [8,5,4,2,1,3,7,6] => 1011011
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [4,5,6,3,2,8,7,1] => [8,5,4,1,2,3,7,6] => 0011011
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [3,5,6,4,2,8,7,1] => [8,5,1,4,2,3,7,6] => 0011011
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [4,3,6,5,2,8,7,1] => [8,5,2,1,4,3,7,6] => 1011011
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [3,4,6,5,2,8,7,1] => [8,5,1,2,4,3,7,6] => 0011011
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [5,4,3,6,2,8,7,1] => [8,5,3,2,1,4,7,6] => 1101011
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => [8,5,3,1,2,4,7,6] => 0101011
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [3,5,4,6,2,8,7,1] => [8,5,1,3,2,4,7,6] => 0101011
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [2,6,5,4,3,8,7,1] => [8,1,5,4,3,2,7,6] => 0111011
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [2,4,6,5,3,8,7,1] => [8,1,5,2,4,3,7,6] => 0011011
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [2,5,4,6,3,8,7,1] => [8,1,5,3,2,4,7,6] => 0101011
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => [8,2,1,5,4,3,7,6] => 1011011
[.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [2,3,5,6,4,8,7,1] => [8,1,2,5,3,4,7,6] => 0001011
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [4,3,2,6,5,8,7,1] => [8,3,2,1,5,4,7,6] => 1101011
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [3,4,2,6,5,8,7,1] => [8,3,1,2,5,4,7,6] => 0101011
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => [8,1,3,2,5,4,7,6] => 0101011
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [3,2,4,6,5,8,7,1] => [8,2,1,3,5,4,7,6] => 1001011
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [2,3,4,6,5,8,7,1] => [8,1,2,3,5,4,7,6] => 0001011
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [5,4,3,2,6,8,7,1] => [8,4,3,2,1,5,7,6] => 1110011
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [4,5,3,2,6,8,7,1] => [8,4,3,1,2,5,7,6] => 0110011
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [3,5,4,2,6,8,7,1] => [8,4,1,3,2,5,7,6] => 0110011
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [4,3,5,2,6,8,7,1] => [8,4,2,1,3,5,7,6] => 1010011
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [2,5,4,3,6,8,7,1] => [8,1,4,3,2,5,7,6] => 0110011
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [2,4,5,3,6,8,7,1] => [8,1,4,2,3,5,7,6] => 0010011
[.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [2,3,5,4,6,8,7,1] => [8,1,2,4,3,5,7,6] => 0010011
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [4,3,2,5,6,8,7,1] => [8,3,2,1,4,5,7,6] => 1100011
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [3,4,2,5,6,8,7,1] => [8,3,1,2,4,5,7,6] => 0100011
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => [8,1,3,2,4,5,7,6] => 0100011
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [3,2,4,5,6,8,7,1] => [8,2,1,3,4,5,7,6] => 1000011
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => [8,1,2,3,4,5,7,6] => 0000011
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [8,6,5,4,3,2,1,7] => 1111101
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [8,6,5,4,3,1,2,7] => 0111101
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [5,7,6,4,3,2,8,1] => [8,6,5,4,1,3,2,7] => 0111101
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [8,6,5,4,2,1,3,7] => 1011101
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => [8,6,5,4,1,2,3,7] => 0011101
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [4,7,6,5,3,2,8,1] => [8,6,5,1,4,3,2,7] => 0111101
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [5,4,7,6,3,2,8,1] => [8,6,5,2,1,4,3,7] => 1011101
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [4,5,7,6,3,2,8,1] => [8,6,5,1,2,4,3,7] => 0011101
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1] => [8,6,5,3,2,1,4,7] => 1101101
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [4,6,5,7,3,2,8,1] => [8,6,5,1,3,2,4,7] => 0101101
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => [5,4,6,7,3,2,8,1] => [8,6,5,2,1,3,4,7] => 1001101
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => [8,6,5,1,2,3,4,7] => 0001101
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [3,7,6,5,4,2,8,1] => [8,6,1,5,4,3,2,7] => 0111101
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [3,5,7,6,4,2,8,1] => [8,6,1,5,2,4,3,7] => 0011101
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [3,6,5,7,4,2,8,1] => [8,6,1,5,3,2,4,7] => 0101101
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [3,5,6,7,4,2,8,1] => [8,6,1,5,2,3,4,7] => 0001101
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [4,3,7,6,5,2,8,1] => [8,6,2,1,5,4,3,7] => 1011101
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [4,3,6,7,5,2,8,1] => [8,6,2,1,5,3,4,7] => 1001101
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [3,4,7,6,5,2,8,1] => [8,6,1,2,5,4,3,7] => 0011101
[.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [3,4,6,7,5,2,8,1] => [8,6,1,2,5,3,4,7] => 0001101
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [5,4,3,7,6,2,8,1] => [8,6,3,2,1,5,4,7] => 1101101
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [4,5,3,7,6,2,8,1] => [8,6,3,1,2,5,4,7] => 0101101
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [4,3,5,7,6,2,8,1] => [8,6,2,1,3,5,4,7] => 1001101
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [3,4,5,7,6,2,8,1] => [8,6,1,2,3,5,4,7] => 0001101
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [8,6,4,3,2,1,5,7] => 1110101
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [5,6,4,3,7,2,8,1] => [8,6,4,3,1,2,5,7] => 0110101
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [4,6,5,3,7,2,8,1] => [8,6,4,1,3,2,5,7] => 0110101
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [8,6,4,2,1,3,5,7] => 1010101
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [3,6,5,4,7,2,8,1] => [8,6,1,4,3,2,5,7] => 0110101
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => [8,6,1,4,2,3,5,7] => 0010101
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => [8,6,2,1,4,3,5,7] => 1010101
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [3,4,6,5,7,2,8,1] => [8,6,1,2,4,3,5,7] => 0010101
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => [8,6,3,2,1,4,5,7] => 1100101
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [3,5,4,6,7,2,8,1] => [8,6,1,3,2,4,5,7] => 0100101
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => [8,6,1,2,3,4,5,7] => 0000101
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1] => [8,1,6,5,4,3,2,7] => 0111101
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [2,5,6,7,4,3,8,1] => [8,1,6,5,2,3,4,7] => 0001101
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [2,4,6,7,5,3,8,1] => [8,1,6,2,5,3,4,7] => 0001101
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [2,5,4,7,6,3,8,1] => [8,1,6,3,2,5,4,7] => 0101101
[.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [2,4,5,7,6,3,8,1] => [8,1,6,2,3,5,4,7] => 0001101
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [2,5,6,4,7,3,8,1] => [8,1,6,4,2,3,5,7] => 0010101
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => [8,1,6,2,4,3,5,7] => 0010101
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [2,5,4,6,7,3,8,1] => [8,1,6,3,2,4,5,7] => 0100101
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [2,4,5,6,7,3,8,1] => [8,1,6,2,3,4,5,7] => 0000101
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [3,2,6,7,5,4,8,1] => [8,2,1,6,5,3,4,7] => 1001101
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => [8,2,1,6,4,3,5,7] => 1010101
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [3,2,5,6,7,4,8,1] => [8,2,1,6,3,4,5,7] => 1000101
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [2,3,7,6,5,4,8,1] => [8,1,2,6,5,4,3,7] => 0011101
[.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [2,3,6,7,5,4,8,1] => [8,1,2,6,5,3,4,7] => 0001101
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [2,3,5,6,7,4,8,1] => [8,1,2,6,3,4,5,7] => 0000101
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1] => [8,3,2,1,6,5,4,7] => 1101101
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [4,3,2,6,7,5,8,1] => [8,3,2,1,6,4,5,7] => 1100101
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [3,4,2,6,7,5,8,1] => [8,3,1,2,6,4,5,7] => 0100101
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [2,4,3,7,6,5,8,1] => [8,1,3,2,6,5,4,7] => 0101101
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [3,2,4,7,6,5,8,1] => [8,2,1,3,6,5,4,7] => 1001101
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [3,2,4,6,7,5,8,1] => [8,2,1,3,6,4,5,7] => 1000101
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [2,3,4,7,6,5,8,1] => [8,1,2,3,6,5,4,7] => 0001101
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [2,3,4,6,7,5,8,1] => [8,1,2,3,6,4,5,7] => 0000101
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [5,4,3,2,7,6,8,1] => [8,4,3,2,1,6,5,7] => 1110101
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => [4,5,3,2,7,6,8,1] => [8,4,3,1,2,6,5,7] => 0110101
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [3,5,4,2,7,6,8,1] => [8,4,1,3,2,6,5,7] => 0110101
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => [8,4,2,1,3,6,5,7] => 1010101
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [2,5,4,3,7,6,8,1] => [8,1,4,3,2,6,5,7] => 0110101
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [2,4,5,3,7,6,8,1] => [8,1,4,2,3,6,5,7] => 0010101
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => [8,2,1,4,3,6,5,7] => 1010101
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [2,3,5,4,7,6,8,1] => [8,1,2,4,3,6,5,7] => 0010101
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [4,3,2,5,7,6,8,1] => [8,3,2,1,4,6,5,7] => 1100101
[.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [3,4,2,5,7,6,8,1] => [8,3,1,2,4,6,5,7] => 0100101
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [2,4,3,5,7,6,8,1] => [8,1,3,2,4,6,5,7] => 0100101
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1] => [8,2,1,3,4,6,5,7] => 1000101
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => [8,1,2,3,4,6,5,7] => 0000101
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => [8,5,4,3,2,1,6,7] => 1111001
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => [4,6,5,3,2,7,8,1] => [8,5,4,1,3,2,6,7] => 0111001
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => [8,5,4,2,1,3,6,7] => 1011001
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => [8,5,4,1,2,3,6,7] => 0011001
[.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [3,5,6,4,2,7,8,1] => [8,5,1,4,2,3,6,7] => 0011001
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [4,3,6,5,2,7,8,1] => [8,5,2,1,4,3,6,7] => 1011001
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [3,4,6,5,2,7,8,1] => [8,5,1,2,4,3,6,7] => 0011001
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => [8,5,3,2,1,4,6,7] => 1101001
[.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [4,5,3,6,2,7,8,1] => [8,5,3,1,2,4,6,7] => 0101001
[.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [3,5,4,6,2,7,8,1] => [8,5,1,3,2,4,6,7] => 0101001
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => [8,5,2,1,3,4,6,7] => 1001001
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => [8,5,1,2,3,4,6,7] => 0001001
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [2,6,5,4,3,7,8,1] => [8,1,5,4,3,2,6,7] => 0111001
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [2,5,6,4,3,7,8,1] => [8,1,5,4,2,3,6,7] => 0011001
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [2,5,4,6,3,7,8,1] => [8,1,5,3,2,4,6,7] => 0101001
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [2,4,5,6,3,7,8,1] => [8,1,5,2,3,4,6,7] => 0001001
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [2,3,6,5,4,7,8,1] => [8,1,2,5,4,3,6,7] => 0011001
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [2,3,5,6,4,7,8,1] => [8,1,2,5,3,4,6,7] => 0001001
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [4,3,2,6,5,7,8,1] => [8,3,2,1,5,4,6,7] => 1101001
[.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [3,4,2,6,5,7,8,1] => [8,3,1,2,5,4,6,7] => 0101001
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [2,4,3,6,5,7,8,1] => [8,1,3,2,5,4,6,7] => 0101001
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [2,3,4,6,5,7,8,1] => [8,1,2,3,5,4,6,7] => 0001001
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [8,4,3,2,1,5,6,7] => 1110001
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [3,5,4,2,6,7,8,1] => [8,4,1,3,2,5,6,7] => 0110001
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => [8,4,2,1,3,5,6,7] => 1010001
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [8,4,1,2,3,5,6,7] => 0010001
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1] => [8,1,4,3,2,5,6,7] => 0110001
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [2,4,5,3,6,7,8,1] => [8,1,4,2,3,5,6,7] => 0010001
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1] => [8,1,2,4,3,5,6,7] => 0010001
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [8,3,2,1,4,5,6,7] => 1100001
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [8,3,1,2,4,5,6,7] => 0100001
