Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
[.,.] => [1] => [1] => [1] =>
[.,[.,.]] => [2,1] => [2,1] => [2,1] => 1
[[.,.],.] => [1,2] => [1,2] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => [3,2,1] => [3,2,1] => 11
[.,[[.,.],.]] => [2,3,1] => [2,3,1] => [3,1,2] => 10
[[.,.],[.,.]] => [1,3,2] => [3,1,2] => [1,3,2] => 01
[[.,[.,.]],.] => [2,1,3] => [2,1,3] => [2,1,3] => 10
[[[.,.],.],.] => [1,2,3] => [1,2,3] => [1,2,3] => 00
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 111
[.,[.,[[.,.],.]]] => [3,4,2,1] => [3,4,2,1] => [4,3,1,2] => 110
[.,[[.,.],[.,.]]] => [2,4,3,1] => [4,2,3,1] => [4,1,3,2] => 101
[.,[[.,[.,.]],.]] => [3,2,4,1] => [3,2,4,1] => [4,2,1,3] => 110
[.,[[[.,.],.],.]] => [2,3,4,1] => [2,3,4,1] => [4,1,2,3] => 100
[[.,.],[.,[.,.]]] => [1,4,3,2] => [4,3,1,2] => [1,4,3,2] => 011
[[.,.],[[.,.],.]] => [1,3,4,2] => [3,1,4,2] => [3,4,1,2] => 010
[[.,[.,.]],[.,.]] => [2,1,4,3] => [4,2,1,3] => [3,1,4,2] => 101
[[[.,.],.],[.,.]] => [1,2,4,3] => [4,1,2,3] => [1,2,4,3] => 001
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 110
[[.,[[.,.],.]],.] => [2,3,1,4] => [2,3,1,4] => [3,1,2,4] => 100
[[[.,.],[.,.]],.] => [1,3,2,4] => [3,1,2,4] => [1,3,2,4] => 010
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 100
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 000
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 1111
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [4,5,3,2,1] => [5,4,3,1,2] => 1110
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [5,3,4,2,1] => [5,4,1,3,2] => 1101
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [4,3,5,2,1] => [5,4,2,1,3] => 1110
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [3,4,5,2,1] => [5,4,1,2,3] => 1100
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [5,4,2,3,1] => [5,1,4,3,2] => 1011
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [4,2,5,3,1] => [5,3,4,1,2] => 1010
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [5,3,2,4,1] => [5,3,1,4,2] => 1101
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [5,2,3,4,1] => [5,1,2,4,3] => 1001
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [4,3,2,5,1] => [5,3,2,1,4] => 1110
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [3,4,2,5,1] => [5,3,1,2,4] => 1100
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [4,2,3,5,1] => [5,1,3,2,4] => 1010
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [3,2,4,5,1] => [5,2,1,3,4] => 1100
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [2,3,4,5,1] => [5,1,2,3,4] => 1000
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [5,4,3,1,2] => [1,5,4,3,2] => 0111
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [4,5,1,3,2] => [2,5,4,1,3] => 0110
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [5,3,1,4,2] => [4,5,1,3,2] => 0101
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [4,3,1,5,2] => [4,5,2,1,3] => 0110
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [3,1,4,5,2] => [3,5,1,2,4] => 0100
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [5,4,2,1,3] => [4,1,5,3,2] => 1011
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [4,2,1,5,3] => [4,3,5,1,2] => 1010
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [5,4,1,2,3] => [1,2,5,4,3] => 0011
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [4,1,2,5,3] => [2,4,5,1,3] => 0010
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [5,3,2,1,4] => [4,3,1,5,2] => 1101
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [5,2,3,1,4] => [4,1,2,5,3] => 1001
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [5,3,1,2,4] => [1,4,2,5,3] => 0101
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [5,2,1,3,4] => [3,1,2,5,4] => 1001
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [5,1,2,3,4] => [1,2,3,5,4] => 0001
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1110
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [3,4,2,1,5] => [4,3,1,2,5] => 1100
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [4,2,3,1,5] => [4,1,3,2,5] => 1010
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [3,2,4,1,5] => [4,2,1,3,5] => 1100
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [2,3,4,1,5] => [4,1,2,3,5] => 1000
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [4,3,1,2,5] => [1,4,3,2,5] => 0110
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => 0100
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [4,2,1,3,5] => [3,1,4,2,5] => 1010
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [4,1,2,3,5] => [1,2,4,3,5] => 0010
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 1100
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => 1000
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [3,1,2,4,5] => [1,3,2,4,5] => 0100
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 1000
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0000
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [6,5,4,3,1,2] => 11110
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [6,5,4,1,3,2] => 11101
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [6,5,4,2,1,3] => 11110
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 11100
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [6,5,1,4,3,2] => 11011
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [5,3,6,4,2,1] => [6,5,3,4,1,2] => 11010
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [6,4,3,5,2,1] => [6,5,3,1,4,2] => 11101
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => [6,5,1,2,4,3] => 11001
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [6,5,3,2,1,4] => 11110
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [6,5,3,1,2,4] => 11100
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => [6,5,1,3,2,4] => 11010
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [6,5,2,1,3,4] => 11100
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,5,1,2,3,4] => 11000
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [6,1,5,4,3,2] => 10111
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [5,6,2,4,3,1] => [6,2,5,4,1,3] => 10110
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [6,4,2,5,3,1] => [6,4,5,1,3,2] => 10101
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [5,4,2,6,3,1] => [6,4,5,2,1,3] => 10110
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [4,2,5,6,3,1] => [6,3,5,1,2,4] => 10100
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [6,5,3,2,4,1] => [6,4,1,5,3,2] => 11011
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [5,3,2,6,4,1] => [6,4,3,5,1,2] => 11010
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => [6,1,2,5,4,3] => 10011
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [5,2,3,6,4,1] => [6,2,4,5,1,3] => 10010
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [6,4,3,2,5,1] => [6,4,3,1,5,2] => 11101
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [6,3,4,2,5,1] => [6,4,1,2,5,3] => 11001
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [6,4,2,3,5,1] => [6,1,4,2,5,3] => 10101
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [6,3,2,4,5,1] => [6,3,1,2,5,4] => 11001
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => [6,1,2,3,5,4] => 10001
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [6,4,3,2,1,5] => 11110
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [6,4,3,1,2,5] => 11100
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => [6,4,1,3,2,5] => 11010
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [6,4,2,1,3,5] => 11100
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,4,1,2,3,5] => 11000
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => [6,1,4,3,2,5] => 10110
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [4,2,5,3,6,1] => [6,3,4,1,2,5] => 10100
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [5,3,2,4,6,1] => [6,3,1,4,2,5] => 11010
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => [6,1,2,4,3,5] => 10010
>>> Load all 1504 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [6,3,2,1,4,5] => 11100
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [6,3,1,2,4,5] => 11000
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => [6,1,3,2,4,5] => 10100
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [6,2,1,3,4,5] => 11000
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 10000
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => [1,6,5,4,3,2] => 01111
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [5,6,4,1,3,2] => [2,6,5,4,1,3] => 01110
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [6,4,5,1,3,2] => [2,6,5,1,4,3] => 01101
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [5,4,6,1,3,2] => [2,6,5,3,1,4] => 01110
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [4,5,1,6,3,2] => [5,6,4,1,2,3] => 01100
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [6,5,3,1,4,2] => [5,6,1,4,3,2] => 01011
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [5,3,1,6,4,2] => [5,6,3,4,1,2] => 01010
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [6,4,3,1,5,2] => [5,6,3,1,4,2] => 01101
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [6,3,1,4,5,2] => [4,6,1,2,5,3] => 01001
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [5,4,3,1,6,2] => [5,6,3,2,1,4] => 01110
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [4,5,1,3,6,2] => [2,6,4,1,3,5] => 01100
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [5,3,1,4,6,2] => [4,6,1,3,2,5] => 01010
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [4,3,1,5,6,2] => [4,6,2,1,3,5] => 01100
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => [3,6,1,2,4,5] => 01000
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [6,5,4,2,1,3] => [5,1,6,4,3,2] => 10111
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 10110
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [6,4,2,1,5,3] => [5,4,6,1,3,2] => 10101
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [5,4,2,1,6,3] => [5,4,6,2,1,3] => 10110
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [4,2,1,5,6,3] => [4,3,6,1,2,5] => 10100
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => [1,2,6,5,4,3] => 00111
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [5,6,1,2,4,3] => [2,3,6,5,1,4] => 00110
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [6,4,1,2,5,3] => [2,5,6,1,4,3] => 00101
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [5,4,1,2,6,3] => [2,5,6,3,1,4] => 00110
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [4,1,2,5,6,3] => [2,4,6,1,3,5] => 00100
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [6,5,3,2,1,4] => [5,4,1,6,3,2] => 11011
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [5,3,2,1,6,4] => [5,4,3,6,1,2] => 11010
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [6,5,2,3,1,4] => [5,1,2,6,4,3] => 10011
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [5,2,3,1,6,4] => [5,2,4,6,1,3] => 10010
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [6,5,3,1,2,4] => [1,5,2,6,4,3] => 01011
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [5,3,1,2,6,4] => [2,5,4,6,1,3] => 01010
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [6,5,2,1,3,4] => [4,1,2,6,5,3] => 10011
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [5,2,1,3,6,4] => [4,2,5,6,1,3] => 10010
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => [1,2,3,6,5,4] => 00011
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [5,1,2,3,6,4] => [2,3,5,6,1,4] => 00010
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [6,4,3,2,1,5] => [5,4,3,1,6,2] => 11101
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [6,3,4,2,1,5] => [5,4,1,2,6,3] => 11001
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [6,4,2,3,1,5] => [5,1,4,2,6,3] => 10101
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [6,3,2,4,1,5] => [5,3,1,2,6,4] => 11001
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [6,2,3,4,1,5] => [5,1,2,3,6,4] => 10001
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [6,4,3,1,2,5] => [1,5,4,2,6,3] => 01101
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [6,3,1,4,2,5] => [4,5,1,2,6,3] => 01001
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [6,4,2,1,3,5] => [4,1,5,2,6,3] => 10101
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [6,4,1,2,3,5] => [1,2,5,3,6,4] => 00101
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [6,3,2,1,4,5] => [4,3,1,2,6,5] => 11001
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [6,2,3,1,4,5] => [4,1,2,3,6,5] => 10001
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [6,3,1,2,4,5] => [1,4,2,3,6,5] => 01001
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [6,2,1,3,4,5] => [3,1,2,4,6,5] => 10001
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => [1,2,3,4,6,5] => 00001
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 11110
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => [5,4,3,1,2,6] => 11100
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [5,3,4,2,1,6] => [5,4,1,3,2,6] => 11010
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => [5,4,2,1,3,6] => 11100
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [5,4,1,2,3,6] => 11000
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => [5,1,4,3,2,6] => 10110
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [4,2,5,3,1,6] => [5,3,4,1,2,6] => 10100
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [5,3,2,4,1,6] => [5,3,1,4,2,6] => 11010
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => [5,1,2,4,3,6] => 10010
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [5,3,2,1,4,6] => 11100
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => [5,3,1,2,4,6] => 11000
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => [5,1,3,2,4,6] => 10100
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [5,2,1,3,4,6] => 11000