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [2,4,3,5,6,7,8,1] => [8,1,3,2,4,5,6,7] => 0100001
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [8,2,1,3,4,5,6,7] => 1000001
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => 0000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0111111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => [1,8,7,6,5,4,2,3] => 0011111
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => [1,8,7,6,5,2,4,3] => 0011111
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => [1,8,7,6,5,3,2,4] => 0101111
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => [1,8,7,6,5,2,3,4] => 0001111
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => [1,8,7,6,2,5,4,3] => 0011111
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,6,5,8,7,4,3,2] => [1,8,7,6,3,2,5,4] => 0101111
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => [1,8,7,6,4,3,2,5] => 0110111
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => [1,8,7,6,4,2,3,5] => 0010111
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,5,7,6,8,4,3,2] => [1,8,7,6,2,4,3,5] => 0010111
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,6,5,7,8,4,3,2] => [1,8,7,6,3,2,4,5] => 0100111
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => [1,8,7,6,2,3,4,5] => 0000111
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => [1,8,7,2,6,5,4,3] => 0011111
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => [1,8,7,2,6,5,3,4] => 0001111
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => [1,8,7,2,6,3,5,4] => 0001111
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,4,6,7,8,5,3,2] => [1,8,7,2,6,3,4,5] => 0000111
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,5,4,7,8,6,3,2] => [1,8,7,3,2,6,4,5] => 0100111
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,4,5,8,7,6,3,2] => [1,8,7,2,3,6,5,4] => 0001111
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,4,5,7,8,6,3,2] => [1,8,7,2,3,6,4,5] => 0000111
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,6,5,4,8,7,3,2] => [1,8,7,4,3,2,6,5] => 0110111
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,5,6,4,8,7,3,2] => [1,8,7,4,2,3,6,5] => 0010111
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,5,4,6,8,7,3,2] => [1,8,7,3,2,4,6,5] => 0100111
[[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,4,5,6,8,7,3,2] => [1,8,7,2,3,4,6,5] => 0000111
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => [1,8,7,5,4,3,2,6] => 0111011
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,6,5,7,4,8,3,2] => [1,8,7,5,3,2,4,6] => 0101011
[[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [1,5,6,7,4,8,3,2] => [1,8,7,5,2,3,4,6] => 0001011
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,4,7,6,5,8,3,2] => [1,8,7,2,5,4,3,6] => 0011011
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,4,6,7,5,8,3,2] => [1,8,7,2,5,3,4,6] => 0001011
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,5,4,7,6,8,3,2] => [1,8,7,3,2,5,4,6] => 0101011
[[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,4,5,7,6,8,3,2] => [1,8,7,2,3,5,4,6] => 0001011
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,6,5,4,7,8,3,2] => [1,8,7,4,3,2,5,6] => 0110011
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,5,6,4,7,8,3,2] => [1,8,7,4,2,3,5,6] => 0010011
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,5,4,6,7,8,3,2] => [1,8,7,3,2,4,5,6] => 0100011
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,4,5,6,7,8,3,2] => [1,8,7,2,3,4,5,6] => 0000011
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => [1,8,2,7,6,5,4,3] => 0011111
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,3,6,8,7,5,4,2] => [1,8,2,7,6,3,5,4] => 0001111
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,3,7,6,8,5,4,2] => [1,8,2,7,6,4,3,5] => 0010111
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,3,6,7,8,5,4,2] => [1,8,2,7,6,3,4,5] => 0000111
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,3,5,8,7,6,4,2] => [1,8,2,7,3,6,5,4] => 0001111
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => [1,8,2,7,3,6,4,5] => 0000111
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,3,6,5,8,7,4,2] => [1,8,2,7,4,3,6,5] => 0010111
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,3,5,6,8,7,4,2] => [1,8,2,7,3,4,6,5] => 0000111
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,3,7,6,5,8,4,2] => [1,8,2,7,5,4,3,6] => 0011011
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,3,6,7,5,8,4,2] => [1,8,2,7,5,3,4,6] => 0001011
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,3,5,7,6,8,4,2] => [1,8,2,7,3,5,4,6] => 0001011
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => [1,8,2,7,4,3,5,6] => 0010011
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => [1,8,2,7,3,4,5,6] => 0000011
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => [1,8,3,2,7,6,5,4] => 0101111
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => [1,8,3,2,7,6,4,5] => 0100111
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,4,3,7,6,8,5,2] => [1,8,3,2,7,5,4,6] => 0101011
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => [1,8,2,3,7,6,5,4] => 0001111
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,3,4,7,8,6,5,2] => [1,8,2,3,7,6,4,5] => 0000111
[[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,3,4,7,6,8,5,2] => [1,8,2,3,7,5,4,6] => 0001011
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,5,4,3,8,7,6,2] => [1,8,4,3,2,7,6,5] => 0110111
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,5,4,3,7,8,6,2] => [1,8,4,3,2,7,5,6] => 0110011
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,4,5,3,8,7,6,2] => [1,8,4,2,3,7,6,5] => 0010111
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,4,5,3,7,8,6,2] => [1,8,4,2,3,7,5,6] => 0010011
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,3,5,4,8,7,6,2] => [1,8,2,4,3,7,6,5] => 0010111
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,3,5,4,7,8,6,2] => [1,8,2,4,3,7,5,6] => 0010011
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,4,3,5,7,8,6,2] => [1,8,3,2,4,7,5,6] => 0100011
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,3,4,5,8,7,6,2] => [1,8,2,3,4,7,6,5] => 0000111
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => [1,8,2,3,4,7,5,6] => 0000011
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => [1,8,5,4,3,2,7,6] => 0111011
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => [1,8,5,4,2,3,7,6] => 0011011
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,5,4,6,3,8,7,2] => [1,8,5,3,2,4,7,6] => 0101011
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,4,5,6,3,8,7,2] => [1,8,5,2,3,4,7,6] => 0001011
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,3,5,6,4,8,7,2] => [1,8,2,5,3,4,7,6] => 0001011
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => [1,8,3,2,5,4,7,6] => 0101011
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,5,4,3,6,8,7,2] => [1,8,4,3,2,5,7,6] => 0110011
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,4,5,3,6,8,7,2] => [1,8,4,2,3,5,7,6] => 0010011
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,4,3,5,6,8,7,2] => [1,8,3,2,4,5,7,6] => 0100011
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => [1,8,2,3,4,5,7,6] => 0000011
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => [1,8,6,5,4,3,2,7] => 0111101
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,6,7,5,4,3,8,2] => [1,8,6,5,4,2,3,7] => 0011101
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,6,5,7,4,3,8,2] => [1,8,6,5,3,2,4,7] => 0101101
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => [1,8,6,2,5,3,4,7] => 0001101
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,5,4,7,6,3,8,2] => [1,8,6,3,2,5,4,7] => 0101101
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => [1,8,6,4,2,3,5,7] => 0010101
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,4,6,5,7,3,8,2] => [1,8,6,2,4,3,5,7] => 0010101
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => [1,8,6,3,2,4,5,7] => 0100101
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => [1,8,6,2,3,4,5,7] => 0000101
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,3,6,7,5,4,8,2] => [1,8,2,6,5,3,4,7] => 0001101
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,3,5,7,6,4,8,2] => [1,8,2,6,3,5,4,7] => 0001101
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,3,6,5,7,4,8,2] => [1,8,2,6,4,3,5,7] => 0010101
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,3,5,6,7,4,8,2] => [1,8,2,6,3,4,5,7] => 0000101
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,4,3,6,7,5,8,2] => [1,8,3,2,6,4,5,7] => 0100101
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,3,4,7,6,5,8,2] => [1,8,2,3,6,5,4,7] => 0001101
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,3,4,6,7,5,8,2] => [1,8,2,3,6,4,5,7] => 0000101
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,3,5,4,7,6,8,2] => [1,8,2,4,3,6,5,7] => 0010101
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,3,4,5,7,6,8,2] => [1,8,2,3,4,6,5,7] => 0000101
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,6,5,4,3,7,8,2] => [1,8,5,4,3,2,6,7] => 0111001
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,5,6,4,3,7,8,2] => [1,8,5,4,2,3,6,7] => 0011001
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,5,4,6,3,7,8,2] => [1,8,5,3,2,4,6,7] => 0101001
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,3,5,6,4,7,8,2] => [1,8,2,5,3,4,6,7] => 0001001
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,4,3,6,5,7,8,2] => [1,8,3,2,5,4,6,7] => 0101001
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,3,4,6,5,7,8,2] => [1,8,2,3,5,4,6,7] => 0001001
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,5,4,3,6,7,8,2] => [1,8,4,3,2,5,6,7] => 0110001
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => [1,8,4,2,3,5,6,7] => 0010001
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,3,5,4,6,7,8,2] => [1,8,2,4,3,5,6,7] => 0010001
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => [1,8,3,2,4,5,6,7] => 0100001
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => 0000001
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1011111
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [2,1,7,8,6,5,4,3] => [2,1,8,7,6,5,3,4] => 1001111
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [2,1,6,8,7,5,4,3] => [2,1,8,7,6,3,5,4] => 1001111
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => [2,1,8,7,6,4,3,5] => 1010111
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [2,1,8,7,6,3,4,5] => 1000111
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [2,1,5,8,7,6,4,3] => [2,1,8,7,3,6,5,4] => 1001111
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => [2,1,8,7,3,6,4,5] => 1000111
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [2,1,6,5,8,7,4,3] => [2,1,8,7,4,3,6,5] => 1010111
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [2,1,5,6,8,7,4,3] => [2,1,8,7,3,4,6,5] => 1000111
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [2,1,7,6,5,8,4,3] => [2,1,8,7,5,4,3,6] => 1011011
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => [2,1,8,7,5,3,4,6] => 1001011
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [2,1,5,7,6,8,4,3] => [2,1,8,7,3,5,4,6] => 1001011
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => [2,1,8,7,4,3,5,6] => 1010011
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => [2,1,8,7,3,4,5,6] => 1000011
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => [2,1,8,3,7,6,5,4] => 1001111
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [2,1,4,7,8,6,5,3] => [2,1,8,3,7,6,4,5] => 1000111
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => [2,1,8,3,7,4,6,5] => 1000111
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [2,1,4,7,6,8,5,3] => [2,1,8,3,7,5,4,6] => 1001011
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [2,1,4,6,7,8,5,3] => [2,1,8,3,7,4,5,6] => 1000011
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [2,1,5,4,8,7,6,3] => [2,1,8,4,3,7,6,5] => 1010111
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [2,1,5,4,7,8,6,3] => [2,1,8,4,3,7,5,6] => 1010011
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => [2,1,8,3,4,7,6,5] => 1000111
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [2,1,4,5,7,8,6,3] => [2,1,8,3,4,7,5,6] => 1000011
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [2,1,6,5,4,8,7,3] => [2,1,8,5,4,3,7,6] => 1011011
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [2,1,5,6,4,8,7,3] => [2,1,8,5,3,4,7,6] => 1001011
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => [2,1,8,3,5,4,7,6] => 1001011
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [2,1,5,4,6,8,7,3] => [2,1,8,4,3,5,7,6] => 1010011
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [2,1,7,6,5,4,8,3] => [2,1,8,6,5,4,3,7] => 1011101
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [2,1,5,7,6,4,8,3] => [2,1,8,6,3,5,4,7] => 1001101
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => [2,1,8,6,4,3,5,7] => 1010101
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [2,1,4,6,7,5,8,3] => [2,1,8,3,6,4,5,7] => 1000101
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => [2,1,8,4,3,6,5,7] => 1010101
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [2,1,6,5,4,7,8,3] => [2,1,8,5,4,3,6,7] => 1011001
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [2,1,5,6,4,7,8,3] => [2,1,8,5,3,4,6,7] => 1001001
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => [2,1,8,3,4,5,6,7] => 1000001
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => [1,2,8,7,6,5,4,3] => 0011111
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => [1,2,8,7,6,5,3,4] => 0001111
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,2,6,8,7,5,4,3] => [1,2,8,7,6,3,5,4] => 0001111
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,2,7,6,8,5,4,3] => [1,2,8,7,6,4,3,5] => 0010111
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => [1,2,8,7,6,3,4,5] => 0000111
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,2,5,8,7,6,4,3] => [1,2,8,7,3,6,5,4] => 0001111
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,2,6,5,8,7,4,3] => [1,2,8,7,4,3,6,5] => 0010111
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,2,5,6,8,7,4,3] => [1,2,8,7,3,4,6,5] => 0000111
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => [1,2,8,7,5,4,3,6] => 0011011
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,2,5,7,6,8,4,3] => [1,2,8,7,3,5,4,6] => 0001011
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,2,5,6,7,8,4,3] => [1,2,8,7,3,4,5,6] => 0000011
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => [1,2,8,3,7,6,5,4] => 0001111
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,2,4,7,8,6,5,3] => [1,2,8,3,7,6,4,5] => 0000111
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,2,4,6,8,7,5,3] => [1,2,8,3,7,4,6,5] => 0000111
[[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,2,4,7,6,8,5,3] => [1,2,8,3,7,5,4,6] => 0001011
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => [1,2,8,3,7,4,5,6] => 0000011
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,2,5,4,8,7,6,3] => [1,2,8,4,3,7,6,5] => 0010111
[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,2,5,4,7,8,6,3] => [1,2,8,4,3,7,5,6] => 0010011
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,2,4,5,8,7,6,3] => [1,2,8,3,4,7,6,5] => 0000111
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,2,4,6,5,8,7,3] => [1,2,8,3,5,4,7,6] => 0001011
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,2,5,4,6,8,7,3] => [1,2,8,4,3,5,7,6] => 0010011
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,2,4,5,6,8,7,3] => [1,2,8,3,4,5,7,6] => 0000011
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,2,7,6,5,4,8,3] => [1,2,8,6,5,4,3,7] => 0011101
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,2,6,5,7,4,8,3] => [1,2,8,6,4,3,5,7] => 0010101
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => [1,2,8,6,3,4,5,7] => 0000101
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,2,4,7,6,5,8,3] => [1,2,8,3,6,5,4,7] => 0001101
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,2,4,6,7,5,8,3] => [1,2,8,3,6,4,5,7] => 0000101
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,2,5,4,7,6,8,3] => [1,2,8,4,3,6,5,7] => 0010101
[[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,2,4,5,7,6,8,3] => [1,2,8,3,4,6,5,7] => 0000101
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,2,6,5,4,7,8,3] => [1,2,8,5,4,3,6,7] => 0011001
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,2,5,6,4,7,8,3] => [1,2,8,5,3,4,6,7] => 0001001
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,2,4,6,5,7,8,3] => [1,2,8,3,5,4,6,7] => 0001001
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => [1,2,8,4,3,5,6,7] => 0010001
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => [1,2,8,3,4,5,6,7] => 0000001
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 1101111
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [3,2,1,7,8,6,5,4] => [3,2,1,8,7,6,4,5] => 1100111
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [3,2,1,6,8,7,5,4] => [3,2,1,8,7,4,6,5] => 1100111
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [3,2,1,7,6,8,5,4] => [3,2,1,8,7,5,4,6] => 1101011
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => [3,2,1,8,7,4,5,6] => 1100011
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => [3,2,1,8,4,7,6,5] => 1100111
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => [3,2,1,8,4,7,5,6] => 1100011
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => [3,2,1,8,5,4,7,6] => 1101011
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => [3,2,1,8,4,5,7,6] => 1100011
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => [3,2,1,8,6,5,4,7] => 1101101
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => [3,2,1,8,6,4,5,7] => 1100101
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [3,2,1,5,7,6,8,4] => [3,2,1,8,4,6,5,7] => 1100101
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [3,2,1,6,5,7,8,4] => [3,2,1,8,5,4,6,7] => 1101001
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => [3,2,1,8,4,5,6,7] => 1100001
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => [3,1,2,8,7,6,5,4] => 0101111
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [2,3,1,7,8,6,5,4] => [3,1,2,8,7,6,4,5] => 0100111
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [2,3,1,6,8,7,5,4] => [3,1,2,8,7,4,6,5] => 0100111
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [2,3,1,7,6,8,5,4] => [3,1,2,8,7,5,4,6] => 0101011
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [2,3,1,6,7,8,5,4] => [3,1,2,8,7,4,5,6] => 0100011
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [2,3,1,5,7,8,6,4] => [3,1,2,8,4,7,5,6] => 0100011
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [2,3,1,6,5,8,7,4] => [3,1,2,8,5,4,7,6] => 0101011
[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [2,3,1,5,6,8,7,4] => [3,1,2,8,4,5,7,6] => 0100011
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [2,3,1,7,6,5,8,4] => [3,1,2,8,6,5,4,7] => 0101101
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [2,3,1,6,7,5,8,4] => [3,1,2,8,6,4,5,7] => 0100101
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [2,3,1,5,6,7,8,4] => [3,1,2,8,4,5,6,7] => 0100001
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => [1,3,2,8,7,6,5,4] => 0101111
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,3,2,7,8,6,5,4] => [1,3,2,8,7,6,4,5] => 0100111
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => [1,3,2,8,7,4,6,5] => 0100111
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,3,2,7,6,8,5,4] => [1,3,2,8,7,5,4,6] => 0101011
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,3,2,6,7,8,5,4] => [1,3,2,8,7,4,5,6] => 0100011
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,3,2,5,7,8,6,4] => [1,3,2,8,4,7,5,6] => 0100011
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,3,2,6,5,8,7,4] => [1,3,2,8,5,4,7,6] => 0101011
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,3,2,5,6,8,7,4] => [1,3,2,8,4,5,7,6] => 0100011
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,3,2,7,6,5,8,4] => [1,3,2,8,6,5,4,7] => 0101101
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,3,2,6,7,5,8,4] => [1,3,2,8,6,4,5,7] => 0100101
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,3,2,5,7,6,8,4] => [1,3,2,8,4,6,5,7] => 0100101
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,3,2,6,5,7,8,4] => [1,3,2,8,5,4,6,7] => 0101001
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,3,2,5,6,7,8,4] => [1,3,2,8,4,5,6,7] => 0100001
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => [2,1,3,8,7,6,5,4] => 1001111
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [2,1,3,7,8,6,5,4] => [2,1,3,8,7,6,4,5] => 1000111
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [2,1,3,6,8,7,5,4] => [2,1,3,8,7,4,6,5] => 1000111
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [2,1,3,7,6,8,5,4] => [2,1,3,8,7,5,4,6] => 1001011
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [2,1,3,6,7,8,5,4] => [2,1,3,8,7,4,5,6] => 1000011
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [2,1,3,5,8,7,6,4] => [2,1,3,8,4,7,6,5] => 1000111
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [2,1,3,5,7,8,6,4] => [2,1,3,8,4,7,5,6] => 1000011
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [2,1,3,6,5,8,7,4] => [2,1,3,8,5,4,7,6] => 1001011
[[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [2,1,3,5,6,8,7,4] => [2,1,3,8,4,5,7,6] => 1000011
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [2,1,3,7,6,5,8,4] => [2,1,3,8,6,5,4,7] => 1001101
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [2,1,3,6,7,5,8,4] => [2,1,3,8,6,4,5,7] => 1000101
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [2,1,3,5,7,6,8,4] => [2,1,3,8,4,6,5,7] => 1000101
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [2,1,3,6,5,7,8,4] => [2,1,3,8,5,4,6,7] => 1001001
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [2,1,3,5,6,7,8,4] => [2,1,3,8,4,5,6,7] => 1000001
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => [1,2,3,8,7,6,5,4] => 0001111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => [1,2,3,8,7,6,4,5] => 0000111
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => [1,2,3,8,7,4,6,5] => 0000111
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => [1,2,3,8,7,5,4,6] => 0001011
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => [1,2,3,8,7,4,5,6] => 0000011
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => [1,2,3,8,4,7,6,5] => 0000111
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => [1,2,3,8,4,7,5,6] => 0000011
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => [1,2,3,8,5,4,7,6] => 0001011
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => [1,2,3,8,4,5,7,6] => 0000011
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => [1,2,3,8,6,5,4,7] => 0001101
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => [1,2,3,8,6,4,5,7] => 0000101
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => [1,2,3,8,4,6,5,7] => 0000101
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => [1,2,3,8,5,4,6,7] => 0001001
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => 0000001
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 1110111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => [4,3,2,1,8,7,5,6] => 1110011
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => [4,3,2,1,8,5,7,6] => 1110011
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => [4,3,2,1,8,6,5,7] => 1110101
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => [4,3,2,1,8,5,6,7] => 1110001
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => [4,3,1,2,8,7,6,5] => 0110111
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => [4,3,1,2,8,7,5,6] => 0110011
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => [4,3,1,2,8,5,7,6] => 0110011
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => [4,3,1,2,8,6,5,7] => 0110101
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [3,4,2,1,6,7,8,5] => [4,3,1,2,8,5,6,7] => 0110001
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => [4,1,3,2,8,7,6,5] => 0110111
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [2,4,3,1,7,8,6,5] => [4,1,3,2,8,7,5,6] => 0110011
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => [4,1,3,2,8,5,7,6] => 0110011
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => [4,1,3,2,8,6,5,7] => 0110101
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [2,4,3,1,6,7,8,5] => [4,1,3,2,8,5,6,7] => 0110001
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => [4,2,1,3,8,7,6,5] => 1010111
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => [4,2,1,3,8,7,5,6] => 1010011
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => [4,2,1,3,8,5,7,6] => 1010011
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => [4,2,1,3,8,6,5,7] => 1010101
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [3,2,4,1,6,7,8,5] => [4,2,1,3,8,5,6,7] => 1010001
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => [4,1,2,3,8,7,6,5] => 0010111
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [2,3,4,1,7,8,6,5] => [4,1,2,3,8,7,5,6] => 0010011
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [2,3,4,1,6,8,7,5] => [4,1,2,3,8,5,7,6] => 0010011
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => [4,1,2,3,8,6,5,7] => 0010101
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => [4,1,2,3,8,5,6,7] => 0010001
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => [1,4,3,2,8,7,6,5] => 0110111
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => [1,4,3,2,8,6,5,7] => 0110101
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => [1,4,3,2,8,5,6,7] => 0110001
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => [1,4,2,3,8,7,6,5] => 0010111
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,3,4,2,7,8,6,5] => [1,4,2,3,8,7,5,6] => 0010011
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,3,4,2,6,8,7,5] => [1,4,2,3,8,5,7,6] => 0010011
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => [1,4,2,3,8,6,5,7] => 0010101
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,3,4,2,6,7,8,5] => [1,4,2,3,8,5,6,7] => 0010001