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => 10000
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => [1,5,4,3,2,6] => 01110
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [4,5,1,3,2,6] => [2,5,4,1,3,6] => 01100
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [5,3,1,4,2,6] => [4,5,1,3,2,6] => 01010
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [4,3,1,5,2,6] => [4,5,2,1,3,6] => 01100
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => [3,5,1,2,4,6] => 01000
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [5,4,2,1,3,6] => [4,1,5,3,2,6] => 10110
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [4,2,1,5,3,6] => [4,3,5,1,2,6] => 10100
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => [1,2,5,4,3,6] => 00110
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [4,1,2,5,3,6] => [2,4,5,1,3,6] => 00100
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [5,3,2,1,4,6] => [4,3,1,5,2,6] => 11010
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [5,2,3,1,4,6] => [4,1,2,5,3,6] => 10010
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [5,3,1,2,4,6] => [1,4,2,5,3,6] => 01010
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [5,2,1,3,4,6] => [3,1,2,5,4,6] => 10010
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => [1,2,3,5,4,6] => 00010
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 11100
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => 11000
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => [4,1,3,2,5,6] => 10100
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => [4,2,1,3,5,6] => 11000
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => 10000
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => [1,4,3,2,5,6] => 01100
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => 01000
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [4,2,1,3,5,6] => [3,1,4,2,5,6] => 10100
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => [1,2,4,3,5,6] => 00100
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 11000
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => 10000
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => 01000
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [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] => [1,2,3,4,5,6] => 00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [6,7,5,4,3,2,1] => [7,6,5,4,3,1,2] => 111110
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [7,5,6,4,3,2,1] => [7,6,5,4,1,3,2] => 111101
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [6,5,7,4,3,2,1] => [7,6,5,4,2,1,3] => 111110
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [5,6,7,4,3,2,1] => [7,6,5,4,1,2,3] => 111100
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [7,6,4,5,3,2,1] => [7,6,5,1,4,3,2] => 111011
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [6,4,7,5,3,2,1] => [7,6,5,3,4,1,2] => 111010
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [7,5,4,6,3,2,1] => [7,6,5,3,1,4,2] => 111101
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [7,4,5,6,3,2,1] => [7,6,5,1,2,4,3] => 111001
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [6,5,4,7,3,2,1] => [7,6,5,3,2,1,4] => 111110
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [5,6,4,7,3,2,1] => [7,6,5,3,1,2,4] => 111100
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [6,4,5,7,3,2,1] => [7,6,5,1,3,2,4] => 111010
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [5,4,6,7,3,2,1] => [7,6,5,2,1,3,4] => 111100
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [4,5,6,7,3,2,1] => [7,6,5,1,2,3,4] => 111000
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [7,6,5,3,4,2,1] => [7,6,1,5,4,3,2] => 110111
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [6,7,3,5,4,2,1] => [7,6,2,5,4,1,3] => 110110
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [7,5,3,6,4,2,1] => [7,6,4,5,1,3,2] => 110101
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [6,5,3,7,4,2,1] => [7,6,4,5,2,1,3] => 110110
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [5,3,6,7,4,2,1] => [7,6,3,5,1,2,4] => 110100
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [7,6,4,3,5,2,1] => [7,6,4,1,5,3,2] => 111011
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [6,4,3,7,5,2,1] => [7,6,4,3,5,1,2] => 111010
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [7,6,3,4,5,2,1] => [7,6,1,2,5,4,3] => 110011
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [6,3,4,7,5,2,1] => [7,6,2,4,5,1,3] => 110010
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [7,5,4,3,6,2,1] => [7,6,4,3,1,5,2] => 111101
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [7,4,5,3,6,2,1] => [7,6,4,1,2,5,3] => 111001
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [7,5,3,4,6,2,1] => [7,6,1,4,2,5,3] => 110101
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [7,4,3,5,6,2,1] => [7,6,3,1,2,5,4] => 111001
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [7,3,4,5,6,2,1] => [7,6,1,2,3,5,4] => 110001
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [6,5,4,3,7,2,1] => [7,6,4,3,2,1,5] => 111110
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [5,6,4,3,7,2,1] => [7,6,4,3,1,2,5] => 111100
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [6,4,5,3,7,2,1] => [7,6,4,1,3,2,5] => 111010
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [5,4,6,3,7,2,1] => [7,6,4,2,1,3,5] => 111100
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [4,5,6,3,7,2,1] => [7,6,4,1,2,3,5] => 111000
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [6,5,3,4,7,2,1] => [7,6,1,4,3,2,5] => 110110
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [5,3,6,4,7,2,1] => [7,6,3,4,1,2,5] => 110100
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [6,4,3,5,7,2,1] => [7,6,3,1,4,2,5] => 111010
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [6,3,4,5,7,2,1] => [7,6,1,2,4,3,5] => 110010
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [5,4,3,6,7,2,1] => [7,6,3,2,1,4,5] => 111100
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [4,5,3,6,7,2,1] => [7,6,3,1,2,4,5] => 111000
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [5,3,4,6,7,2,1] => [7,6,1,3,2,4,5] => 110100
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [4,3,5,6,7,2,1] => [7,6,2,1,3,4,5] => 111000
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [3,4,5,6,7,2,1] => [7,6,1,2,3,4,5] => 110000
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [7,6,5,4,2,3,1] => [7,1,6,5,4,3,2] => 101111
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [6,7,5,2,4,3,1] => [7,2,6,5,4,1,3] => 101110
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [7,5,6,2,4,3,1] => [7,2,6,5,1,4,3] => 101101
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [6,5,7,2,4,3,1] => [7,2,6,5,3,1,4] => 101110
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [5,6,2,7,4,3,1] => [7,5,6,4,1,2,3] => 101100
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [7,6,4,2,5,3,1] => [7,5,6,1,4,3,2] => 101011
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [6,4,2,7,5,3,1] => [7,5,6,3,4,1,2] => 101010
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [7,5,4,2,6,3,1] => [7,5,6,3,1,4,2] => 101101
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [7,4,2,5,6,3,1] => [7,4,6,1,2,5,3] => 101001
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [6,5,4,2,7,3,1] => [7,5,6,3,2,1,4] => 101110
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [5,6,2,4,7,3,1] => [7,2,6,4,1,3,5] => 101100
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [6,4,2,5,7,3,1] => [7,4,6,1,3,2,5] => 101010
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [5,4,2,6,7,3,1] => [7,4,6,2,1,3,5] => 101100
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [4,2,5,6,7,3,1] => [7,3,6,1,2,4,5] => 101000
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [7,6,5,3,2,4,1] => [7,5,1,6,4,3,2] => 110111
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [6,7,3,2,5,4,1] => [7,5,2,6,4,1,3] => 110110
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [7,5,3,2,6,4,1] => [7,5,4,6,1,3,2] => 110101
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [6,5,3,2,7,4,1] => [7,5,4,6,2,1,3] => 110110
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [5,3,2,6,7,4,1] => [7,4,3,6,1,2,5] => 110100
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [7,6,5,2,3,4,1] => [7,1,2,6,5,4,3] => 100111
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [6,7,2,3,5,4,1] => [7,2,3,6,5,1,4] => 100110
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [7,5,2,3,6,4,1] => [7,2,5,6,1,4,3] => 100101
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [6,5,2,3,7,4,1] => [7,2,5,6,3,1,4] => 100110
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [5,2,3,6,7,4,1] => [7,2,4,6,1,3,5] => 100100
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [7,6,4,3,2,5,1] => [7,5,4,1,6,3,2] => 111011
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => [6,4,3,2,7,5,1] => [7,5,4,3,6,1,2] => 111010
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [7,6,3,4,2,5,1] => [7,5,1,2,6,4,3] => 110011
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [6,3,4,2,7,5,1] => [7,5,2,4,6,1,3] => 110010
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [7,6,4,2,3,5,1] => [7,1,5,2,6,4,3] => 101011
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [6,4,2,3,7,5,1] => [7,2,5,4,6,1,3] => 101010
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [7,6,3,2,4,5,1] => [7,4,1,2,6,5,3] => 110011
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [6,3,2,4,7,5,1] => [7,4,2,5,6,1,3] => 110010
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [7,6,2,3,4,5,1] => [7,1,2,3,6,5,4] => 100011
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [6,2,3,4,7,5,1] => [7,2,3,5,6,1,4] => 100010
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [7,5,4,3,2,6,1] => [7,5,4,3,1,6,2] => 111101
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [7,4,5,3,2,6,1] => [7,5,4,1,2,6,3] => 111001
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [7,5,3,4,2,6,1] => [7,5,1,4,2,6,3] => 110101
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => [7,4,3,5,2,6,1] => [7,5,3,1,2,6,4] => 111001
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [7,3,4,5,2,6,1] => [7,5,1,2,3,6,4] => 110001
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [7,5,4,2,3,6,1] => [7,1,5,4,2,6,3] => 101101
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [7,4,2,5,3,6,1] => [7,4,5,1,2,6,3] => 101001
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [7,5,3,2,4,6,1] => [7,4,1,5,2,6,3] => 110101
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [7,5,2,3,4,6,1] => [7,1,2,5,3,6,4] => 100101
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [7,4,3,2,5,6,1] => [7,4,3,1,2,6,5] => 111001
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [7,3,4,2,5,6,1] => [7,4,1,2,3,6,5] => 110001
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [7,4,2,3,5,6,1] => [7,1,4,2,3,6,5] => 101001
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [7,3,2,4,5,6,1] => [7,3,1,2,4,6,5] => 110001
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [7,2,3,4,5,6,1] => [7,1,2,3,4,6,5] => 100001
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => [7,5,4,3,2,1,6] => 111110
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [5,6,4,3,2,7,1] => [7,5,4,3,1,2,6] => 111100
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [6,4,5,3,2,7,1] => [7,5,4,1,3,2,6] => 111010
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [5,4,6,3,2,7,1] => [7,5,4,2,1,3,6] => 111100
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [4,5,6,3,2,7,1] => [7,5,4,1,2,3,6] => 111000
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => [6,5,3,4,2,7,1] => [7,5,1,4,3,2,6] => 110110
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [5,3,6,4,2,7,1] => [7,5,3,4,1,2,6] => 110100
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [6,4,3,5,2,7,1] => [7,5,3,1,4,2,6] => 111010
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [6,3,4,5,2,7,1] => [7,5,1,2,4,3,6] => 110010
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [5,4,3,6,2,7,1] => [7,5,3,2,1,4,6] => 111100
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [4,5,3,6,2,7,1] => [7,5,3,1,2,4,6] => 111000
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [5,3,4,6,2,7,1] => [7,5,1,3,2,4,6] => 110100
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [4,3,5,6,2,7,1] => [7,5,2,1,3,4,6] => 111000
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [3,4,5,6,2,7,1] => [7,5,1,2,3,4,6] => 110000
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [6,5,4,2,3,7,1] => [7,1,5,4,3,2,6] => 101110
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [5,6,2,4,3,7,1] => [7,2,5,4,1,3,6] => 101100
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [6,4,2,5,3,7,1] => [7,4,5,1,3,2,6] => 101010
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [5,4,2,6,3,7,1] => [7,4,5,2,1,3,6] => 101100
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [4,2,5,6,3,7,1] => [7,3,5,1,2,4,6] => 101000
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [6,5,3,2,4,7,1] => [7,4,1,5,3,2,6] => 110110
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [5,3,2,6,4,7,1] => [7,4,3,5,1,2,6] => 110100
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [6,5,2,3,4,7,1] => [7,1,2,5,4,3,6] => 100110
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [5,2,3,6,4,7,1] => [7,2,4,5,1,3,6] => 100100
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => [6,4,3,2,5,7,1] => [7,4,3,1,5,2,6] => 111010
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [6,3,4,2,5,7,1] => [7,4,1,2,5,3,6] => 110010
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [6,4,2,3,5,7,1] => [7,1,4,2,5,3,6] => 101010
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [6,3,2,4,5,7,1] => [7,3,1,2,5,4,6] => 110010