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 1010111
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [2,1,4,3,8,7,5,6] => 1010011
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => [2,1,4,3,8,5,7,6] => 1010011
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,6,5,7] => 1010101
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,5,6,7] => 1010001
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => [1,2,4,3,8,7,6,5] => 0010111
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,2,4,3,7,8,6,5] => [1,2,4,3,8,7,5,6] => 0010011
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => [1,2,4,3,8,5,7,6] => 0010011
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => [1,2,4,3,8,6,5,7] => 0010101
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,5,6,7] => 0010001
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => [3,2,1,4,8,7,6,5] => 1100111
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [3,2,1,4,7,8,6,5] => [3,2,1,4,8,7,5,6] => 1100011
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [3,2,1,4,6,8,7,5] => [3,2,1,4,8,5,7,6] => 1100011
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [3,2,1,4,7,6,8,5] => [3,2,1,4,8,6,5,7] => 1100101
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [3,2,1,4,6,7,8,5] => [3,2,1,4,8,5,6,7] => 1100001
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => [3,1,2,4,8,7,6,5] => 0100111
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [2,3,1,4,7,8,6,5] => [3,1,2,4,8,7,5,6] => 0100011
[[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [2,3,1,4,6,8,7,5] => [3,1,2,4,8,5,7,6] => 0100011
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => [3,1,2,4,8,6,5,7] => 0100101
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [2,3,1,4,6,7,8,5] => [3,1,2,4,8,5,6,7] => 0100001
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => [1,3,2,4,8,7,6,5] => 0100111
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,3,2,4,6,8,7,5] => [1,3,2,4,8,5,7,6] => 0100011
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => [1,3,2,4,8,6,5,7] => 0100101
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,5,6,7] => 0100001
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => [2,1,3,4,8,7,6,5] => 1000111
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [2,1,3,4,7,8,6,5] => [2,1,3,4,8,7,5,6] => 1000011
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [2,1,3,4,6,8,7,5] => [2,1,3,4,8,5,7,6] => 1000011
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,6,5,7] => 1000101
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,5,6,7] => 1000001
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => [1,2,3,4,8,7,6,5] => 0000111
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => [1,2,3,4,8,7,5,6] => 0000011
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => [1,2,3,4,8,5,7,6] => 0000011
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,6,5,7] => 0000101
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,5,6,7] => 0000001
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 1111011
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => [5,4,3,2,1,8,6,7] => 1111001
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [4,5,3,2,1,8,7,6] => [5,4,3,1,2,8,7,6] => 0111011
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [4,5,3,2,1,7,8,6] => [5,4,3,1,2,8,6,7] => 0111001
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [3,5,4,2,1,8,7,6] => [5,4,1,3,2,8,7,6] => 0111011
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [3,5,4,2,1,7,8,6] => [5,4,1,3,2,8,6,7] => 0111001
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [4,3,5,2,1,8,7,6] => [5,4,2,1,3,8,7,6] => 1011011
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [3,4,5,2,1,8,7,6] => [5,4,1,2,3,8,7,6] => 0011011
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [3,4,5,2,1,7,8,6] => [5,4,1,2,3,8,6,7] => 0011001
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [2,5,4,3,1,8,7,6] => [5,1,4,3,2,8,7,6] => 0111011
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [2,4,5,3,1,8,7,6] => [5,1,4,2,3,8,7,6] => 0011011
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [2,4,5,3,1,7,8,6] => [5,1,4,2,3,8,6,7] => 0011001
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => [5,2,1,4,3,8,7,6] => 1011011
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [3,2,5,4,1,7,8,6] => [5,2,1,4,3,8,6,7] => 1011001
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [2,3,5,4,1,8,7,6] => [5,1,2,4,3,8,7,6] => 0011011
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => [5,3,2,1,4,8,7,6] => 1101011
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [4,3,2,5,1,7,8,6] => [5,3,2,1,4,8,6,7] => 1101001
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => [5,3,1,2,4,8,7,6] => 0101011
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [3,4,2,5,1,7,8,6] => [5,3,1,2,4,8,6,7] => 0101001
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [2,4,3,5,1,8,7,6] => [5,1,3,2,4,8,7,6] => 0101011
[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [2,4,3,5,1,7,8,6] => [5,1,3,2,4,8,6,7] => 0101001
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [3,2,4,5,1,8,7,6] => [5,2,1,3,4,8,7,6] => 1001011
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [2,3,4,5,1,8,7,6] => [5,1,2,3,4,8,7,6] => 0001011
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => [5,1,2,3,4,8,6,7] => 0001001
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => [1,5,4,3,2,8,7,6] => 0111011
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,4,5,3,2,8,7,6] => [1,5,4,2,3,8,7,6] => 0011011
[[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,4,5,3,2,7,8,6] => [1,5,4,2,3,8,6,7] => 0011001
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,3,5,4,2,8,7,6] => [1,5,2,4,3,8,7,6] => 0011011
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,3,5,4,2,7,8,6] => [1,5,2,4,3,8,6,7] => 0011001
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,4,3,5,2,8,7,6] => [1,5,3,2,4,8,7,6] => 0101011
[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,4,3,5,2,7,8,6] => [1,5,3,2,4,8,6,7] => 0101001
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,3,4,5,2,8,7,6] => [1,5,2,3,4,8,7,6] => 0001011
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,3,4,5,2,7,8,6] => [1,5,2,3,4,8,6,7] => 0001001
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [2,1,5,4,3,8,7,6] => [2,1,5,4,3,8,7,6] => 1011011
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => [1,2,5,4,3,8,7,6] => 0011011
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,2,5,4,3,7,8,6] => [1,2,5,4,3,8,6,7] => 0011001
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => [1,2,5,3,4,8,7,6] => 0001011
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,2,4,5,3,7,8,6] => [1,2,5,3,4,8,6,7] => 0001001
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,8,7,6] => 0101011
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,6,7] => 0101001
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [2,1,3,5,4,8,7,6] => [2,1,3,5,4,8,7,6] => 1001011
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => [1,2,3,5,4,8,7,6] => 0001011
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,6,7] => 0001001
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => [4,3,2,1,5,8,7,6] => 1110011
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => [4,3,2,1,5,8,6,7] => 1110001
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [3,4,2,1,5,8,7,6] => [4,3,1,2,5,8,7,6] => 0110011
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => [4,2,1,3,5,8,7,6] => 1010011
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => [4,2,1,3,5,8,6,7] => 1010001
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [2,3,4,1,5,8,7,6] => [4,1,2,3,5,8,7,6] => 0010011
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [2,3,4,1,5,7,8,6] => [4,1,2,3,5,8,6,7] => 0010001
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => [1,4,3,2,5,8,7,6] => 0110011
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,4,3,2,5,7,8,6] => [1,4,3,2,5,8,6,7] => 0110001
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,3,4,2,5,8,7,6] => [1,4,2,3,5,8,7,6] => 0010011
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,3,4,2,5,7,8,6] => [1,4,2,3,5,8,6,7] => 0010001
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [2,1,4,3,5,8,7,6] => [2,1,4,3,5,8,7,6] => 1010011
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,6,7] => 1010001
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,2,4,3,5,8,7,6] => [1,2,4,3,5,8,7,6] => 0010011
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,6,7] => 0010001
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6] => 1100011
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [3,2,1,4,5,7,8,6] => [3,2,1,4,5,8,6,7] => 1100001
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => [3,1,2,4,5,8,6,7] => 0100001
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,3,2,4,5,8,7,6] => [1,3,2,4,5,8,7,6] => 0100011
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,6,7] => 0100001
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [2,1,3,4,5,8,7,6] => [2,1,3,4,5,8,7,6] => 1000011
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,6,7] => 1000001
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,8,7,6] => 0000011
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => 0000001
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1111101
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [5,6,4,3,2,1,8,7] => [6,5,4,3,1,2,8,7] => 0111101
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [4,6,5,3,2,1,8,7] => [6,5,4,1,3,2,8,7] => 0111101
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [5,4,6,3,2,1,8,7] => [6,5,4,2,1,3,8,7] => 1011101
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => [6,5,4,1,2,3,8,7] => 0011101
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [3,6,5,4,2,1,8,7] => [6,5,1,4,3,2,8,7] => 0111101
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => [6,5,1,4,2,3,8,7] => 0011101
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [4,3,6,5,2,1,8,7] => [6,5,2,1,4,3,8,7] => 1011101
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [3,4,6,5,2,1,8,7] => [6,5,1,2,4,3,8,7] => 0011101
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [5,4,3,6,2,1,8,7] => [6,5,3,2,1,4,8,7] => 1101101
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [4,5,3,6,2,1,8,7] => [6,5,3,1,2,4,8,7] => 0101101
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [4,3,5,6,2,1,8,7] => [6,5,2,1,3,4,8,7] => 1001101
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [3,4,5,6,2,1,8,7] => [6,5,1,2,3,4,8,7] => 0001101
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [2,6,5,4,3,1,8,7] => [6,1,5,4,3,2,8,7] => 0111101
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [2,5,6,4,3,1,8,7] => [6,1,5,4,2,3,8,7] => 0011101
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [2,4,6,5,3,1,8,7] => [6,1,5,2,4,3,8,7] => 0011101
[[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [2,4,5,6,3,1,8,7] => [6,1,5,2,3,4,8,7] => 0001101
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [3,2,6,5,4,1,8,7] => [6,2,1,5,4,3,8,7] => 1011101
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [3,2,5,6,4,1,8,7] => [6,2,1,5,3,4,8,7] => 1001101
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [2,3,6,5,4,1,8,7] => [6,1,2,5,4,3,8,7] => 0011101
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [4,3,2,6,5,1,8,7] => [6,3,2,1,5,4,8,7] => 1101101
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [3,4,2,6,5,1,8,7] => [6,3,1,2,5,4,8,7] => 0101101
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => [6,1,3,2,5,4,8,7] => 0101101
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [5,4,3,2,6,1,8,7] => [6,4,3,2,1,5,8,7] => 1110101
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [4,5,3,2,6,1,8,7] => [6,4,3,1,2,5,8,7] => 0110101
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [3,5,4,2,6,1,8,7] => [6,4,1,3,2,5,8,7] => 0110101
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [6,4,2,1,3,5,8,7] => 1010101
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [2,4,5,3,6,1,8,7] => [6,1,4,2,3,5,8,7] => 0010101
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [6,2,1,4,3,5,8,7] => 1010101
[[.,[[[[.,.],.],[.,.]],.]],[.,.]] => [2,3,5,4,6,1,8,7] => [6,1,2,4,3,5,8,7] => 0010101
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [4,3,2,5,6,1,8,7] => [6,3,2,1,4,5,8,7] => 1100101
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [3,4,2,5,6,1,8,7] => [6,3,1,2,4,5,8,7] => 0100101
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [2,4,3,5,6,1,8,7] => [6,1,3,2,4,5,8,7] => 0100101
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => [6,1,2,3,4,5,8,7] => 0000101
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => [1,6,5,4,3,2,8,7] => 0111101
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => [1,6,5,4,2,3,8,7] => 0011101
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,5,4,6,3,2,8,7] => [1,6,5,3,2,4,8,7] => 0101101