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [6,2,3,4,5,7,1] => [7,1,2,3,5,4,6] => 100010
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => [7,4,3,2,1,5,6] => 111100
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [4,5,3,2,6,7,1] => [7,4,3,1,2,5,6] => 111000
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [5,3,4,2,6,7,1] => [7,4,1,3,2,5,6] => 110100
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [4,3,5,2,6,7,1] => [7,4,2,1,3,5,6] => 111000
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1] => [7,4,1,2,3,5,6] => 110000
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [5,4,2,3,6,7,1] => [7,1,4,3,2,5,6] => 101100
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [4,2,5,3,6,7,1] => [7,3,4,1,2,5,6] => 101000
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [5,3,2,4,6,7,1] => [7,3,1,4,2,5,6] => 110100
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [5,2,3,4,6,7,1] => [7,1,2,4,3,5,6] => 100100
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => [7,3,2,1,4,5,6] => 111000
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [3,4,2,5,6,7,1] => [7,3,1,2,4,5,6] => 110000
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [4,2,3,5,6,7,1] => [7,1,3,2,4,5,6] => 101000
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => [7,2,1,3,4,5,6] => 110000
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => 100000
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [7,6,5,4,3,1,2] => [1,7,6,5,4,3,2] => 011111
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [6,7,5,4,1,3,2] => [2,7,6,5,4,1,3] => 011110
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [7,5,6,4,1,3,2] => [2,7,6,5,1,4,3] => 011101
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [6,5,7,4,1,3,2] => [2,7,6,5,3,1,4] => 011110
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [5,6,7,1,4,3,2] => [3,7,6,5,1,2,4] => 011100
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [7,6,4,5,1,3,2] => [2,7,6,1,5,4,3] => 011011
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [6,4,7,1,5,3,2] => [3,7,6,4,5,1,2] => 011010
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [7,5,4,6,1,3,2] => [2,7,6,4,1,5,3] => 011101
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [7,4,5,1,6,3,2] => [6,7,5,1,2,4,3] => 011001
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [6,5,4,7,1,3,2] => [2,7,6,4,3,1,5] => 011110
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [5,6,4,1,7,3,2] => [6,7,5,3,1,2,4] => 011100
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [6,4,5,1,7,3,2] => [6,7,5,1,3,2,4] => 011010
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [5,4,6,1,7,3,2] => [6,7,5,2,1,3,4] => 011100
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [4,5,1,6,7,3,2] => [5,7,6,1,2,3,4] => 011000
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [7,6,5,3,1,4,2] => [6,7,1,5,4,3,2] => 010111
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [6,7,3,1,5,4,2] => [6,7,2,5,4,1,3] => 010110
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [7,5,3,1,6,4,2] => [6,7,4,5,1,3,2] => 010101
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [6,5,3,1,7,4,2] => [6,7,4,5,2,1,3] => 010110
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [5,3,1,6,7,4,2] => [5,7,3,6,1,2,4] => 010100
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [7,6,4,3,1,5,2] => [6,7,4,1,5,3,2] => 011011
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [6,4,3,1,7,5,2] => [6,7,4,3,5,1,2] => 011010
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [7,6,3,1,4,5,2] => [5,7,1,2,6,4,3] => 010011
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [6,3,1,4,7,5,2] => [5,7,2,4,6,1,3] => 010010
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [7,5,4,3,1,6,2] => [6,7,4,3,1,5,2] => 011101
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [7,4,5,1,3,6,2] => [2,7,5,1,3,6,4] => 011001
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [7,5,3,1,4,6,2] => [5,7,1,4,2,6,3] => 010101
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [7,4,3,1,5,6,2] => [5,7,3,1,2,6,4] => 011001
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [7,3,1,4,5,6,2] => [4,7,1,2,3,6,5] => 010001
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [6,5,4,3,1,7,2] => [6,7,4,3,2,1,5] => 011110
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [5,6,4,1,3,7,2] => [2,7,5,4,1,3,6] => 011100
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [6,4,5,1,3,7,2] => [2,7,5,1,4,3,6] => 011010
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [5,4,6,1,3,7,2] => [2,7,5,3,1,4,6] => 011100
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [4,5,1,6,3,7,2] => [5,7,4,1,2,3,6] => 011000
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [6,5,3,1,4,7,2] => [5,7,1,4,3,2,6] => 010110
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [5,3,1,6,4,7,2] => [5,7,3,4,1,2,6] => 010100
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [6,4,3,1,5,7,2] => [5,7,3,1,4,2,6] => 011010
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [6,3,1,4,5,7,2] => [4,7,1,2,5,3,6] => 010010
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [5,4,3,1,6,7,2] => [5,7,3,2,1,4,6] => 011100
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [4,5,1,3,6,7,2] => [2,7,4,1,3,5,6] => 011000
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [5,3,1,4,6,7,2] => [4,7,1,3,2,5,6] => 010100
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [4,3,1,5,6,7,2] => [4,7,2,1,3,5,6] => 011000
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [3,1,4,5,6,7,2] => [3,7,1,2,4,5,6] => 010000
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [7,6,5,4,2,1,3] => [6,1,7,5,4,3,2] => 101111
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [6,7,5,2,1,4,3] => [6,2,7,5,4,1,3] => 101110
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [7,5,6,2,1,4,3] => [6,2,7,5,1,4,3] => 101101
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [6,5,7,2,1,4,3] => [6,2,7,5,3,1,4] => 101110
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [5,6,2,1,7,4,3] => [6,5,7,4,1,2,3] => 101100
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [7,6,4,2,1,5,3] => [6,5,7,1,4,3,2] => 101011
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [6,4,2,1,7,5,3] => [6,5,7,3,4,1,2] => 101010
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [7,5,4,2,1,6,3] => [6,5,7,3,1,4,2] => 101101
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [7,4,2,1,5,6,3] => [5,4,7,1,2,6,3] => 101001
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [6,5,4,2,1,7,3] => [6,5,7,3,2,1,4] => 101110
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [5,6,2,1,4,7,3] => [5,2,7,4,1,3,6] => 101100
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [6,4,2,1,5,7,3] => [5,4,7,1,3,2,6] => 101010
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [5,4,2,1,6,7,3] => [5,4,7,2,1,3,6] => 101100
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [4,2,1,5,6,7,3] => [4,3,7,1,2,5,6] => 101000
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => [1,2,7,6,5,4,3] => 001111
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [6,7,5,1,2,4,3] => [2,3,7,6,5,1,4] => 001110
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [7,5,6,1,2,4,3] => [2,3,7,6,1,5,4] => 001101
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [6,5,7,1,2,4,3] => [2,3,7,6,4,1,5] => 001110
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [5,6,1,2,7,4,3] => [3,6,7,5,1,2,4] => 001100
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [7,6,4,1,2,5,3] => [2,6,7,1,5,4,3] => 001011
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [6,4,1,2,7,5,3] => [3,6,7,4,5,1,2] => 001010
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [7,5,4,1,2,6,3] => [2,6,7,4,1,5,3] => 001101
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [7,4,1,2,5,6,3] => [2,5,7,1,3,6,4] => 001001
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [6,5,4,1,2,7,3] => [2,6,7,4,3,1,5] => 001110
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [5,6,1,2,4,7,3] => [2,3,7,5,1,4,6] => 001100
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [6,4,1,2,5,7,3] => [2,5,7,1,4,3,6] => 001010
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [5,4,1,2,6,7,3] => [2,5,7,3,1,4,6] => 001100
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [4,1,2,5,6,7,3] => [2,4,7,1,3,5,6] => 001000
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [7,6,5,3,2,1,4] => [6,5,1,7,4,3,2] => 110111
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [6,7,3,2,1,5,4] => [6,5,2,7,4,1,3] => 110110
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [7,5,3,2,1,6,4] => [6,5,4,7,1,3,2] => 110101
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [6,5,3,2,1,7,4] => [6,5,4,7,2,1,3] => 110110
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [5,3,2,1,6,7,4] => [5,4,3,7,1,2,6] => 110100
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [7,6,5,2,3,1,4] => [6,1,2,7,5,4,3] => 100111
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [6,7,2,3,1,5,4] => [6,2,3,7,5,1,4] => 100110
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [7,5,2,3,1,6,4] => [6,2,5,7,1,4,3] => 100101
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [6,5,2,3,1,7,4] => [6,2,5,7,3,1,4] => 100110
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [5,2,3,1,6,7,4] => [5,2,4,7,1,3,6] => 100100
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [7,6,5,3,1,2,4] => [1,6,2,7,5,4,3] => 010111
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [6,7,3,1,2,5,4] => [2,6,3,7,5,1,4] => 010110
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [7,5,3,1,2,6,4] => [2,6,5,7,1,4,3] => 010101
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [6,5,3,1,2,7,4] => [2,6,5,7,3,1,4] => 010110
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [5,3,1,2,6,7,4] => [2,5,4,7,1,3,6] => 010100
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [7,6,5,2,1,3,4] => [5,1,2,7,6,4,3] => 100111
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [6,7,2,1,3,5,4] => [5,2,3,7,6,1,4] => 100110
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [7,5,2,1,3,6,4] => [5,2,6,7,1,4,3] => 100101
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [6,5,2,1,3,7,4] => [5,2,6,7,3,1,4] => 100110
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [5,2,1,3,6,7,4] => [4,2,5,7,1,3,6] => 100100
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => 000111
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [6,7,1,2,3,5,4] => [2,3,4,7,6,1,5] => 000110
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [7,5,1,2,3,6,4] => [2,3,6,7,1,5,4] => 000101
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [6,5,1,2,3,7,4] => [2,3,6,7,4,1,5] => 000110
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [5,1,2,3,6,7,4] => [2,3,5,7,1,4,6] => 000100
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [7,6,4,3,2,1,5] => [6,5,4,1,7,3,2] => 111011
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [6,4,3,2,1,7,5] => [6,5,4,3,7,1,2] => 111010
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [7,6,3,4,2,1,5] => [6,5,1,2,7,4,3] => 110011
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [6,3,4,2,1,7,5] => [6,5,2,4,7,1,3] => 110010
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [7,6,4,2,3,1,5] => [6,1,5,2,7,4,3] => 101011
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [6,4,2,3,1,7,5] => [6,2,5,4,7,1,3] => 101010
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [7,6,3,2,4,1,5] => [6,4,1,2,7,5,3] => 110011
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [6,3,2,4,1,7,5] => [6,4,2,5,7,1,3] => 110010
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [7,6,2,3,4,1,5] => [6,1,2,3,7,5,4] => 100011
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [6,2,3,4,1,7,5] => [6,2,3,5,7,1,4] => 100010
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [7,6,4,3,1,2,5] => [1,6,5,2,7,4,3] => 011011
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [6,4,3,1,2,7,5] => [2,6,5,4,7,1,3] => 011010
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [7,6,3,1,4,2,5] => [5,6,1,2,7,4,3] => 010011
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [6,3,1,4,2,7,5] => [5,6,2,4,7,1,3] => 010010
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [7,6,4,2,1,3,5] => [5,1,6,2,7,4,3] => 101011
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [6,4,2,1,3,7,5] => [5,2,6,4,7,1,3] => 101010
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [7,6,4,1,2,3,5] => [1,2,6,3,7,5,4] => 001011
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [6,4,1,2,3,7,5] => [2,3,6,5,7,1,4] => 001010
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [7,6,3,2,1,4,5] => [5,4,1,2,7,6,3] => 110011
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [6,3,2,1,4,7,5] => [5,4,2,6,7,1,3] => 110010
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [7,6,2,3,1,4,5] => [5,1,2,3,7,6,4] => 100011
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [6,2,3,1,4,7,5] => [5,2,3,6,7,1,4] => 100010
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [7,6,3,1,2,4,5] => [1,5,2,3,7,6,4] => 010011
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [6,3,1,2,4,7,5] => [2,5,3,6,7,1,4] => 010010
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [7,6,2,1,3,4,5] => [4,1,2,3,7,6,5] => 100011
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [6,2,1,3,4,7,5] => [4,2,3,6,7,1,5] => 100010
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => [1,2,3,4,7,6,5] => 000011
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [6,1,2,3,4,7,5] => [2,3,4,6,7,1,5] => 000010
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [7,5,4,3,2,1,6] => [6,5,4,3,1,7,2] => 111101
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [7,4,5,3,2,1,6] => [6,5,4,1,2,7,3] => 111001