[[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,4,5,6,3,2,8,7] => [1,6,5,2,3,4,8,7] => 0001101
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,3,5,6,4,2,8,7] => [1,6,2,5,3,4,8,7] => 0001101
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,4,5,3,6,2,8,7] => [1,6,4,2,3,5,8,7] => 0010101
[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,3,5,4,6,2,8,7] => [1,6,2,4,3,5,8,7] => 0010101
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,3,4,5,6,2,8,7] => [1,6,2,3,4,5,8,7] => 0000101
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => 1011101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [2,1,6,5,3,4,8,7] => 1001101
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => [2,1,6,3,5,4,8,7] => 1001101
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [2,1,6,4,3,5,8,7] => 1010101
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => [2,1,6,3,4,5,8,7] => 1000101
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,2,4,5,6,3,8,7] => [1,2,6,3,4,5,8,7] => 0000101
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [3,2,1,6,5,4,8,7] => [3,2,1,6,5,4,8,7] => 1101101
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [2,3,1,5,6,4,8,7] => [3,1,2,6,4,5,8,7] => 0100101
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,3,2,6,5,4,8,7] => [1,3,2,6,5,4,8,7] => 0101101
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [2,1,3,6,5,4,8,7] => [2,1,3,6,5,4,8,7] => 1001101
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [2,1,3,5,6,4,8,7] => [2,1,3,6,4,5,8,7] => 1000101
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,2,3,6,5,4,8,7] => [1,2,3,6,5,4,8,7] => 0001101
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,2,3,5,6,4,8,7] => [1,2,3,6,4,5,8,7] => 0000101
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 1110101
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => [4,3,1,2,6,5,8,7] => 0110101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => [4,1,3,2,6,5,8,7] => 0110101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [4,2,1,3,6,5,8,7] => 1010101
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => [4,1,2,3,6,5,8,7] => 0010101
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => [1,4,2,3,6,5,8,7] => 0010101
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => 0010101
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [2,3,1,4,6,5,8,7] => [3,1,2,4,6,5,8,7] => 0100101
[[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => 0100101
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => 1000101
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => 0000101
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => [5,4,3,2,1,6,8,7] => 1111001
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [2,5,4,3,1,6,8,7] => [5,1,4,3,2,6,8,7] => 0111001
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [3,2,5,4,1,6,8,7] => [5,2,1,4,3,6,8,7] => 1011001
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [2,3,5,4,1,6,8,7] => [5,1,2,4,3,6,8,7] => 0011001
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [4,3,2,5,1,6,8,7] => [5,3,2,1,4,6,8,7] => 1101001
[[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [3,4,2,5,1,6,8,7] => [5,3,1,2,4,6,8,7] => 0101001
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [2,4,3,5,1,6,8,7] => [5,1,3,2,4,6,8,7] => 0101001
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [2,3,4,5,1,6,8,7] => [5,1,2,3,4,6,8,7] => 0001001
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,4,5,3,2,6,8,7] => [1,5,4,2,3,6,8,7] => 0011001
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,3,5,4,2,6,8,7] => [1,5,2,4,3,6,8,7] => 0011001
[[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,4,3,5,2,6,8,7] => [1,5,3,2,4,6,8,7] => 0101001
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,3,4,5,2,6,8,7] => [1,5,2,3,4,6,8,7] => 0001001
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => [2,1,5,4,3,6,8,7] => 1011001
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => [2,1,5,3,4,6,8,7] => 1001001
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,2,5,4,3,6,8,7] => [1,2,5,4,3,6,8,7] => 0011001
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,2,4,5,3,6,8,7] => [1,2,5,3,4,6,8,7] => 0001001
[[[[.,[[.,.],.]],[.,.]],.],[.,.]] => [2,3,1,5,4,6,8,7] => [3,1,2,5,4,6,8,7] => 0101001
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => 1001001
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => 0001001
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => 1110001
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [3,4,2,1,5,6,8,7] => [4,3,1,2,5,6,8,7] => 0110001
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => [4,2,1,3,5,6,8,7] => 1010001
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [2,3,4,1,5,6,8,7] => [4,1,2,3,5,6,8,7] => 0010001
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,4,3,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => 0110001
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,3,4,2,5,6,8,7] => [1,4,2,3,5,6,8,7] => 0010001
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => 1010001
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => 0010001
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [3,2,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => 1100001
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [2,3,1,4,5,6,8,7] => [3,1,2,4,5,6,8,7] => 0100001
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => 0100001
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => 1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 0000001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 1111110
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [7,6,5,4,3,1,2,8] => 0111110
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => [7,6,5,4,1,3,2,8] => 0111110
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [7,6,5,4,2,1,3,8] => 1011110
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [7,6,5,4,1,2,3,8] => 0011110
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => [7,6,5,1,4,3,2,8] => 0111110
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [4,6,7,5,3,2,1,8] => [7,6,5,1,4,2,3,8] => 0011110
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [5,4,7,6,3,2,1,8] => [7,6,5,2,1,4,3,8] => 1011110
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [4,5,7,6,3,2,1,8] => [7,6,5,1,2,4,3,8] => 0011110
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [7,6,5,3,2,1,4,8] => 1101110
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [4,6,5,7,3,2,1,8] => [7,6,5,1,3,2,4,8] => 0101110
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => [7,6,5,2,1,3,4,8] => 1001110
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => [7,6,5,1,2,3,4,8] => 0001110
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [3,5,7,6,4,2,1,8] => [7,6,1,5,2,4,3,8] => 0011110
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [4,3,7,6,5,2,1,8] => [7,6,2,1,5,4,3,8] => 1011110
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => [7,6,1,2,5,4,3,8] => 0011110
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [5,4,3,7,6,2,1,8] => [7,6,3,2,1,5,4,8] => 1101110
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [4,5,3,7,6,2,1,8] => [7,6,3,1,2,5,4,8] => 0101110
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [3,4,5,7,6,2,1,8] => [7,6,1,2,3,5,4,8] => 0001110
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => [7,6,4,3,2,1,5,8] => 1110110
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => [7,6,4,3,1,2,5,8] => 0110110
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => [7,6,4,2,1,3,5,8] => 1010110
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [3,6,5,4,7,2,1,8] => [7,6,1,4,3,2,5,8] => 0110110
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [3,5,6,4,7,2,1,8] => [7,6,1,4,2,3,5,8] => 0010110
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => [7,6,3,2,1,4,5,8] => 1100110
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => [7,6,1,2,3,4,5,8] => 0000110
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => [7,1,6,5,4,3,2,8] => 0111110
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [2,6,7,5,4,3,1,8] => [7,1,6,5,4,2,3,8] => 0011110
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [2,5,7,6,4,3,1,8] => [7,1,6,5,2,4,3,8] => 0011110
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.] => [2,6,5,7,4,3,1,8] => [7,1,6,5,3,2,4,8] => 0101110
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [2,4,7,6,5,3,1,8] => [7,1,6,2,5,4,3,8] => 0011110
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => [7,1,6,2,5,3,4,8] => 0001110
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [2,5,4,7,6,3,1,8] => [7,1,6,3,2,5,4,8] => 0101110
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [2,5,6,4,7,3,1,8] => [7,1,6,4,2,3,5,8] => 0010110
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [2,4,5,6,7,3,1,8] => [7,1,6,2,3,4,5,8] => 0000110
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => [7,2,1,6,5,4,3,8] => 1011110
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [3,2,6,7,5,4,1,8] => [7,2,1,6,5,3,4,8] => 1001110
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [3,2,5,7,6,4,1,8] => [7,2,1,6,3,5,4,8] => 1001110
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [2,3,7,6,5,4,1,8] => [7,1,2,6,5,4,3,8] => 0011110
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [2,3,6,7,5,4,1,8] => [7,1,2,6,5,3,4,8] => 0001110
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [2,3,5,7,6,4,1,8] => [7,1,2,6,3,5,4,8] => 0001110
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [2,3,6,5,7,4,1,8] => [7,1,2,6,4,3,5,8] => 0010110
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [2,3,5,6,7,4,1,8] => [7,1,2,6,3,4,5,8] => 0000110
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [4,3,2,6,7,5,1,8] => [7,3,2,1,6,4,5,8] => 1100110
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [3,4,2,6,7,5,1,8] => [7,3,1,2,6,4,5,8] => 0100110
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [2,3,4,7,6,5,1,8] => [7,1,2,3,6,5,4,8] => 0001110
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [2,3,4,6,7,5,1,8] => [7,1,2,3,6,4,5,8] => 0000110
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => [7,4,3,2,1,6,5,8] => 1110110
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [4,5,3,2,7,6,1,8] => [7,4,3,1,2,6,5,8] => 0110110
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [3,5,4,2,7,6,1,8] => [7,4,1,3,2,6,5,8] => 0110110
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => [7,2,1,4,3,6,5,8] => 1010110
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [4,3,2,5,7,6,1,8] => [7,3,2,1,4,6,5,8] => 1100110
[[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [3,4,2,5,7,6,1,8] => [7,3,1,2,4,6,5,8] => 0100110
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => [7,1,2,3,4,6,5,8] => 0000110
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => [7,5,4,3,2,1,6,8] => 1111010
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => [4,6,5,3,2,7,1,8] => [7,5,4,1,3,2,6,8] => 0111010
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [3,5,6,4,2,7,1,8] => [7,5,1,4,2,3,6,8] => 0011010
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [3,4,6,5,2,7,1,8] => [7,5,1,2,4,3,6,8] => 0011010
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [7,5,3,2,1,4,6,8] => 1101010
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [7,5,3,1,2,4,6,8] => 0101010
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => [7,5,1,3,2,4,6,8] => 0101010
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [7,5,1,2,3,4,6,8] => 0001010
[[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [2,5,6,4,3,7,1,8] => [7,1,5,4,2,3,6,8] => 0011010
[[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [2,4,6,5,3,7,1,8] => [7,1,5,2,4,3,6,8] => 0011010
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [2,5,4,6,3,7,1,8] => [7,1,5,3,2,4,6,8] => 0101010
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [3,2,6,5,4,7,1,8] => [7,2,1,5,4,3,6,8] => 1011010
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [2,3,5,6,4,7,1,8] => [7,1,2,5,3,4,6,8] => 0001010
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [4,3,2,6,5,7,1,8] => [7,3,2,1,5,4,6,8] => 1101010
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [3,4,2,6,5,7,1,8] => [7,3,1,2,5,4,6,8] => 0101010
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [2,4,3,6,5,7,1,8] => [7,1,3,2,5,4,6,8] => 0101010
[[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [3,2,4,6,5,7,1,8] => [7,2,1,3,5,4,6,8] => 1001010
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => [7,1,2,3,5,4,6,8] => 0001010
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [7,4,3,2,1,5,6,8] => 1110010
[[.,[[[.,[.,[[.,.],.]]],.],.]],.] => [4,5,3,2,6,7,1,8] => [7,4,3,1,2,5,6,8] => 0110010
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [3,5,4,2,6,7,1,8] => [7,4,1,3,2,5,6,8] => 0110010
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => [7,4,1,2,3,5,6,8] => 0010010
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [2,5,4,3,6,7,1,8] => [7,1,4,3,2,5,6,8] => 0110010