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [7,5,3,4,2,1,6] => [6,5,1,4,2,7,3] => 110101
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [7,4,3,5,2,1,6] => [6,5,3,1,2,7,4] => 111001
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [7,3,4,5,2,1,6] => [6,5,1,2,3,7,4] => 110001
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [7,5,4,2,3,1,6] => [6,1,5,4,2,7,3] => 101101
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [7,4,2,5,3,1,6] => [6,4,5,1,2,7,3] => 101001
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [7,5,3,2,4,1,6] => [6,4,1,5,2,7,3] => 110101
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [7,5,2,3,4,1,6] => [6,1,2,5,3,7,4] => 100101
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [7,4,3,2,5,1,6] => [6,4,3,1,2,7,5] => 111001
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [7,3,4,2,5,1,6] => [6,4,1,2,3,7,5] => 110001
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [7,4,2,3,5,1,6] => [6,1,4,2,3,7,5] => 101001
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [7,3,2,4,5,1,6] => [6,3,1,2,4,7,5] => 110001
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [7,2,3,4,5,1,6] => [6,1,2,3,4,7,5] => 100001
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [7,5,4,3,1,2,6] => [1,6,5,4,2,7,3] => 011101
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [7,4,5,1,3,2,6] => [2,6,5,1,3,7,4] => 011001
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [7,5,3,1,4,2,6] => [5,6,1,4,2,7,3] => 010101
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [7,4,3,1,5,2,6] => [5,6,3,1,2,7,4] => 011001
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [7,3,1,4,5,2,6] => [4,6,1,2,3,7,5] => 010001
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [7,5,4,2,1,3,6] => [5,1,6,4,2,7,3] => 101101
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [7,4,2,1,5,3,6] => [5,4,6,1,2,7,3] => 101001
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [7,5,4,1,2,3,6] => [1,2,6,5,3,7,4] => 001101
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [7,4,1,2,5,3,6] => [2,5,6,1,3,7,4] => 001001
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [7,5,3,2,1,4,6] => [5,4,1,6,2,7,3] => 110101
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [7,5,2,3,1,4,6] => [5,1,2,6,3,7,4] => 100101
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [7,5,3,1,2,4,6] => [1,5,2,6,3,7,4] => 010101
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [7,5,2,1,3,4,6] => [4,1,2,6,3,7,5] => 100101
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [7,5,1,2,3,4,6] => [1,2,3,6,4,7,5] => 000101
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [7,4,3,2,1,5,6] => [5,4,3,1,2,7,6] => 111001
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [7,3,4,2,1,5,6] => [5,4,1,2,3,7,6] => 110001
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [7,4,2,3,1,5,6] => [5,1,4,2,3,7,6] => 101001
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [7,3,2,4,1,5,6] => [5,3,1,2,4,7,6] => 110001
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [7,2,3,4,1,5,6] => [5,1,2,3,4,7,6] => 100001
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [7,4,3,1,2,5,6] => [1,5,4,2,3,7,6] => 011001
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [7,3,1,4,2,5,6] => [4,5,1,2,3,7,6] => 010001
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [7,4,2,1,3,5,6] => [4,1,5,2,3,7,6] => 101001
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [7,4,1,2,3,5,6] => [1,2,5,3,4,7,6] => 001001
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [7,3,2,1,4,5,6] => [4,3,1,2,5,7,6] => 110001
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [7,2,3,1,4,5,6] => [4,1,2,3,5,7,6] => 100001
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [7,3,1,2,4,5,6] => [1,4,2,3,5,7,6] => 010001
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [7,2,1,3,4,5,6] => [3,1,2,4,5,7,6] => 100001
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => [1,2,3,4,5,7,6] => 000001
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 111110
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1,7] => [6,5,4,3,1,2,7] => 111100
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [6,4,5,3,2,1,7] => [6,5,4,1,3,2,7] => 111010
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1,7] => [6,5,4,2,1,3,7] => 111100
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => [6,5,4,1,2,3,7] => 111000
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [6,5,3,4,2,1,7] => [6,5,1,4,3,2,7] => 110110
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [5,3,6,4,2,1,7] => [6,5,3,4,1,2,7] => 110100
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [6,4,3,5,2,1,7] => [6,5,3,1,4,2,7] => 111010
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [6,3,4,5,2,1,7] => [6,5,1,2,4,3,7] => 110010
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1,7] => [6,5,3,2,1,4,7] => 111100
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1,7] => [6,5,3,1,2,4,7] => 111000
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [5,3,4,6,2,1,7] => [6,5,1,3,2,4,7] => 110100
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1,7] => [6,5,2,1,3,4,7] => 111000
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1,7] => [6,5,1,2,3,4,7] => 110000
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [6,5,4,2,3,1,7] => [6,1,5,4,3,2,7] => 101110
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [5,6,2,4,3,1,7] => [6,2,5,4,1,3,7] => 101100
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [6,4,2,5,3,1,7] => [6,4,5,1,3,2,7] => 101010
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [5,4,2,6,3,1,7] => [6,4,5,2,1,3,7] => 101100
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [4,2,5,6,3,1,7] => [6,3,5,1,2,4,7] => 101000
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [6,5,3,2,4,1,7] => [6,4,1,5,3,2,7] => 110110
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [5,3,2,6,4,1,7] => [6,4,3,5,1,2,7] => 110100
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [6,5,2,3,4,1,7] => [6,1,2,5,4,3,7] => 100110
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [5,2,3,6,4,1,7] => [6,2,4,5,1,3,7] => 100100
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [6,4,3,2,5,1,7] => [6,4,3,1,5,2,7] => 111010
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [6,3,4,2,5,1,7] => [6,4,1,2,5,3,7] => 110010
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [6,4,2,3,5,1,7] => [6,1,4,2,5,3,7] => 101010
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [6,3,2,4,5,1,7] => [6,3,1,2,5,4,7] => 110010
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [6,2,3,4,5,1,7] => [6,1,2,3,5,4,7] => 100010
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => [6,4,3,2,1,5,7] => 111100
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1,7] => [6,4,3,1,2,5,7] => 111000
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [5,3,4,2,6,1,7] => [6,4,1,3,2,5,7] => 110100
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1,7] => [6,4,2,1,3,5,7] => 111000
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1,7] => [6,4,1,2,3,5,7] => 110000
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [5,4,2,3,6,1,7] => [6,1,4,3,2,5,7] => 101100
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [4,2,5,3,6,1,7] => [6,3,4,1,2,5,7] => 101000
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [5,3,2,4,6,1,7] => [6,3,1,4,2,5,7] => 110100
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [5,2,3,4,6,1,7] => [6,1,2,4,3,5,7] => 100100
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => [6,3,2,1,4,5,7] => 111000
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1,7] => [6,3,1,2,4,5,7] => 110000
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [4,2,3,5,6,1,7] => [6,1,3,2,4,5,7] => 101000
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => [6,2,1,3,4,5,7] => 110000
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => 100000
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [6,5,4,3,1,2,7] => [1,6,5,4,3,2,7] => 011110
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [5,6,4,1,3,2,7] => [2,6,5,4,1,3,7] => 011100
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [6,4,5,1,3,2,7] => [2,6,5,1,4,3,7] => 011010
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [5,4,6,1,3,2,7] => [2,6,5,3,1,4,7] => 011100
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [4,5,1,6,3,2,7] => [5,6,4,1,2,3,7] => 011000
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [6,5,3,1,4,2,7] => [5,6,1,4,3,2,7] => 010110
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [5,3,1,6,4,2,7] => [5,6,3,4,1,2,7] => 010100
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [6,4,3,1,5,2,7] => [5,6,3,1,4,2,7] => 011010
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [6,3,1,4,5,2,7] => [4,6,1,2,5,3,7] => 010010
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [5,4,3,1,6,2,7] => [5,6,3,2,1,4,7] => 011100
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [4,5,1,3,6,2,7] => [2,6,4,1,3,5,7] => 011000
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [5,3,1,4,6,2,7] => [4,6,1,3,2,5,7] => 010100
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [4,3,1,5,6,2,7] => [4,6,2,1,3,5,7] => 011000
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [3,1,4,5,6,2,7] => [3,6,1,2,4,5,7] => 010000
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [6,5,4,2,1,3,7] => [5,1,6,4,3,2,7] => 101110
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [5,6,2,1,4,3,7] => [5,2,6,4,1,3,7] => 101100
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [6,4,2,1,5,3,7] => [5,4,6,1,3,2,7] => 101010
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [5,4,2,1,6,3,7] => [5,4,6,2,1,3,7] => 101100
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [4,2,1,5,6,3,7] => [4,3,6,1,2,5,7] => 101000
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => [1,2,6,5,4,3,7] => 001110
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [5,6,1,2,4,3,7] => [2,3,6,5,1,4,7] => 001100
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [6,4,1,2,5,3,7] => [2,5,6,1,4,3,7] => 001010
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [5,4,1,2,6,3,7] => [2,5,6,3,1,4,7] => 001100
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => [2,4,6,1,3,5,7] => 001000
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [6,5,3,2,1,4,7] => [5,4,1,6,3,2,7] => 110110
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [5,3,2,1,6,4,7] => [5,4,3,6,1,2,7] => 110100
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [6,5,2,3,1,4,7] => [5,1,2,6,4,3,7] => 100110
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [5,2,3,1,6,4,7] => [5,2,4,6,1,3,7] => 100100
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [6,5,3,1,2,4,7] => [1,5,2,6,4,3,7] => 010110
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [5,3,1,2,6,4,7] => [2,5,4,6,1,3,7] => 010100
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [6,5,2,1,3,4,7] => [4,1,2,6,5,3,7] => 100110
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [5,2,1,3,6,4,7] => [4,2,5,6,1,3,7] => 100100
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => [1,2,3,6,5,4,7] => 000110
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [5,1,2,3,6,4,7] => [2,3,5,6,1,4,7] => 000100
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [6,4,3,2,1,5,7] => [5,4,3,1,6,2,7] => 111010
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [6,3,4,2,1,5,7] => [5,4,1,2,6,3,7] => 110010
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [6,4,2,3,1,5,7] => [5,1,4,2,6,3,7] => 101010
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [6,3,2,4,1,5,7] => [5,3,1,2,6,4,7] => 110010
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [6,2,3,4,1,5,7] => [5,1,2,3,6,4,7] => 100010
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [6,4,3,1,2,5,7] => [1,5,4,2,6,3,7] => 011010
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [6,3,1,4,2,5,7] => [4,5,1,2,6,3,7] => 010010
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [6,4,2,1,3,5,7] => [4,1,5,2,6,3,7] => 101010
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [6,4,1,2,3,5,7] => [1,2,5,3,6,4,7] => 001010
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [6,3,2,1,4,5,7] => [4,3,1,2,6,5,7] => 110010
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [6,2,3,1,4,5,7] => [4,1,2,3,6,5,7] => 100010
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [6,3,1,2,4,5,7] => [1,4,2,3,6,5,7] => 010010
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [6,2,1,3,4,5,7] => [3,1,2,4,6,5,7] => 100010
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => [1,2,3,4,6,5,7] => 000010
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 111100
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6,7] => [5,4,3,1,2,6,7] => 111000
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [5,3,4,2,1,6,7] => [5,4,1,3,2,6,7] => 110100
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6,7] => [5,4,2,1,3,6,7] => 111000
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7] => [5,4,1,2,3,6,7] => 110000
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [5,4,2,3,1,6,7] => [5,1,4,3,2,6,7] => 101100
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [4,2,5,3,1,6,7] => [5,3,4,1,2,6,7] => 101000
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [5,3,2,4,1,6,7] => [5,3,1,4,2,6,7] => 110100
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [5,2,3,4,1,6,7] => [5,1,2,4,3,6,7] => 100100
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => [5,3,2,1,4,6,7] => 111000
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6,7] => [5,3,1,2,4,6,7] => 110000
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [4,2,3,5,1,6,7] => [5,1,3,2,4,6,7] => 101000
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => [5,2,1,3,4,6,7] => 110000
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => 100000
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [5,4,3,1,2,6,7] => [1,5,4,3,2,6,7] => 011100
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [4,5,1,3,2,6,7] => [2,5,4,1,3,6,7] => 011000
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [5,3,1,4,2,6,7] => [4,5,1,3,2,6,7] => 010100
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [4,3,1,5,2,6,7] => [4,5,2,1,3,6,7] => 011000
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [3,1,4,5,2,6,7] => [3,5,1,2,4,6,7] => 010000
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [5,4,2,1,3,6,7] => [4,1,5,3,2,6,7] => 101100
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [4,2,1,5,3,6,7] => [4,3,5,1,2,6,7] => 101000
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => [1,2,5,4,3,6,7] => 001100
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [4,1,2,5,3,6,7] => [2,4,5,1,3,6,7] => 001000
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [5,3,2,1,4,6,7] => [4,3,1,5,2,6,7] => 110100
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [5,2,3,1,4,6,7] => [4,1,2,5,3,6,7] => 100100
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [5,3,1,2,4,6,7] => [1,4,2,5,3,6,7] => 010100
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [5,2,1,3,4,6,7] => [3,1,2,5,4,6,7] => 100100
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => [1,2,3,5,4,6,7] => 000100
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 111000
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6,7] => [4,3,1,2,5,6,7] => 110000
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [4,2,3,1,5,6,7] => [4,1,3,2,5,6,7] => 101000
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => [4,2,1,3,5,6,7] => 110000
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => 100000
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [4,3,1,2,5,6,7] => [1,4,3,2,5,6,7] => 011000
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => 010000
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [4,2,1,3,5,6,7] => [3,1,4,2,5,6,7] => 101000
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => [1,2,4,3,5,6,7] => 001000
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 110000
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => 100000
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => 010000
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 100000
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [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] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [7,8,6,5,4,3,2,1] => [8,7,6,5,4,3,1,2] => 1111110
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [6,8,7,5,4,3,2,1] => [8,6,7,5,4,3,2,1] => [8,7,6,5,4,1,3,2] => 1111101
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [7,6,8,5,4,3,2,1] => [8,7,6,5,4,2,1,3] => 1111110
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [6,7,8,5,4,3,2,1] => [8,7,6,5,4,1,2,3] => 1111100
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [5,8,7,6,4,3,2,1] => [8,7,5,6,4,3,2,1] => [8,7,6,5,1,4,3,2] => 1111011
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [5,7,8,6,4,3,2,1] => [7,5,8,6,4,3,2,1] => [8,7,6,5,3,4,1,2] => 1111010
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => [8,6,5,7,4,3,2,1] => [8,7,6,5,3,1,4,2] => 1111101
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [5,6,8,7,4,3,2,1] => [8,5,6,7,4,3,2,1] => [8,7,6,5,1,2,4,3] => 1111001
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [7,6,5,8,4,3,2,1] => [8,7,6,5,3,2,1,4] => 1111110
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => [6,7,5,8,4,3,2,1] => [8,7,6,5,3,1,2,4] => 1111100
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => [7,5,6,8,4,3,2,1] => [8,7,6,5,1,3,2,4] => 1111010
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [6,5,7,8,4,3,2,1] => [8,7,6,5,2,1,3,4] => 1111100
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [5,6,7,8,4,3,2,1] => [8,7,6,5,1,2,3,4] => 1111000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => [8,7,6,4,5,3,2,1] => [8,7,6,1,5,4,3,2] => 1110111
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => [8,6,4,7,5,3,2,1] => [8,7,6,4,5,1,3,2] => 1110101
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [4,7,6,8,5,3,2,1] => [7,6,4,8,5,3,2,1] => [8,7,6,4,5,2,1,3] => 1110110
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [4,6,7,8,5,3,2,1] => [6,4,7,8,5,3,2,1] => [8,7,6,3,5,1,2,4] => 1110100
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [5,4,8,7,6,3,2,1] => [8,7,5,4,6,3,2,1] => [8,7,6,4,1,5,3,2] => 1111011
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [4,5,8,7,6,3,2,1] => [8,7,4,5,6,3,2,1] => [8,7,6,1,2,5,4,3] => 1110011
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [4,5,7,8,6,3,2,1] => [7,4,5,8,6,3,2,1] => [8,7,6,2,4,5,1,3] => 1110010
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [6,5,4,8,7,3,2,1] => [8,6,5,4,7,3,2,1] => [8,7,6,4,3,1,5,2] => 1111101
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [5,6,4,8,7,3,2,1] => [8,5,6,4,7,3,2,1] => [8,7,6,4,1,2,5,3] => 1111001
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [4,6,5,8,7,3,2,1] => [8,6,4,5,7,3,2,1] => [8,7,6,1,4,2,5,3] => 1110101
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => [8,4,5,6,7,3,2,1] => [8,7,6,1,2,3,5,4] => 1110001
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [7,6,5,4,8,3,2,1] => [8,7,6,4,3,2,1,5] => 1111110
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => [6,7,5,4,8,3,2,1] => [8,7,6,4,3,1,2,5] => 1111100
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [5,7,6,4,8,3,2,1] => [7,5,6,4,8,3,2,1] => [8,7,6,4,1,3,2,5] => 1111010
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [6,5,7,4,8,3,2,1] => [8,7,6,4,2,1,3,5] => 1111100
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => [5,6,7,4,8,3,2,1] => [8,7,6,4,1,2,3,5] => 1111000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1] => [7,6,4,5,8,3,2,1] => [8,7,6,1,4,3,2,5] => 1110110
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [4,6,7,5,8,3,2,1] => [6,4,7,5,8,3,2,1] => [8,7,6,3,4,1,2,5] => 1110100
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [5,4,7,6,8,3,2,1] => [7,5,4,6,8,3,2,1] => [8,7,6,3,1,4,2,5] => 1111010
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [4,5,7,6,8,3,2,1] => [7,4,5,6,8,3,2,1] => [8,7,6,1,2,4,3,5] => 1110010
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => [6,5,4,7,8,3,2,1] => [8,7,6,3,2,1,4,5] => 1111100
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => [5,6,4,7,8,3,2,1] => [8,7,6,3,1,2,4,5] => 1111000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [4,6,5,7,8,3,2,1] => [6,4,5,7,8,3,2,1] => [8,7,6,1,3,2,4,5] => 1110100
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => [5,4,6,7,8,3,2,1] => [8,7,6,2,1,3,4,5] => 1111000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [4,5,6,7,8,3,2,1] => [8,7,6,1,2,3,4,5] => 1110000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [3,8,7,6,5,4,2,1] => [8,7,6,5,3,4,2,1] => [8,7,1,6,5,4,3,2] => 1101111
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [3,7,8,6,5,4,2,1] => [7,8,6,3,5,4,2,1] => [8,7,2,6,5,4,1,3] => 1101110
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [3,6,8,7,5,4,2,1] => [8,6,7,3,5,4,2,1] => [8,7,2,6,5,1,4,3] => 1101101
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => [8,7,5,3,6,4,2,1] => [8,7,5,6,1,4,3,2] => 1101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => [7,5,3,8,6,4,2,1] => [8,7,5,6,3,4,1,2] => 1101010
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [3,6,5,8,7,4,2,1] => [8,6,5,3,7,4,2,1] => [8,7,5,6,3,1,4,2] => 1101101
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [3,7,6,5,8,4,2,1] => [7,6,5,3,8,4,2,1] => [8,7,5,6,3,2,1,4] => 1101110
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [3,6,7,5,8,4,2,1] => [6,7,3,5,8,4,2,1] => [8,7,2,6,4,1,3,5] => 1101100
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [3,5,6,7,8,4,2,1] => [5,3,6,7,8,4,2,1] => [8,7,3,6,1,2,4,5] => 1101000
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => [8,7,6,4,3,5,2,1] => [8,7,5,1,6,4,3,2] => 1110111
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [4,3,6,8,7,5,2,1] => [8,6,4,3,7,5,2,1] => [8,7,5,4,6,1,3,2] => 1110101
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [4,3,6,7,8,5,2,1] => [6,4,3,7,8,5,2,1] => [8,7,4,3,6,1,2,5] => 1110100
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [3,4,8,7,6,5,2,1] => [8,7,6,3,4,5,2,1] => [8,7,1,2,6,5,4,3] => 1100111
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => [6,3,4,7,8,5,2,1] => [8,7,2,4,6,1,3,5] => 1100100
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [5,4,3,8,7,6,2,1] => [8,7,5,4,3,6,2,1] => [8,7,5,4,1,6,3,2] => 1111011
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [4,5,3,8,7,6,2,1] => [8,7,4,5,3,6,2,1] => [8,7,5,1,2,6,4,3] => 1110011
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [3,5,4,7,8,6,2,1] => [7,5,3,4,8,6,2,1] => [8,7,2,5,4,6,1,3] => 1101010
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [4,3,5,8,7,6,2,1] => [8,7,4,3,5,6,2,1] => [8,7,4,1,2,6,5,3] => 1110011
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [4,3,5,7,8,6,2,1] => [7,4,3,5,8,6,2,1] => [8,7,4,2,5,6,1,3] => 1110010
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [3,4,5,8,7,6,2,1] => [8,7,3,4,5,6,2,1] => [8,7,1,2,3,6,5,4] => 1100011
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [6,5,4,3,8,7,2,1] => [8,6,5,4,3,7,2,1] => [8,7,5,4,3,1,6,2] => 1111101
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [5,4,6,3,8,7,2,1] => [8,5,4,6,3,7,2,1] => [8,7,5,3,1,2,6,4] => 1111001
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [3,5,6,4,8,7,2,1] => [8,5,3,6,4,7,2,1] => [8,7,4,5,1,2,6,3] => 1101001
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => [8,6,4,3,5,7,2,1] => [8,7,4,1,5,2,6,3] => 1110101
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [4,3,5,6,8,7,2,1] => [8,4,3,5,6,7,2,1] => [8,7,3,1,2,4,6,5] => 1110001
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [3,4,5,6,8,7,2,1] => [8,3,4,5,6,7,2,1] => [8,7,1,2,3,4,6,5] => 1100001
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,8,2,1] => [8,7,5,4,3,2,1,6] => 1111110
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => [6,7,5,4,3,8,2,1] => [8,7,5,4,3,1,2,6] => 1111100
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [5,7,6,4,3,8,2,1] => [7,5,6,4,3,8,2,1] => [8,7,5,4,1,3,2,6] => 1111010
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => [5,6,7,4,3,8,2,1] => [8,7,5,4,1,2,3,6] => 1111000
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [4,7,6,5,3,8,2,1] => [7,6,4,5,3,8,2,1] => [8,7,5,1,4,3,2,6] => 1110110
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [5,4,7,6,3,8,2,1] => [7,5,4,6,3,8,2,1] => [8,7,5,3,1,4,2,6] => 1111010
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [4,5,7,6,3,8,2,1] => [7,4,5,6,3,8,2,1] => [8,7,5,1,2,4,3,6] => 1110010
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => [6,5,4,7,3,8,2,1] => [8,7,5,3,2,1,4,6] => 1111100
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [5,4,6,7,3,8,2,1] => [8,7,5,2,1,3,4,6] => 1111000
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => [4,5,6,7,3,8,2,1] => [8,7,5,1,2,3,4,6] => 1110000
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [3,6,7,5,4,8,2,1] => [6,7,3,5,4,8,2,1] => [8,7,2,5,4,1,3,6] => 1101100
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [3,5,7,6,4,8,2,1] => [7,5,3,6,4,8,2,1] => [8,7,4,5,1,3,2,6] => 1101010
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [3,5,6,7,4,8,2,1] => [5,3,6,7,4,8,2,1] => [8,7,3,5,1,2,4,6] => 1101000
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [3,4,7,6,5,8,2,1] => [7,6,3,4,5,8,2,1] => [8,7,1,2,5,4,3,6] => 1100110
[.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [3,4,6,7,5,8,2,1] => [6,3,4,7,5,8,2,1] => [8,7,2,4,5,1,3,6] => 1100100
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [5,4,3,7,6,8,2,1] => [7,5,4,3,6,8,2,1] => [8,7,4,3,1,5,2,6] => 1111010
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [3,5,4,7,6,8,2,1] => [7,5,3,4,6,8,2,1] => [8,7,1,4,2,5,3,6] => 1101010
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => [6,5,4,3,7,8,2,1] => [8,7,4,3,2,1,5,6] => 1111100
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => [4,5,6,3,7,8,2,1] => [8,7,4,1,2,3,5,6] => 1110000
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [3,6,5,4,7,8,2,1] => [6,5,3,4,7,8,2,1] => [8,7,1,4,3,2,5,6] => 1101100
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [3,5,6,4,7,8,2,1] => [5,3,6,4,7,8,2,1] => [8,7,3,4,1,2,5,6] => 1101000
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [3,4,6,5,7,8,2,1] => [6,3,4,5,7,8,2,1] => [8,7,1,2,4,3,5,6] => 1100100
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => [5,4,3,6,7,8,2,1] => [8,7,3,2,1,4,5,6] => 1111000
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [3,5,4,6,7,8,2,1] => [5,3,4,6,7,8,2,1] => [8,7,1,3,2,4,5,6] => 1101000
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,8,2,1] => [8,7,2,1,3,4,5,6] => 1110000
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [3,4,5,6,7,8,2,1] => [8,7,1,2,3,4,5,6] => 1100000
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => [8,7,6,5,4,2,3,1] => [8,1,7,6,5,4,3,2] => 1011111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [2,7,8,6,5,4,3,1] => [7,8,6,5,2,4,3,1] => [8,2,7,6,5,4,1,3] => 1011110
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => [8,6,7,5,2,4,3,1] => [8,2,7,6,5,1,4,3] => 1011101
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [2,6,5,8,7,4,3,1] => [8,6,5,7,2,4,3,1] => [8,2,7,6,4,1,5,3] => 1011101
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [2,7,6,5,8,4,3,1] => [7,6,5,8,2,4,3,1] => [8,2,7,6,4,3,1,5] => 1011110
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [2,6,7,5,8,4,3,1] => [6,7,5,2,8,4,3,1] => [8,6,7,5,3,1,2,4] => 1011100