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [2,4,5,3,6,7,1,8] => [7,1,4,2,3,5,6,8] => 0010010
[[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [3,2,5,4,6,7,1,8] => [7,2,1,4,3,5,6,8] => 1010010
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [2,3,5,4,6,7,1,8] => [7,1,2,4,3,5,6,8] => 0010010
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => [7,3,2,1,4,5,6,8] => 1100010
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => [7,3,1,2,4,5,6,8] => 0100010
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [2,4,3,5,6,7,1,8] => [7,1,3,2,4,5,6,8] => 0100010
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [7,2,1,3,4,5,6,8] => 1000010
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8] => 0000010
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => [1,7,6,5,4,3,2,8] => 0111110
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => [1,7,6,5,4,2,3,8] => 0011110
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,5,7,6,4,3,2,8] => [1,7,6,5,2,4,3,8] => 0011110
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,6,5,7,4,3,2,8] => [1,7,6,5,3,2,4,8] => 0101110
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,5,4,7,6,3,2,8] => [1,7,6,3,2,5,4,8] => 0101110
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,5,6,4,7,3,2,8] => [1,7,6,4,2,3,5,8] => 0010110
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,4,6,5,7,3,2,8] => [1,7,6,2,4,3,5,8] => 0010110
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,5,4,6,7,3,2,8] => [1,7,6,3,2,4,5,8] => 0100110
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => [1,7,6,2,3,4,5,8] => 0000110
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,3,7,6,5,4,2,8] => [1,7,2,6,5,4,3,8] => 0011110
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,3,5,7,6,4,2,8] => [1,7,2,6,3,5,4,8] => 0001110
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,3,6,5,7,4,2,8] => [1,7,2,6,4,3,5,8] => 0010110
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,3,5,6,7,4,2,8] => [1,7,2,6,3,4,5,8] => 0000110
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => [1,7,2,3,6,4,5,8] => 0000110
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,3,5,4,7,6,2,8] => [1,7,2,4,3,6,5,8] => 0010110
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,4,3,5,7,6,2,8] => [1,7,3,2,4,6,5,8] => 0100110
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,3,4,5,7,6,2,8] => [1,7,2,3,4,6,5,8] => 0000110
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,6,5,4,3,7,2,8] => [1,7,5,4,3,2,6,8] => 0111010
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,5,4,6,3,7,2,8] => [1,7,5,3,2,4,6,8] => 0101010
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,4,5,6,3,7,2,8] => [1,7,5,2,3,4,6,8] => 0001010
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,3,6,5,4,7,2,8] => [1,7,2,5,4,3,6,8] => 0011010
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => [1,7,2,5,3,4,6,8] => 0001010
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,4,3,6,5,7,2,8] => [1,7,3,2,5,4,6,8] => 0101010
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,3,4,6,5,7,2,8] => [1,7,2,3,5,4,6,8] => 0001010
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,5,4,3,6,7,2,8] => [1,7,4,3,2,5,6,8] => 0110010
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,4,5,3,6,7,2,8] => [1,7,4,2,3,5,6,8] => 0010010
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,3,5,4,6,7,2,8] => [1,7,2,4,3,5,6,8] => 0010010
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,4,3,5,6,7,2,8] => [1,7,3,2,4,5,6,8] => 0100010
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,3,4,5,6,7,2,8] => [1,7,2,3,4,5,6,8] => 0000010
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [2,1,7,6,5,4,3,8] => [2,1,7,6,5,4,3,8] => 1011110
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [2,1,6,7,5,4,3,8] => [2,1,7,6,5,3,4,8] => 1001110
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [2,1,5,6,7,4,3,8] => [2,1,7,6,3,4,5,8] => 1000110
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [2,1,4,6,7,5,3,8] => [2,1,7,3,6,4,5,8] => 1000110
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [2,1,4,5,6,7,3,8] => [2,1,7,3,4,5,6,8] => 1000010
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8] => [1,2,7,6,5,4,3,8] => 0011110
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,2,6,5,7,4,3,8] => [1,2,7,6,4,3,5,8] => 0010110
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,2,5,6,7,4,3,8] => [1,2,7,6,3,4,5,8] => 0000110
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,2,4,6,7,5,3,8] => [1,2,7,3,6,4,5,8] => 0000110
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,2,4,5,7,6,3,8] => [1,2,7,3,4,6,5,8] => 0000110
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,2,5,6,4,7,3,8] => [1,2,7,5,3,4,6,8] => 0001010
[[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,2,4,6,5,7,3,8] => [1,2,7,3,5,4,6,8] => 0001010
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,2,5,4,6,7,3,8] => [1,2,7,4,3,5,6,8] => 0010010
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,2,4,5,6,7,3,8] => [1,2,7,3,4,5,6,8] => 0000010
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => [3,2,1,7,6,5,4,8] => 1101110
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [3,2,1,6,7,5,4,8] => [3,2,1,7,6,4,5,8] => 1100110
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [3,2,1,5,7,6,4,8] => [3,2,1,7,4,6,5,8] => 1100110
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [3,2,1,6,5,7,4,8] => [3,2,1,7,5,4,6,8] => 1101010
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [3,2,1,5,6,7,4,8] => [3,2,1,7,4,5,6,8] => 1100010
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [2,3,1,6,7,5,4,8] => [3,1,2,7,6,4,5,8] => 0100110
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [2,3,1,6,5,7,4,8] => [3,1,2,7,5,4,6,8] => 0101010
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => [3,1,2,7,4,5,6,8] => 0100010
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,3,2,7,6,5,4,8] => [1,3,2,7,6,5,4,8] => 0101110
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,3,2,6,7,5,4,8] => [1,3,2,7,6,4,5,8] => 0100110
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,3,2,5,7,6,4,8] => [1,3,2,7,4,6,5,8] => 0100110
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,3,2,6,5,7,4,8] => [1,3,2,7,5,4,6,8] => 0101010
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,3,2,5,6,7,4,8] => [1,3,2,7,4,5,6,8] => 0100010
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => [1,2,3,7,6,5,4,8] => 0001110
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => [1,2,3,7,6,4,5,8] => 0000110
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,2,3,5,7,6,4,8] => [1,2,3,7,4,6,5,8] => 0000110
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,2,3,6,5,7,4,8] => [1,2,3,7,5,4,6,8] => 0001010
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => [1,2,3,7,4,5,6,8] => 0000010
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => [4,3,2,1,7,6,5,8] => 1110110
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => [4,3,2,1,7,5,6,8] => 1110010
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8] => [4,2,1,3,7,6,5,8] => 1010110
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => [4,2,1,3,7,5,6,8] => 1010010
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8] => [4,1,2,3,7,6,5,8] => 0010110
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [2,3,4,1,6,7,5,8] => [4,1,2,3,7,5,6,8] => 0010010
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => 0110110
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [1,4,2,3,7,5,6,8] => 0010010
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,2,4,3,6,7,5,8] => [1,2,4,3,7,5,6,8] => 0010010
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => [3,2,1,4,7,6,5,8] => 1100110
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => [3,1,2,4,7,5,6,8] => 0100010
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8] => [1,3,2,4,7,6,5,8] => 0100110
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [2,1,3,4,6,7,5,8] => [2,1,3,4,7,5,6,8] => 1000010
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => [1,2,3,4,7,6,5,8] => 0000110
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,5,6,8] => 0000010
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8] => [5,4,3,2,1,7,6,8] => 1111010
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [4,5,3,2,1,7,6,8] => [5,4,3,1,2,7,6,8] => 0111010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [3,2,5,4,1,7,6,8] => [5,2,1,4,3,7,6,8] => 1011010
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [2,3,5,4,1,7,6,8] => [5,1,2,4,3,7,6,8] => 0011010
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [4,3,2,5,1,7,6,8] => [5,3,2,1,4,7,6,8] => 1101010
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [3,4,2,5,1,7,6,8] => [5,3,1,2,4,7,6,8] => 0101010
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8] => [5,1,3,2,4,7,6,8] => 0101010
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => [1,5,4,3,2,7,6,8] => 0111010
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,4,5,3,2,7,6,8] => [1,5,4,2,3,7,6,8] => 0011010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => [1,5,2,4,3,7,6,8] => 0011010
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,4,3,5,2,7,6,8] => [1,5,3,2,4,7,6,8] => 0101010
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => [1,5,2,3,4,7,6,8] => 0001010
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [2,1,5,4,3,7,6,8] => [2,1,5,4,3,7,6,8] => 1011010
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,2,4,5,3,7,6,8] => [1,2,5,3,4,7,6,8] => 0001010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => 1101010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => [3,1,2,5,4,7,6,8] => 0101010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => 0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => 0001010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => 1110010
[[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [3,4,2,1,5,7,6,8] => [4,3,1,2,5,7,6,8] => 0110010
[[[[.,[[.,.],[.,.]]],.],[.,.]],.] => [2,4,3,1,5,7,6,8] => [4,1,3,2,5,7,6,8] => 0110010
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => [4,2,1,3,5,7,6,8] => 1010010
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [2,3,4,1,5,7,6,8] => [4,1,2,3,5,7,6,8] => 0010010
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => 0110010
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,3,4,2,5,7,6,8] => [1,4,2,3,5,7,6,8] => 0010010
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => 0010010
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [3,2,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => 1100010
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8] => [3,1,2,4,5,7,6,8] => 0100010
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => 0100010
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => 1000010
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 0000010
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 1111100
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => [6,5,4,3,1,2,7,8] => 0111100
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => [6,5,4,2,1,3,7,8] => 1011100
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => [6,5,4,1,2,3,7,8] => 0011100
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [3,6,5,4,2,1,7,8] => [6,5,1,4,3,2,7,8] => 0111100
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => [6,5,3,2,1,4,7,8] => 1101100
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [2,4,5,6,3,1,7,8] => [6,1,5,2,3,4,7,8] => 0001100
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [3,2,6,5,4,1,7,8] => [6,2,1,5,4,3,7,8] => 1011100
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [2,3,5,6,4,1,7,8] => [6,1,2,5,3,4,7,8] => 0001100
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [4,3,2,6,5,1,7,8] => [6,3,2,1,5,4,7,8] => 1101100
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => [6,1,2,3,5,4,7,8] => 0001100
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [6,4,3,2,1,5,7,8] => 1110100
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => [6,4,3,1,2,5,7,8] => 0110100
[[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [3,5,4,2,6,1,7,8] => [6,4,1,3,2,5,7,8] => 0110100
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [6,4,2,1,3,5,7,8] => 1010100
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => [6,4,1,2,3,5,7,8] => 0010100
[[[.,[[[.,.],[[.,.],.]],.]],.],.] => [2,4,5,3,6,1,7,8] => [6,1,4,2,3,5,7,8] => 0010100
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [3,2,5,4,6,1,7,8] => [6,2,1,4,3,5,7,8] => 1010100
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => [6,1,2,4,3,5,7,8] => 0010100
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => [6,3,2,1,4,5,7,8] => 1100100
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => [6,3,1,2,4,5,7,8] => 0100100
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => [6,2,1,3,4,5,7,8] => 1000100
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [6,1,2,3,4,5,7,8] => 0000100
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => [1,6,5,4,3,2,7,8] => 0111100