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [2,5,7,6,8,4,3,1] => [7,5,6,2,8,4,3,1] => [8,6,7,5,1,3,2,4] => 1011010
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [2,5,6,7,8,4,3,1] => [5,6,2,7,8,4,3,1] => [8,5,7,6,1,2,3,4] => 1011000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [2,4,8,7,6,5,3,1] => [8,7,6,4,2,5,3,1] => [8,6,7,1,5,4,3,2] => 1010111
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => [8,6,4,2,7,5,3,1] => [8,6,7,4,5,1,3,2] => 1010101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [2,6,5,4,8,7,3,1] => [8,6,5,4,2,7,3,1] => [8,6,7,4,3,1,5,2] => 1011101
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [2,4,6,5,8,7,3,1] => [8,6,4,2,5,7,3,1] => [8,5,7,1,4,2,6,3] => 1010101
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [2,4,5,6,8,7,3,1] => [8,4,2,5,6,7,3,1] => [8,4,7,1,2,3,6,5] => 1010001
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [2,7,6,5,4,8,3,1] => [7,6,5,4,2,8,3,1] => [8,6,7,4,3,2,1,5] => 1011110
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [2,6,7,5,4,8,3,1] => [6,7,5,2,4,8,3,1] => [8,2,7,5,4,1,3,6] => 1011100
[.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [2,5,6,7,4,8,3,1] => [5,6,2,7,4,8,3,1] => [8,5,7,4,1,2,3,6] => 1011000
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [2,4,7,6,5,8,3,1] => [7,6,4,2,5,8,3,1] => [8,5,7,1,4,3,2,6] => 1010110
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [2,5,4,7,6,8,3,1] => [7,5,4,2,6,8,3,1] => [8,5,7,3,1,4,2,6] => 1011010
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [2,5,6,4,7,8,3,1] => [5,6,2,4,7,8,3,1] => [8,2,7,4,1,3,5,6] => 1011000
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [2,4,5,6,7,8,3,1] => [4,2,5,6,7,8,3,1] => [8,3,7,1,2,4,5,6] => 1010000
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => [8,7,6,5,3,2,4,1] => [8,6,1,7,5,4,3,2] => 1101111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [3,2,7,8,6,5,4,1] => [7,8,6,3,2,5,4,1] => [8,6,2,7,5,4,1,3] => 1101110
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [3,2,7,6,8,5,4,1] => [7,6,8,3,2,5,4,1] => [8,6,2,7,5,3,1,4] => 1101110
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [3,2,5,8,7,6,4,1] => [8,7,5,3,2,6,4,1] => [8,6,5,7,1,4,3,2] => 1101011
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [3,2,5,7,8,6,4,1] => [7,5,3,2,8,6,4,1] => [8,6,5,7,3,4,1,2] => 1101010
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [3,2,7,6,5,8,4,1] => [7,6,5,3,2,8,4,1] => [8,6,5,7,3,2,1,4] => 1101110
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [3,2,6,7,5,8,4,1] => [6,7,3,2,5,8,4,1] => [8,5,2,7,4,1,3,6] => 1101100
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => [8,7,6,5,2,3,4,1] => [8,1,2,7,6,5,4,3] => 1001111
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [2,3,6,7,8,5,4,1] => [6,7,2,3,8,5,4,1] => [8,3,6,7,5,1,2,4] => 1001100
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => [8,5,2,3,6,7,4,1] => [8,2,5,7,1,3,6,4] => 1001001
[.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [2,3,6,5,7,8,4,1] => [6,5,2,3,7,8,4,1] => [8,2,5,7,3,1,4,6] => 1001100
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [2,3,5,6,7,8,4,1] => [5,2,3,6,7,8,4,1] => [8,2,4,7,1,3,5,6] => 1001000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => [8,7,6,4,3,2,5,1] => [8,6,5,1,7,4,3,2] => 1110111
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [4,3,2,6,8,7,5,1] => [8,6,4,3,2,7,5,1] => [8,6,5,4,7,1,3,2] => 1110101
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => [8,7,6,3,4,2,5,1] => [8,6,1,2,7,5,4,3] => 1100111
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [3,4,2,6,7,8,5,1] => [6,3,4,2,7,8,5,1] => [8,5,2,4,7,1,3,6] => 1100100
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [2,4,3,6,8,7,5,1] => [8,6,4,2,3,7,5,1] => [8,2,6,5,7,1,4,3] => 1010101
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [3,2,4,8,7,6,5,1] => [8,7,6,3,2,4,5,1] => [8,5,1,2,7,6,4,3] => 1100111
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => [8,7,6,2,3,4,5,1] => [8,1,2,3,7,6,5,4] => 1000111
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [2,3,4,7,8,6,5,1] => [7,8,2,3,4,6,5,1] => [8,2,3,4,7,6,1,5] => 1000110
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [2,3,4,6,7,8,5,1] => [6,2,3,4,7,8,5,1] => [8,2,3,5,7,1,4,6] => 1000100
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [5,4,3,2,7,8,6,1] => [7,5,4,3,2,8,6,1] => [8,6,5,4,3,7,1,2] => 1111010
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [4,5,3,2,7,8,6,1] => [7,4,5,3,2,8,6,1] => [8,6,5,2,4,7,1,3] => 1110010
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [4,3,5,2,8,7,6,1] => [8,7,4,3,5,2,6,1] => [8,6,4,1,2,7,5,3] => 1110011
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => [8,7,5,4,2,3,6,1] => [8,1,6,5,2,7,4,3] => 1011011
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [2,4,5,3,8,7,6,1] => [8,7,4,2,5,3,6,1] => [8,5,6,1,2,7,4,3] => 1010011
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [2,3,5,4,7,8,6,1] => [7,5,2,3,4,8,6,1] => [8,2,3,6,5,7,1,4] => 1001010
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [4,3,2,5,8,7,6,1] => [8,7,4,3,2,5,6,1] => [8,5,4,1,2,7,6,3] => 1110011
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [2,3,4,5,8,7,6,1] => [8,7,2,3,4,5,6,1] => [8,1,2,3,4,7,6,5] => 1000011
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [2,3,4,5,7,8,6,1] => [7,2,3,4,5,8,6,1] => [8,2,3,4,6,7,1,5] => 1000010
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [6,5,4,3,2,8,7,1] => [8,6,5,4,3,2,7,1] => [8,6,5,4,3,1,7,2] => 1111101
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [5,6,4,3,2,8,7,1] => [8,5,6,4,3,2,7,1] => [8,6,5,4,1,2,7,3] => 1111001
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [5,4,6,3,2,8,7,1] => [8,5,4,6,3,2,7,1] => [8,6,5,3,1,2,7,4] => 1111001
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [4,3,6,5,2,8,7,1] => [8,6,4,3,5,2,7,1] => [8,6,4,1,5,2,7,3] => 1110101
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => [8,4,5,3,6,2,7,1] => [8,6,4,1,2,3,7,5] => 1110001
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [3,4,5,6,2,8,7,1] => [8,3,4,5,6,2,7,1] => [8,6,1,2,3,4,7,5] => 1100001
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => [8,6,5,3,2,4,7,1] => [8,5,1,6,4,2,7,3] => 1101101
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [4,3,2,6,5,8,7,1] => [8,6,4,3,2,5,7,1] => [8,5,4,1,6,2,7,3] => 1110101
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => [8,6,4,2,3,5,7,1] => [8,1,5,2,6,3,7,4] => 1010101
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [2,3,4,6,5,8,7,1] => [8,6,2,3,4,5,7,1] => [8,1,2,3,6,4,7,5] => 1000101
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [4,5,3,2,6,8,7,1] => [8,4,5,3,2,6,7,1] => [8,5,4,1,2,3,7,6] => 1110001
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [3,5,4,2,6,8,7,1] => [8,5,3,4,2,6,7,1] => [8,5,1,4,2,3,7,6] => 1101001
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [4,3,2,5,6,8,7,1] => [8,4,3,2,5,6,7,1] => [8,4,3,1,2,5,7,6] => 1110001
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => [8,4,2,3,5,6,7,1] => [8,1,4,2,3,5,7,6] => 1010001
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [3,2,4,5,6,8,7,1] => [8,3,2,4,5,6,7,1] => [8,3,1,2,4,5,7,6] => 1100001
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => [8,2,3,4,5,6,7,1] => [8,1,2,3,4,5,7,6] => 1000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1] => [8,6,5,4,3,2,1,7] => 1111110
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [6,7,5,4,3,2,8,1] => [8,6,5,4,3,1,2,7] => 1111100
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [5,7,6,4,3,2,8,1] => [7,5,6,4,3,2,8,1] => [8,6,5,4,1,3,2,7] => 1111010
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [6,5,7,4,3,2,8,1] => [8,6,5,4,2,1,3,7] => 1111100
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => [5,6,7,4,3,2,8,1] => [8,6,5,4,1,2,3,7] => 1111000
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [4,7,6,5,3,2,8,1] => [7,6,4,5,3,2,8,1] => [8,6,5,1,4,3,2,7] => 1110110
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [4,6,7,5,3,2,8,1] => [6,4,7,5,3,2,8,1] => [8,6,5,3,4,1,2,7] => 1110100
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [4,5,7,6,3,2,8,1] => [7,4,5,6,3,2,8,1] => [8,6,5,1,2,4,3,7] => 1110010
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1] => [6,5,4,7,3,2,8,1] => [8,6,5,3,2,1,4,7] => 1111100
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [4,6,5,7,3,2,8,1] => [6,4,5,7,3,2,8,1] => [8,6,5,1,3,2,4,7] => 1110100
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => [4,5,6,7,3,2,8,1] => [8,6,5,1,2,3,4,7] => 1110000
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [3,7,6,5,4,2,8,1] => [7,6,5,3,4,2,8,1] => [8,6,1,5,4,3,2,7] => 1101110
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [4,3,7,6,5,2,8,1] => [7,6,4,3,5,2,8,1] => [8,6,4,1,5,3,2,7] => 1110110
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [3,4,7,6,5,2,8,1] => [7,6,3,4,5,2,8,1] => [8,6,1,2,5,4,3,7] => 1100110
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [4,5,3,7,6,2,8,1] => [7,4,5,3,6,2,8,1] => [8,6,4,1,2,5,3,7] => 1110010
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [3,5,4,7,6,2,8,1] => [7,5,3,4,6,2,8,1] => [8,6,1,4,2,5,3,7] => 1101010
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [3,4,5,7,6,2,8,1] => [7,3,4,5,6,2,8,1] => [8,6,1,2,3,5,4,7] => 1100010
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [6,5,4,3,7,2,8,1] => [8,6,4,3,2,1,5,7] => 1111100
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [4,6,5,3,7,2,8,1] => [6,4,5,3,7,2,8,1] => [8,6,4,1,3,2,5,7] => 1110100
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,8,1] => [8,6,4,2,1,3,5,7] => 1111000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => [4,5,6,3,7,2,8,1] => [8,6,4,1,2,3,5,7] => 1110000
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [3,6,5,4,7,2,8,1] => [6,5,3,4,7,2,8,1] => [8,6,1,4,3,2,5,7] => 1101100
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => [5,3,6,4,7,2,8,1] => [8,6,3,4,1,2,5,7] => 1101000
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => [6,4,3,5,7,2,8,1] => [8,6,3,1,4,2,5,7] => 1110100
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [3,4,6,5,7,2,8,1] => [6,3,4,5,7,2,8,1] => [8,6,1,2,4,3,5,7] => 1100100
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => [3,4,5,6,7,2,8,1] => [8,6,1,2,3,4,5,7] => 1100000
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1] => [7,6,5,4,2,3,8,1] => [8,1,6,5,4,3,2,7] => 1011110
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [2,5,7,6,4,3,8,1] => [7,5,6,2,4,3,8,1] => [8,2,6,5,1,4,3,7] => 1011010
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [2,5,6,7,4,3,8,1] => [5,6,2,7,4,3,8,1] => [8,5,6,4,1,2,3,7] => 1011000
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [2,4,6,7,5,3,8,1] => [6,4,2,7,5,3,8,1] => [8,5,6,3,4,1,2,7] => 1010100
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [2,5,4,7,6,3,8,1] => [7,5,4,2,6,3,8,1] => [8,5,6,3,1,4,2,7] => 1011010
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [2,5,6,4,7,3,8,1] => [5,6,2,4,7,3,8,1] => [8,2,6,4,1,3,5,7] => 1011000
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => [6,4,2,5,7,3,8,1] => [8,4,6,1,3,2,5,7] => 1010100
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [2,5,4,6,7,3,8,1] => [5,4,2,6,7,3,8,1] => [8,4,6,2,1,3,5,7] => 1011000
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [2,4,5,6,7,3,8,1] => [4,2,5,6,7,3,8,1] => [8,3,6,1,2,4,5,7] => 1010000
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [2,3,7,6,5,4,8,1] => [7,6,5,2,3,4,8,1] => [8,1,2,6,5,4,3,7] => 1001110
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [2,3,5,6,7,4,8,1] => [5,2,3,6,7,4,8,1] => [8,2,4,6,1,3,5,7] => 1001000
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [2,4,3,7,6,5,8,1] => [7,6,4,2,3,5,8,1] => [8,1,5,2,6,4,3,7] => 1010110
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [2,4,3,6,7,5,8,1] => [6,4,2,3,7,5,8,1] => [8,2,5,4,6,1,3,7] => 1010100
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [3,2,4,7,6,5,8,1] => [7,6,3,2,4,5,8,1] => [8,4,1,2,6,5,3,7] => 1100110
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [2,3,4,7,6,5,8,1] => [7,6,2,3,4,5,8,1] => [8,1,2,3,6,5,4,7] => 1000110
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [2,3,4,6,7,5,8,1] => [6,2,3,4,7,5,8,1] => [8,2,3,5,6,1,4,7] => 1000100
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [2,5,4,3,7,6,8,1] => [7,5,4,2,3,6,8,1] => [8,1,5,4,2,6,3,7] => 1011010
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => [7,5,3,2,4,6,8,1] => [8,4,1,5,2,6,3,7] => 1101010
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [4,3,2,5,7,6,8,1] => [7,4,3,2,5,6,8,1] => [8,4,3,1,2,6,5,7] => 1110010
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [2,4,3,5,7,6,8,1] => [7,4,2,3,5,6,8,1] => [8,1,4,2,3,6,5,7] => 1010010
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1] => [7,3,2,4,5,6,8,1] => [8,3,1,2,4,6,5,7] => 1100010
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => [7,2,3,4,5,6,8,1] => [8,1,2,3,4,6,5,7] => 1000010
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => [6,5,4,3,2,7,8,1] => [8,5,4,3,2,1,6,7] => 1111100
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => [5,4,6,3,2,7,8,1] => [8,5,4,2,1,3,6,7] => 1111000
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => [4,5,6,3,2,7,8,1] => [8,5,4,1,2,3,6,7] => 1110000
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [3,4,6,5,2,7,8,1] => [6,3,4,5,2,7,8,1] => [8,5,1,2,4,3,6,7] => 1100100
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => [5,4,3,6,2,7,8,1] => [8,5,3,2,1,4,6,7] => 1111000
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => [4,3,5,6,2,7,8,1] => [8,5,2,1,3,4,6,7] => 1110000
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => [3,4,5,6,2,7,8,1] => [8,5,1,2,3,4,6,7] => 1100000
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [2,6,5,4,3,7,8,1] => [6,5,4,2,3,7,8,1] => [8,1,5,4,3,2,6,7] => 1011100
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [2,3,6,5,4,7,8,1] => [6,5,2,3,4,7,8,1] => [8,1,2,5,4,3,6,7] => 1001100
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [2,3,4,6,5,7,8,1] => [6,2,3,4,5,7,8,1] => [8,1,2,3,5,4,6,7] => 1000100
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,8,1] => [8,4,3,2,1,5,6,7] => 1111000
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [3,5,4,2,6,7,8,1] => [5,3,4,2,6,7,8,1] => [8,4,1,3,2,5,6,7] => 1101000
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => [4,3,5,2,6,7,8,1] => [8,4,2,1,3,5,6,7] => 1110000
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,8,1] => [8,4,1,2,3,5,6,7] => 1100000
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1] => [5,4,2,3,6,7,8,1] => [8,1,4,3,2,5,6,7] => 1011000
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [2,4,5,3,6,7,8,1] => [4,2,5,3,6,7,8,1] => [8,3,4,1,2,5,6,7] => 1010000
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1] => [5,2,3,4,6,7,8,1] => [8,1,2,4,3,5,6,7] => 1001000
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,8,1] => [8,3,2,1,4,5,6,7] => 1110000
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,8,1] => [8,3,1,2,4,5,6,7] => 1100000
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [2,4,3,5,6,7,8,1] => [4,2,3,5,6,7,8,1] => [8,1,3,2,4,5,6,7] => 1010000
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1] => [8,2,1,3,4,5,6,7] => 1100000
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => 1000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [8,7,6,5,4,3,1,2] => [1,8,7,6,5,4,3,2] => 0111111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => [7,8,6,5,4,1,3,2] => [2,8,7,6,5,4,1,3] => 0111110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => [8,6,7,5,4,1,3,2] => [2,8,7,6,5,1,4,3] => 0111101
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => [6,7,8,5,1,4,3,2] => [3,8,7,6,5,1,2,4] => 0111100
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => [8,7,5,6,4,1,3,2] => [2,8,7,6,1,5,4,3] => 0111011
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,5,6,8,7,4,3,2] => [8,5,6,7,1,4,3,2] => [3,8,7,6,1,2,5,4] => 0111001
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => [7,6,5,8,4,1,3,2] => [2,8,7,6,4,3,1,5] => 0111110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => [6,7,5,8,1,4,3,2] => [3,8,7,6,4,1,2,5] => 0111100
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,5,7,6,8,4,3,2] => [7,5,6,8,1,4,3,2] => [3,8,7,6,1,4,2,5] => 0111010
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,6,5,7,8,4,3,2] => [6,5,7,8,1,4,3,2] => [3,8,7,6,2,1,4,5] => 0111100
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => [5,6,7,1,8,4,3,2] => [7,8,6,5,1,2,3,4] => 0111000
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => [8,7,6,4,5,1,3,2] => [2,8,7,1,6,5,4,3] => 0110111
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => [8,6,4,7,1,5,3,2] => [3,8,7,5,6,1,4,2] => 0110101
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,4,7,6,8,5,3,2] => [7,6,4,8,1,5,3,2] => [3,8,7,5,6,2,1,4] => 0110110
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,5,4,8,7,6,3,2] => [8,7,5,4,6,1,3,2] => [2,8,7,5,1,6,4,3] => 0111011
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,5,4,7,8,6,3,2] => [7,5,4,8,1,6,3,2] => [3,8,7,5,4,6,1,2] => 0111010
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,5,4,6,8,7,3,2] => [8,5,4,6,1,7,3,2] => [7,8,6,3,1,2,5,4] => 0111001
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => [7,6,5,4,8,1,3,2] => [2,8,7,5,4,3,1,6] => 0111110
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,5,4,6,7,8,3,2] => [5,4,6,1,7,8,3,2] => [6,8,7,2,1,3,4,5] => 0111000
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => [8,7,6,5,3,1,4,2] => [7,8,1,6,5,4,3,2] => 0101111
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,3,7,8,6,5,4,2] => [7,8,6,3,1,5,4,2] => [7,8,2,6,5,4,1,3] => 0101110
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,3,7,6,8,5,4,2] => [7,6,8,3,1,5,4,2] => [7,8,2,6,5,3,1,4] => 0101110
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,3,6,7,8,5,4,2] => [6,7,3,1,8,5,4,2] => [7,8,5,6,4,1,2,3] => 0101100
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,3,5,8,7,6,4,2] => [8,7,5,3,1,6,4,2] => [7,8,5,6,1,4,3,2] => 0101011
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => [7,5,3,1,8,6,4,2] => [7,8,5,6,3,4,1,2] => 0101010
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,3,7,6,5,8,4,2] => [7,6,5,3,1,8,4,2] => [7,8,5,6,3,2,1,4] => 0101110
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,3,5,7,6,8,4,2] => [7,5,3,1,6,8,4,2] => [6,8,4,7,1,3,2,5] => 0101010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => [6,5,3,1,7,8,4,2] => [6,8,4,7,2,1,3,5] => 0101100
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => [5,3,1,6,7,8,4,2] => [5,8,3,7,1,2,4,6] => 0101000
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => [8,7,6,4,3,1,5,2] => [7,8,5,1,6,4,3,2] => 0110111
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,3,4,7,8,6,5,2] => [7,8,3,1,4,6,5,2] => [6,8,2,3,7,5,1,4] => 0100110
[[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,3,4,6,8,7,5,2] => [8,6,3,1,4,7,5,2] => [6,8,2,5,7,1,4,3] => 0100101
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,3,4,6,7,8,5,2] => [6,3,1,4,7,8,5,2] => [5,8,2,4,7,1,3,6] => 0100100
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,5,4,3,8,7,6,2] => [8,7,5,4,3,1,6,2] => [7,8,5,4,1,6,3,2] => 0111011
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,5,4,3,7,8,6,2] => [7,5,4,3,1,8,6,2] => [7,8,5,4,3,6,1,2] => 0111010
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,3,5,4,8,7,6,2] => [8,7,5,3,1,4,6,2] => [6,8,1,5,2,7,4,3] => 0101011
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,3,5,4,7,8,6,2] => [7,5,3,1,4,8,6,2] => [6,8,2,5,4,7,1,3] => 0101010
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,4,3,5,8,7,6,2] => [8,7,4,3,1,5,6,2] => [6,8,4,1,2,7,5,3] => 0110011
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,3,4,5,8,7,6,2] => [8,7,3,1,4,5,6,2] => [5,8,1,2,3,7,6,4] => 0100011
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => [8,6,5,4,3,1,7,2] => [7,8,5,4,3,1,6,2] => 0111101
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,3,5,6,4,8,7,2] => [8,5,3,1,6,4,7,2] => [6,8,4,5,1,2,7,3] => 0101001
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => [8,6,4,3,1,5,7,2] => [6,8,4,1,5,2,7,3] => 0110101
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,3,4,6,5,8,7,2] => [8,6,3,1,4,5,7,2] => [5,8,1,2,6,3,7,4] => 0100101
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,3,5,4,6,8,7,2] => [8,5,3,1,4,6,7,2] => [5,8,1,4,2,3,7,6] => 0101001
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,4,3,5,6,8,7,2] => [8,4,3,1,5,6,7,2] => [5,8,3,1,2,4,7,6] => 0110001
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => [8,3,1,4,5,6,7,2] => [4,8,1,2,3,5,7,6] => 0100001
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => [7,6,5,4,3,1,8,2] => [7,8,5,4,3,2,1,6] => 0111110
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,6,5,7,4,3,8,2] => [6,5,7,4,1,3,8,2] => [2,8,6,5,3,1,4,7] => 0111100
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => [6,4,7,1,5,3,8,2] => [3,8,6,4,5,1,2,7] => 0110100
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => [5,4,6,1,7,3,8,2] => [6,8,5,2,1,3,4,7] => 0111000
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => [4,5,1,6,7,3,8,2] => [5,8,6,1,2,3,4,7] => 0110000
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,3,5,7,6,4,8,2] => [7,5,3,1,6,4,8,2] => [6,8,4,5,1,3,2,7] => 0101010
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,3,5,6,7,4,8,2] => [5,3,1,6,7,4,8,2] => [5,8,3,6,1,2,4,7] => 0101000
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,4,3,6,7,5,8,2] => [6,4,3,1,7,5,8,2] => [6,8,4,3,5,1,2,7] => 0110100
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,3,4,6,7,5,8,2] => [6,3,1,4,7,5,8,2] => [5,8,2,4,6,1,3,7] => 0100100
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,3,5,4,7,6,8,2] => [7,5,3,1,4,6,8,2] => [5,8,1,4,2,6,3,7] => 0101010
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,4,3,5,7,6,8,2] => [7,4,3,1,5,6,8,2] => [5,8,3,1,2,6,4,7] => 0110010
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,3,4,5,7,6,8,2] => [7,3,1,4,5,6,8,2] => [4,8,1,2,3,6,5,7] => 0100010
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,6,5,4,3,7,8,2] => [6,5,4,3,1,7,8,2] => [6,8,4,3,2,1,5,7] => 0111100
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,5,4,6,3,7,8,2] => [5,4,6,1,3,7,8,2] => [2,8,5,3,1,4,6,7] => 0111000
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,4,3,6,5,7,8,2] => [6,4,3,1,5,7,8,2] => [5,8,3,1,4,2,6,7] => 0110100
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,3,4,6,5,7,8,2] => [6,3,1,4,5,7,8,2] => [4,8,1,2,5,3,6,7] => 0100100
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => [4,5,1,3,6,7,8,2] => [2,8,4,1,3,5,6,7] => 0110000
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => [4,3,1,5,6,7,8,2] => [4,8,2,1,3,5,6,7] => 0110000
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => [3,1,4,5,6,7,8,2] => [3,8,1,2,4,5,6,7] => 0100000
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [8,7,6,5,4,2,1,3] => [7,1,8,6,5,4,3,2] => 1011111
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [2,1,7,8,6,5,4,3] => [7,8,6,5,2,1,4,3] => [7,2,8,6,5,4,1,3] => 1011110
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [2,1,6,8,7,5,4,3] => [8,6,7,5,2,1,4,3] => [7,2,8,6,5,1,4,3] => 1011101
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => [7,6,8,5,2,1,4,3] => [7,2,8,6,5,3,1,4] => 1011110
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [6,7,8,2,1,5,4,3] => [7,3,8,6,5,1,2,4] => 1011100
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => [7,5,8,2,1,6,4,3] => [7,3,8,6,4,5,1,2] => 1011010
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [2,1,7,6,5,8,4,3] => [7,6,5,8,2,1,4,3] => [7,2,8,6,4,3,1,5] => 1011110
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => [6,7,5,2,1,8,4,3] => [7,6,8,5,3,1,2,4] => 1011100
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [2,1,5,7,6,8,4,3] => [7,5,6,2,1,8,4,3] => [7,6,8,5,1,3,2,4] => 1011010
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => [6,5,7,2,1,8,4,3] => [7,6,8,5,2,1,3,4] => 1011100
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => [5,6,2,1,7,8,4,3] => [6,5,8,7,1,2,3,4] => 1011000
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => [8,7,6,4,2,1,5,3] => [7,6,8,1,5,4,3,2] => 1010111
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [2,1,5,4,8,7,6,3] => [8,7,5,4,2,1,6,3] => [7,6,8,4,1,5,3,2] => 1011011
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => [8,7,4,2,1,5,6,3] => [6,5,8,1,2,7,4,3] => 1010011
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [2,1,6,5,4,8,7,3] => [8,6,5,4,2,1,7,3] => [7,6,8,4,3,1,5,2] => 1011101
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [2,1,5,6,4,8,7,3] => [8,5,6,2,1,4,7,3] => [6,2,8,5,1,3,7,4] => 1011001
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => [8,6,4,2,1,5,7,3] => [6,5,8,1,4,2,7,3] => 1010101
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [2,1,5,4,6,8,7,3] => [8,5,4,2,1,6,7,3] => [6,5,8,3,1,2,7,4] => 1011001
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [2,1,4,5,6,8,7,3] => [8,4,2,1,5,6,7,3] => [5,4,8,1,2,3,7,6] => 1010001
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [2,1,7,6,5,4,8,3] => [7,6,5,4,2,1,8,3] => [7,6,8,4,3,2,1,5] => 1011110
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [2,1,6,7,5,4,8,3] => [6,7,5,2,1,4,8,3] => [6,2,8,5,4,1,3,7] => 1011100
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [2,1,4,7,6,5,8,3] => [7,6,4,2,1,5,8,3] => [6,5,8,1,4,3,2,7] => 1010110
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [2,1,4,6,7,5,8,3] => [6,4,2,1,7,5,8,3] => [6,5,8,3,4,1,2,7] => 1010100
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [2,1,6,5,4,7,8,3] => [6,5,4,2,1,7,8,3] => [6,5,8,3,2,1,4,7] => 1011100
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [2,1,5,6,4,7,8,3] => [5,6,2,1,4,7,8,3] => [5,2,8,4,1,3,6,7] => 1011000
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [2,1,5,4,6,7,8,3] => [5,4,2,1,6,7,8,3] => [5,4,8,2,1,3,6,7] => 1011000
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => [8,7,6,5,4,1,2,3] => [1,2,8,7,6,5,4,3] => 0011111
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => [7,8,6,5,1,2,4,3] => [2,3,8,7,6,5,1,4] => 0011110
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => [6,7,8,1,2,5,4,3] => [3,4,8,7,6,1,2,5] => 0011100
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,2,5,8,7,6,4,3] => [8,7,5,6,1,2,4,3] => [2,3,8,7,1,6,5,4] => 0011011
[[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,2,5,7,8,6,4,3] => [7,5,8,1,2,6,4,3] => [3,4,8,7,5,6,1,2] => 0011010
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => [7,6,5,8,1,2,4,3] => [2,3,8,7,5,4,1,6] => 0011110
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,2,5,7,6,8,4,3] => [7,5,6,1,2,8,4,3] => [3,7,8,6,1,4,2,5] => 0011010
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => [8,7,6,4,1,2,5,3] => [2,7,8,1,6,5,4,3] => 0010111
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,2,4,6,8,7,5,3] => [8,6,4,1,2,7,5,3] => [3,7,8,5,6,1,4,2] => 0010101
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,2,4,5,8,7,6,3] => [8,7,4,1,2,5,6,3] => [2,6,8,1,3,7,5,4] => 0010011
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,2,6,5,4,8,7,3] => [8,6,5,4,1,2,7,3] => [2,7,8,5,4,1,6,3] => 0011101
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,2,4,6,5,8,7,3] => [8,6,4,1,2,5,7,3] => [2,6,8,1,5,3,7,4] => 0010101
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,2,4,5,6,8,7,3] => [8,4,1,2,5,6,7,3] => [2,5,8,1,3,4,7,6] => 0010001
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,2,7,6,5,4,8,3] => [7,6,5,4,1,2,8,3] => [2,7,8,5,4,3,1,6] => 0011110