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,5,4,6,3,2,7,8] => [1,6,5,3,2,4,7,8] => 0101100
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => [1,6,2,5,3,4,7,8] => 0001100
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,4,3,6,5,2,7,8] => [1,6,3,2,5,4,7,8] => 0101100
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,5,4,3,6,2,7,8] => [1,6,4,3,2,5,7,8] => 0110100
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,4,5,3,6,2,7,8] => [1,6,4,2,3,5,7,8] => 0010100
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,3,5,4,6,2,7,8] => [1,6,2,4,3,5,7,8] => 0010100
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,4,3,5,6,2,7,8] => [1,6,3,2,4,5,7,8] => 0100100
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => [1,6,2,3,4,5,7,8] => 0000100
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [2,1,5,4,6,3,7,8] => [2,1,6,4,3,5,7,8] => 1010100
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => [1,2,6,5,4,3,7,8] => 0011100
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => [1,2,6,5,3,4,7,8] => 0001100
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,2,4,6,5,3,7,8] => [1,2,6,3,5,4,7,8] => 0001100
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,2,5,4,6,3,7,8] => [1,2,6,4,3,5,7,8] => 0010100
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => [1,2,6,3,4,5,7,8] => 0000100
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [3,2,1,6,5,4,7,8] => [3,2,1,6,5,4,7,8] => 1101100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [3,2,1,5,6,4,7,8] => [3,2,1,6,4,5,7,8] => 1100100
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => [1,3,2,6,5,4,7,8] => 0101100
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,3,2,5,6,4,7,8] => [1,3,2,6,4,5,7,8] => 0100100
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [2,1,3,5,6,4,7,8] => [2,1,3,6,4,5,7,8] => 1000100
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => [1,2,3,6,5,4,7,8] => 0001100
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,2,3,5,6,4,7,8] => [1,2,3,6,4,5,7,8] => 0000100
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => 1110100
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [3,4,2,1,6,5,7,8] => [4,3,1,2,6,5,7,8] => 0110100
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => [4,2,1,3,6,5,7,8] => 1010100
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [2,3,4,1,6,5,7,8] => [4,1,2,3,6,5,7,8] => 0010100
[[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,3,4,2,6,5,7,8] => [1,4,2,3,6,5,7,8] => 0010100
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => 1010100
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => 0010100
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => 0100100
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => 1000100
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => 0000100
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => 1111000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => [5,4,3,1,2,6,7,8] => 0111000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [3,5,4,2,1,6,7,8] => [5,4,1,3,2,6,7,8] => 0111000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => [5,4,2,1,3,6,7,8] => 1011000
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => [5,4,1,2,3,6,7,8] => 0011000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [2,5,4,3,1,6,7,8] => [5,1,4,3,2,6,7,8] => 0111000
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => [5,1,4,2,3,6,7,8] => 0011000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [3,2,5,4,1,6,7,8] => [5,2,1,4,3,6,7,8] => 1011000
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [2,3,5,4,1,6,7,8] => [5,1,2,4,3,6,7,8] => 0011000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => [5,3,2,1,4,6,7,8] => 1101000
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [5,3,1,2,4,6,7,8] => 0101000
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => [5,1,3,2,4,6,7,8] => 0101000
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => [5,2,1,3,4,6,7,8] => 1001000
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [5,1,2,3,4,6,7,8] => 0001000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => [1,5,4,3,2,6,7,8] => 0111000
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,4,5,3,2,6,7,8] => [1,5,4,2,3,6,7,8] => 0011000
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,3,5,4,2,6,7,8] => [1,5,2,4,3,6,7,8] => 0011000
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,4,3,5,2,6,7,8] => [1,5,3,2,4,6,7,8] => 0101000
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => [1,5,2,3,4,6,7,8] => 0001000
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8] => [2,1,5,4,3,6,7,8] => 1011000
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => [2,1,5,3,4,6,7,8] => 1001000
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => [1,2,5,4,3,6,7,8] => 0011000
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,2,4,5,3,6,7,8] => [1,2,5,3,4,6,7,8] => 0001000
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [3,2,1,5,4,6,7,8] => [3,2,1,5,4,6,7,8] => 1101000
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => 0101000
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => 1001000
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 0001000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 1110000
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => [4,3,1,2,5,6,7,8] => 0110000
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => [4,1,3,2,5,6,7,8] => 0110000
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [4,2,1,3,5,6,7,8] => 1010000
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => 0010000
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => 0110000
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => 0010000
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => 1010000
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => 0010000
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => 1100000
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => 0100000
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 0100000
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 1000000
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1,2] => 01111111
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [9,8,7,6,5,4,1,2,3] => 00111111
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => [9,8,7,6,5,1,2,3,4] => 00011111
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => [9,8,7,6,1,2,3,4,5] => 00001111
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => [9,8,7,1,2,3,4,5,6] => 00000111
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => [9,8,1,2,3,4,5,6,7] => 00000011
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => 00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,1,2] => 011111111
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [7,9,8,6,5,4,3,2,1] => [9,8,7,6,5,4,1,3,2] => 01111111
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,1,2,3] => 001111111
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => [10,9,8,7,6,5,1,2,3,4] => 000111111
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [10,9,8,7,6,1,2,3,4,5] => 000011111
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => [10,9,8,7,1,2,3,4,5,6] => 000001111
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [3,5,6,7,8,9,4,2,1] => [9,8,1,7,2,3,4,5,6] => 00000111
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => [10,9,8,1,2,3,4,5,6,7] => 000000111
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [2,4,5,6,7,8,9,3,1] => [9,1,8,2,3,4,5,6,7] => 00000011
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => [10,9,1,2,3,4,5,6,7,8] => 000000011
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8] => 00000001
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => 000000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [9,8,7,6,5,4,2,1,3] => 10111111
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [9,8,7,6,5,3,2,1,4] => 11011111
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [9,8,7,6,4,3,2,1,5] => 11101111
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [9,8,7,5,4,3,2,1,6] => 11110111
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [9,8,6,5,4,3,2,1,7] => 11111011
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [9,7,6,5,4,3,2,1,8] => 11111101
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 11111110
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,2,1,3] => 101111111
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [10,9,8,7,6,5,3,2,1,4] => 110111111
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [10,9,8,7,6,4,3,2,1,5] => 111011111
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [10,9,8,7,5,4,3,2,1,6] => 111101111
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [10,9,8,6,5,4,3,2,1,7] => 111110111
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [10,9,7,6,5,4,3,2,1,8] => 111111011
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,8,7,6,5,4,3,2,9] => [1,8,7,6,5,4,3,2,9] => 01111110
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [10,8,7,6,5,4,3,2,1,9] => 111111101
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => 111111110
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => [9,7,5,3,1,2,4,6,8,10] => 010101010
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,10,9,1] => [10,1,3,2,5,4,7,6,9,8] => 010101011
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,1,4,6,5,3,8,10,9,7] => [2,1,6,3,5,4,10,7,9,8] => 100110011
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,1,4,6,5,3,8,7,10,9] => [2,1,6,3,5,4,8,7,10,9] => 100110101
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => 101010101
[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,10,9,12,11,1] => [12,1,3,2,5,4,7,6,9,8,11,10] => 01010101011
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3,8,7,10,12,11,9] => [2,1,6,3,5,4,8,7,12,9,11,10] => 10011010011
[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,10,9,7,12,11] => [2,1,6,3,5,4,10,7,9,8,12,11] => 10011001101
[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [2,1,4,6,5,3,8,7,10,9,12,11] => [2,1,6,3,5,4,8,7,10,9,12,11] => 10011010101
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => 10101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 000000001
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => 10000001
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [9,2,1,3,4,5,6,7,8] => 10000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => 100000001
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => 01000001
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [2,3,1,4,5,6,7,9,8] => [3,1,2,4,5,6,7,9,8] => 01000001
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [2,4,3,5,6,7,8,9,1] => [9,1,3,2,4,5,6,7,8] => 01000001
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => [9,3,1,2,4,5,6,7,8] => 01000001
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => [10,2,1,3,4,5,6,7,8,9] => 100000001
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => 0000000001
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,7,8] => 00000001
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,6,7,8] => 00000001
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,5,6,7,8] => 00000001
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,4,5,6,7,8] => 00000001
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,3] => [1,2,9,3,4,5,6,7,8] => 00000001
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,9,8,7] => 00000011
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,8,9] => 000000001
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,9,7,6,8] => 00000101
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,7,8,9] => 000000001
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,4,7,6,8,9,5] => [1,2,3,4,9,6,5,7,8] => 00001001
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,6,7,8,9] => 000000001
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [1,2,3,6,5,7,8,9,4] => [1,2,3,9,5,4,6,7,8] => 00010001
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,5,6,7,8,9] => 000000001
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [1,2,5,4,6,7,8,9,3] => [1,2,9,4,3,5,6,7,8] => 00100001
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,4,5,6,7,8,9] => 000000001
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,4,3,5,6,7,8,9,2] => [1,9,3,2,4,5,6,7,8] => 01000001
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,3,4,5,6,7,8,9] => 000000001
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9] => 000000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 01111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => [8,7,6,5,4,3,1,2,9] => 01111110
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => [1,9,8,7,6,5,4,2,3] => 00111111
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 011111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,1,2,10] => 011111110
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [8,7,6,5,4,2,1,3,9] => 10111110
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,8,7,9,6,5,4,3,2] => [1,9,8,7,6,5,3,2,4] => 01011111
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,9,10,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,2,3] => 001111111
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => [10,8,6,4,2,1,3,5,7,9] => 101010101
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [5,4,7,6,8,3,9,2,10,1] => [10,8,6,2,1,4,3,5,7,9] => 101010101
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,10,1] => [10,2,1,4,3,6,5,8,7,9] => 101010101
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7,10,9] => [4,2,1,3,6,5,8,7,10,9] => 101010101
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [7,6,8,5,9,4,10,3,11,2,12,1] => [12,10,8,6,4,2,1,3,5,7,9,11] => 10101010101
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,11,10,12,1] => [12,2,1,4,3,6,5,8,7,10,9,11] => 10101010101
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [2,1,9,8,7,6,5,4,3] => [2,1,9,8,7,6,5,4,3] => 10111111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [3,2,1,9,8,7,6,5,4] => [3,2,1,9,8,7,6,5,4] => 11011111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [4,3,2,1,9,8,7,6,5] => [4,3,2,1,9,8,7,6,5] => 11101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [5,4,3,2,1,9,8,7,6] => [5,4,3,2,1,9,8,7,6] => 11110111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [6,5,4,3,2,1,9,8,7] => [6,5,4,3,2,1,9,8,7] => 11111011
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [7,6,5,4,3,2,1,9,8] => [7,6,5,4,3,2,1,9,8] => 11111101
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,9,8,7,6,5,4,3] => [1,2,9,8,7,6,5,4,3] => 00111111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,9,8,7,6,5,4,3] => 101111111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [3,2,1,10,9,8,7,6,5,4] => [3,2,1,10,9,8,7,6,5,4] => 110111111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => [4,3,2,1,10,9,8,7,6,5] => 111011111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [5,4,3,2,1,10,9,8,7,6] => [5,4,3,2,1,10,9,8,7,6] => 111101111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => [6,5,4,3,2,1,10,9,8,7] => 111110111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [6,7,5,4,3,2,1,9,8] => [7,6,5,4,3,1,2,9,8] => 01111101
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [7,6,5,4,3,2,1,10,9,8] => [7,6,5,4,3,2,1,10,9,8] => 111111011
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => 111111101
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => 11111100
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => 11111000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => 11110000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => 11100000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => 11000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 10000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => 111111100
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => 111111000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => 111110000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => 111100000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => 111000000
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,4,3,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => 01100000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => 110000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => 01000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => 100000000
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [4,9,8,7,6,5,3,2,1] => [9,8,7,1,6,5,4,3,2] => 01111111
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [3,9,8,7,6,5,4,2,1] => [9,8,1,7,6,5,4,3,2] => 01111111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => [9,1,8,7,6,5,4,3,2] => 01111111
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [6,10,9,8,7,5,4,3,2,1] => [10,9,8,7,6,1,5,4,3,2] => 011111111
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [2,4,6,8,10,9,7,5,3,1] => [10,1,9,2,8,3,7,4,6,5] => 000011111
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,8,7,5,10,9] => [4,1,3,2,8,5,7,6,10,9] => 011001101
[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => [2,4,3,1,6,5,8,10,9,7] => [4,1,3,2,6,5,10,7,9,8] => 011010011
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7,10,9] => [4,1,3,2,6,5,8,7,10,9] => 011010101
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,3,6,8,7,5,10,9] => [2,1,4,3,8,5,7,6,10,9] => 101001101
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,5,8,10,9,7] => [2,1,4,3,6,5,10,7,9,8] => 101010011
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5,10,12,11,9] => [4,1,3,2,8,5,7,6,12,9,11,10] => 01100110011
[[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,8,7,5,10,9,12,11] => [4,1,3,2,8,5,7,6,10,9,12,11] => 01100110101
[[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5,8,10,9,7,12,11] => [4,1,3,2,6,5,10,7,9,8,12,11] => 01101001101
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,4,3,1,6,5,8,7,10,12,11,9] => [4,1,3,2,6,5,8,7,12,9,11,10] => 01101010011
[[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7,10,9,12,11] => [4,1,3,2,6,5,8,7,10,9,12,11] => 01101010101
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5,10,12,11,9] => [2,1,4,3,8,5,7,6,12,9,11,10] => 10100110011
[[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => [2,1,4,3,6,8,7,5,10,9,12,11] => [2,1,4,3,8,5,7,6,10,9,12,11] => 10100110101
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,3,6,5,8,10,9,7,12,11] => [2,1,4,3,6,5,10,7,9,8,12,11] => 10101001101
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,5,8,7,10,12,11,9] => [2,1,4,3,6,5,8,7,12,9,11,10] => 10101010011
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,9,8,1] => [9,1,2,3,4,5,6,8,7] => 00000011
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => 10000010
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [2,1,3,4,5,6,8,9,7] => [2,1,3,4,5,6,9,7,8] => 10000001
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [2,3,4,5,6,8,9,7,1] => [9,1,2,3,4,5,8,6,7] => 00000011
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,8,10,9,1] => [10,1,2,3,4,5,6,7,9,8] => 000000011
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => 10100000
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [3,2,1,5,4,6,7,8,9] => [3,2,1,5,4,6,7,8,9] => 11010000
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [6,5,4,3,2,1,8,7,9] => [6,5,4,3,2,1,8,7,9] => 11111010
[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]] => [7,8,6,9,5,4,3,2,1] => [9,8,7,6,5,3,1,2,4] => 01011111
[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]] => [6,7,8,5,9,4,3,2,1] => [9,8,7,6,4,1,2,3,5] => 00101111
[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]] => [5,6,7,8,4,9,3,2,1] => [9,8,7,5,1,2,3,4,6] => 00010111
[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]] => [4,5,6,7,8,3,9,2,1] => [9,8,6,1,2,3,4,5,7] => 00001011
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => [9,7,1,2,3,4,5,6,8] => 00000101
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9] => 00000010
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => 01000000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [7,1,2,3,4,5,6,8,9] => 00000100
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => 010000000
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [2,4,3,1,5,6,7,8,9] => [4,1,3,2,5,6,7,8,9] => 01100000
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [2,3,4,5,6,8,7,1,9] => [8,1,2,3,4,5,7,6,9] => 00000110
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10] => 000000010
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => 00100000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => 00010000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => 00001000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => 00000100
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => 00000010
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => 010000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => 001000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => 000100000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => 000010000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => 000001000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => 000000100
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => 000000010
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [1,3,4,5,6,7,9,8,2] => [1,9,2,3,4,5,6,8,7] => 00000011
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [7,6,5,4,3,2,9,8,1] => [9,6,5,4,3,2,1,8,7] => 11111011
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => [9,5,4,3,2,1,6,7,8] => 11110001
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => [7,6,5,4,3,2,8,9,1] => [9,6,5,4,3,2,1,7,8] => 11111001
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]] => [8,7,6,5,4,3,2,9,10,1] => [10,7,6,5,4,3,2,1,8,9] => 111111001
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,7,6,5,4,3,2,9,8] => [1,7,6,5,4,3,2,9,8] => 01111101
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,2,10,9,8,7,6,5,4,3] => [1,2,10,9,8,7,6,5,4,3] => 001111111
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,3,2,9,8,7,6,5,4] => [1,3,2,9,8,7,6,5,4] => 01011111
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [2,1,8,7,6,5,4,3,9] => [2,1,8,7,6,5,4,3,9] => 10111110
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,9,8,7,6,5,4,3,2,10] => [1,9,8,7,6,5,4,3,2,10] => 011111110
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => 01010000
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [8,7,6,5,4,3,2,10,9,1] => [10,7,6,5,4,3,2,1,9,8] => 111111011
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [2,1,4,5,6,7,8,9,3] => [2,1,9,3,4,5,6,7,8] => 10000001
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,3,4,5,6,7,8,2,9] => [1,8,2,3,4,5,6,7,9] => 00000010
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,10,9,8] => 000000011
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => [8,7,6,5,4,1,2,3,9] => 00111110
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,9,8,7,6] => 00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,9,8,7,6,5] => [1,2,3,4,9,8,7,6,5] => 00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,9,8,7,6,5,4] => [1,2,3,9,8,7,6,5,4] => 00011111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => 00000101
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,6,10,9,8,7] => [1,2,3,4,5,6,10,9,8,7] => 000000111
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,4,6,5,9,8,7] => [1,2,3,4,6,5,9,8,7] => 00001011
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,5,10,9,8,7,6] => [1,2,3,4,5,10,9,8,7,6] => 000001111
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,3,5,4,9,8,7,6] => [1,2,3,5,4,9,8,7,6] => 00010111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,4,10,9,8,7,6,5] => [1,2,3,4,10,9,8,7,6,5] => 000011111
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,2,4,3,9,8,7,6,5] => [1,2,4,3,9,8,7,6,5] => 00101111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,3,10,9,8,7,6,5,4] => [1,2,3,10,9,8,7,6,5,4] => 000111111
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => 000000101
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,1,2] => 0111111111
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => [9,7,6,5,4,3,1,2,8] => 01111101
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => [4,3,1,2,5,6,7,8,9] => 01100000
[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10,11] => [3,1,2,4,5,6,7,8,9,10,11] => 0100000000
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.] => [3,4,2,5,1,6,7,8,9] => [5,3,1,2,4,6,7,8,9] => 01010000
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => [8,6,5,4,3,2,1,7,9] => 11111010
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => [7,6,5,8,4,3,2,1,9] => [8,7,6,5,3,2,1,4,9] => 11011110
[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]] => [7,6,5,4,3,8,9,2,1] => [9,8,5,4,3,2,1,6,7] => 11110011
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => [5,4,3,1,2,6,7,8,9] => 01110000
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => [8,2,1,3,4,5,6,7,9] => 10000010
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [5,4,3,2,1,8,7,6,9] => [5,4,3,2,1,8,7,6,9] => 11110110
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [7,6,5,4,3,2,1,9,8,10] => [7,6,5,4,3,2,1,9,8,10] => 111111010
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,8,7,6,5,4,3,9,2] => [1,9,7,6,5,4,3,2,8] => 01111101
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [2,3,4,5,6,7,1,9,8] => [7,1,2,3,4,5,6,9,8] => 00000101
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,3,4,2,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => 00100000
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => [8,7,6,5,4,3,2,9,1,10] => [9,7,6,5,4,3,2,1,8,10] => 111111010
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.] => [5,6,4,3,2,1,7,8,9] => [6,5,4,3,1,2,7,8,9] => 01111000
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
inverse
Description
Sends a permutation to its inverse.
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.