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => [5,6,1,2,7,4,8,3] => [3,6,8,5,1,2,4,7] => 0011000
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,2,4,7,6,5,8,3] => [7,6,4,1,2,5,8,3] => [2,6,8,1,5,4,3,7] => 0010110
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,2,4,6,7,5,8,3] => [6,4,1,2,7,5,8,3] => [3,6,8,4,5,1,2,7] => 0010100
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,2,5,6,4,7,8,3] => [5,6,1,2,4,7,8,3] => [2,3,8,5,1,4,6,7] => 0011000
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => [5,4,1,2,6,7,8,3] => [2,5,8,3,1,4,6,7] => 0011000
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => [4,1,2,5,6,7,8,3] => [2,4,8,1,3,5,6,7] => 0010000
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => [8,7,6,5,3,2,1,4] => [7,6,1,8,5,4,3,2] => 1101111
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => [6,7,3,2,1,8,5,4] => [7,6,5,8,4,1,2,3] => 1101100
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => [8,7,5,3,2,1,6,4] => [7,6,5,8,1,4,3,2] => 1101011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => [7,5,3,2,1,8,6,4] => [7,6,5,8,3,4,1,2] => 1101010
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => [8,6,5,3,2,1,7,4] => [7,6,5,8,3,1,4,2] => 1101101
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => [8,5,3,2,1,6,7,4] => [6,5,4,8,1,2,7,3] => 1101001
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => [7,6,5,3,2,1,8,4] => [7,6,5,8,3,2,1,4] => 1101110
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => [5,3,2,1,6,7,8,4] => [5,4,3,8,1,2,6,7] => 1101000
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => [8,7,6,5,2,3,1,4] => [7,1,2,8,6,5,4,3] => 1001111
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [2,3,1,6,8,7,5,4] => [8,6,7,2,3,1,5,4] => [7,2,3,8,6,1,5,4] => 1001101
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [2,3,1,7,6,8,5,4] => [7,6,8,2,3,1,5,4] => [7,2,3,8,6,4,1,5] => 1001110
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [2,3,1,5,8,7,6,4] => [8,7,5,2,3,1,6,4] => [7,2,6,8,1,5,4,3] => 1001011
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [2,3,1,5,7,8,6,4] => [7,5,2,3,1,8,6,4] => [7,3,6,8,4,5,1,2] => 1001010
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [2,3,1,6,5,8,7,4] => [8,6,5,2,3,1,7,4] => [7,2,6,8,4,1,5,3] => 1001101
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [2,3,1,5,7,6,8,4] => [7,5,2,3,1,6,8,4] => [6,2,5,8,1,4,3,7] => 1001010
[[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [2,3,1,6,5,7,8,4] => [6,5,2,3,1,7,8,4] => [6,2,5,8,3,1,4,7] => 1001100
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [2,3,1,5,6,7,8,4] => [5,2,3,1,6,7,8,4] => [5,2,4,8,1,3,6,7] => 1001000
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,3,2,7,6,8,5,4] => [7,6,8,3,1,2,5,4] => [2,7,3,8,6,4,1,5] => 0101110
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,3,2,5,8,7,6,4] => [8,7,5,3,1,2,6,4] => [2,7,6,8,1,5,4,3] => 0101011
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,3,2,5,7,8,6,4] => [7,5,3,1,2,8,6,4] => [3,7,6,8,4,5,1,2] => 0101010
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,3,2,5,6,8,7,4] => [8,5,3,1,2,6,7,4] => [2,6,5,8,1,3,7,4] => 0101001
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,3,2,7,6,5,8,4] => [7,6,5,3,1,2,8,4] => [2,7,6,8,4,3,1,5] => 0101110
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,3,2,5,7,6,8,4] => [7,5,3,1,2,6,8,4] => [2,6,5,8,1,4,3,7] => 0101010
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,3,2,6,5,7,8,4] => [6,5,3,1,2,7,8,4] => [2,6,5,8,3,1,4,7] => 0101100
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [2,1,3,7,8,6,5,4] => [7,8,6,2,1,3,5,4] => [6,2,3,8,7,5,1,4] => 1001110
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [2,1,3,6,8,7,5,4] => [8,6,7,2,1,3,5,4] => [6,2,3,8,7,1,5,4] => 1001101
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [2,1,3,7,6,8,5,4] => [7,6,8,2,1,3,5,4] => [6,2,3,8,7,4,1,5] => 1001110
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [2,1,3,6,7,8,5,4] => [6,7,2,1,3,8,5,4] => [6,3,7,8,5,1,2,4] => 1001100
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [2,1,3,5,8,7,6,4] => [8,7,5,2,1,3,6,4] => [6,2,7,8,1,5,4,3] => 1001011
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [2,1,3,5,6,7,8,4] => [5,2,1,3,6,7,8,4] => [4,2,5,8,1,3,6,7] => 1001000
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => [8,7,6,5,1,2,3,4] => [1,2,3,8,7,6,5,4] => 0001111
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => [7,6,8,1,2,3,5,4] => [2,3,4,8,7,5,1,6] => 0001110
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => [8,7,5,1,2,3,6,4] => [2,3,7,8,1,6,5,4] => 0001011
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => [7,5,1,2,3,8,6,4] => [3,4,7,8,5,6,1,2] => 0001010
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => [8,6,5,1,2,3,7,4] => [2,3,7,8,5,1,6,4] => 0001101
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => [8,5,1,2,3,6,7,4] => [2,3,6,8,1,4,7,5] => 0001001
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => [6,7,1,2,3,5,8,4] => [2,3,4,8,6,1,5,7] => 0001100
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => [6,5,1,2,3,7,8,4] => [2,3,6,8,4,1,5,7] => 0001100
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => [5,1,2,3,6,7,8,4] => [2,3,5,8,1,4,6,7] => 0001000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [8,7,6,4,3,2,1,5] => [7,6,5,1,8,4,3,2] => 1110111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => [7,8,4,3,2,1,6,5] => [7,6,5,2,8,4,1,3] => 1110110
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => [8,6,4,3,2,1,7,5] => [7,6,5,4,8,1,3,2] => 1110101
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => [7,6,4,3,2,1,8,5] => [7,6,5,4,8,2,1,3] => 1110110
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => [6,4,3,2,1,7,8,5] => [6,5,4,3,8,1,2,7] => 1110100
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => [8,7,6,3,4,2,1,5] => [7,6,1,2,8,5,4,3] => 1100111
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => [7,8,3,4,2,1,6,5] => [7,6,2,3,8,5,1,4] => 1100110
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => [7,6,3,4,2,1,8,5] => [7,6,2,5,8,3,1,4] => 1100110
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [3,4,2,1,6,7,8,5] => [6,3,4,2,1,7,8,5] => [6,5,2,4,8,1,3,7] => 1100100
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => [8,7,6,4,2,3,1,5] => [7,1,6,2,8,5,4,3] => 1010111
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => [8,7,6,3,2,4,1,5] => [7,5,1,2,8,6,4,3] => 1100111
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => [7,8,3,2,4,1,6,5] => [7,5,2,3,8,6,1,4] => 1100110
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => [8,6,3,2,4,1,7,5] => [7,5,2,6,8,1,4,3] => 1100101
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => [8,7,6,2,3,4,1,5] => [7,1,2,3,8,6,5,4] => 1000111
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [2,3,4,1,7,8,6,5] => [7,8,2,3,4,1,6,5] => [7,2,3,4,8,6,1,5] => 1000110
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [2,3,4,1,6,8,7,5] => [8,6,2,3,4,1,7,5] => [7,2,3,6,8,1,5,4] => 1000101
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => [7,6,2,3,4,1,8,5] => [7,2,3,6,8,4,1,5] => 1000110
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => [6,2,3,4,1,7,8,5] => [6,2,3,5,8,1,4,7] => 1000100
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => [8,7,6,4,3,1,2,5] => [1,7,6,2,8,5,4,3] => 0110111
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,4,3,2,7,8,6,5] => [7,8,4,3,1,2,6,5] => [2,7,6,3,8,5,1,4] => 0110110
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => [7,6,4,3,1,2,8,5] => [2,7,6,5,8,3,1,4] => 0110110
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => [6,4,3,1,2,7,8,5] => [2,6,5,4,8,1,3,7] => 0110100
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => [8,7,6,3,1,4,2,5] => [6,7,1,2,8,5,4,3] => 0100111
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,3,4,2,6,8,7,5] => [8,6,3,1,4,2,7,5] => [6,7,2,5,8,1,4,3] => 0100101
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [8,7,6,4,2,1,3,5] => [6,1,7,2,8,5,4,3] => 1010111
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [7,8,4,2,1,3,6,5] => [6,2,7,3,8,5,1,4] => 1010110
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => [8,6,4,2,1,3,7,5] => [6,2,7,5,8,1,4,3] => 1010101
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [7,6,4,2,1,3,8,5] => [6,2,7,5,8,3,1,4] => 1010110
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => [8,7,6,4,1,2,3,5] => [1,2,7,3,8,6,5,4] => 0010111
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => [8,6,4,1,2,3,7,5] => [2,3,7,6,8,1,5,4] => 0010101
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => [6,4,1,2,3,7,8,5] => [2,3,6,5,8,1,4,7] => 0010100
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => [8,7,6,3,2,1,4,5] => [6,5,1,2,8,7,4,3] => 1100111
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [3,2,1,4,7,8,6,5] => [7,8,3,2,1,4,6,5] => [6,5,2,3,8,7,1,4] => 1100110
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [3,2,1,4,6,8,7,5] => [8,6,3,2,1,4,7,5] => [6,5,2,7,8,1,4,3] => 1100101
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [3,2,1,4,6,7,8,5] => [6,3,2,1,4,7,8,5] => [5,4,2,6,8,1,3,7] => 1100100
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => [8,7,6,2,3,1,4,5] => [6,1,2,3,8,7,5,4] => 1000111
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,3,2,4,7,8,6,5] => [7,8,3,1,2,4,6,5] => [2,6,3,4,8,7,1,5] => 0100110
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,3,2,4,6,8,7,5] => [8,6,3,1,2,4,7,5] => [2,6,3,7,8,1,5,4] => 0100101
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => [8,7,6,2,1,3,4,5] => [5,1,2,3,8,7,6,4] => 1000111
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [2,1,3,4,7,8,6,5] => [7,8,2,1,3,4,6,5] => [5,2,3,4,8,7,1,6] => 1000110
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => [6,2,1,3,4,7,8,5] => [4,2,3,6,8,1,5,7] => 1000100
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => [8,7,6,1,2,3,4,5] => [1,2,3,4,8,7,6,5] => 0000111
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => [7,8,1,2,3,4,6,5] => [2,3,4,5,8,7,1,6] => 0000110
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => [8,6,1,2,3,4,7,5] => [2,3,4,7,8,1,6,5] => 0000101
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => [6,1,2,3,4,7,8,5] => [2,3,4,6,8,1,5,7] => 0000100
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => [8,7,5,4,3,2,1,6] => [7,6,5,4,1,8,3,2] => 1111011
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => [7,5,4,3,2,1,8,6] => [7,6,5,4,3,8,1,2] => 1111010
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [4,5,3,2,1,8,7,6] => [8,7,4,5,3,2,1,6] => [7,6,5,1,2,8,4,3] => 1110011
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [3,4,5,2,1,8,7,6] => [8,7,3,4,5,2,1,6] => [7,6,1,2,3,8,5,4] => 1100011
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [2,4,5,3,1,8,7,6] => [8,7,4,2,5,3,1,6] => [7,5,6,1,2,8,4,3] => 1010011
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => [8,7,5,3,2,4,1,6] => [7,5,1,6,2,8,4,3] => 1101011
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [4,3,2,5,1,7,8,6] => [7,4,3,2,5,1,8,6] => [7,5,4,2,6,8,1,3] => 1110010
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => [8,7,3,4,2,5,1,6] => [7,5,1,2,3,8,6,4] => 1100011
[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [2,4,3,5,1,7,8,6] => [7,4,2,3,5,1,8,6] => [7,2,5,3,6,8,1,4] => 1010010
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [2,3,4,5,1,8,7,6] => [8,7,2,3,4,5,1,6] => [7,1,2,3,4,8,6,5] => 1000011
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => [7,2,3,4,5,1,8,6] => [7,2,3,4,6,8,1,5] => 1000010
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => [8,7,5,4,3,1,2,6] => [1,7,6,5,2,8,4,3] => 0111011
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,4,5,3,2,8,7,6] => [8,7,4,5,1,3,2,6] => [2,7,6,1,3,8,5,4] => 0110011
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,3,5,4,2,8,7,6] => [8,7,5,3,1,4,2,6] => [6,7,1,5,2,8,4,3] => 0101011
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,3,5,4,2,7,8,6] => [7,5,3,1,4,2,8,6] => [6,7,2,5,4,8,1,3] => 0101010
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,3,4,5,2,8,7,6] => [8,7,3,1,4,5,2,6] => [5,7,1,2,3,8,6,4] => 0100011
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,3,4,5,2,7,8,6] => [7,3,1,4,5,2,8,6] => [5,7,2,3,6,8,1,4] => 0100010
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => [8,7,5,4,1,2,3,6] => [1,2,7,6,3,8,5,4] => 0011011
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,2,5,4,3,7,8,6] => [7,5,4,1,2,3,8,6] => [2,3,7,6,5,8,1,4] => 0011010
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => [8,7,4,1,2,5,3,6] => [2,6,7,1,3,8,5,4] => 0010011
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [3,2,1,5,4,8,7,6] => [8,7,5,3,2,1,4,6] => [6,5,1,7,2,8,4,3] => 1101011
[[[.,[[.,.],.]],[.,.]],[[.,.],.]] => [2,3,1,5,4,7,8,6] => [7,5,2,3,1,4,8,6] => [6,2,3,7,5,8,1,4] => 1001010
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => [8,7,5,3,1,2,4,6] => [1,6,2,7,3,8,5,4] => 0101011
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,3,2,5,4,7,8,6] => [7,5,3,1,2,4,8,6] => [2,6,3,7,5,8,1,4] => 0101010
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [2,1,3,5,4,8,7,6] => [8,7,5,2,1,3,4,6] => [5,1,2,7,3,8,6,4] => 1001011
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => [8,7,5,1,2,3,4,6] => [1,2,3,7,4,8,6,5] => 0001011
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,2,3,5,4,7,8,6] => [7,5,1,2,3,4,8,6] => [2,3,4,7,6,8,1,5] => 0001010
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => [7,4,3,2,1,5,8,6] => [6,5,4,2,7,8,1,3] => 1110010
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [3,4,2,1,5,7,8,6] => [7,3,4,2,1,5,8,6] => [6,5,2,3,7,8,1,4] => 1100010
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => [8,7,3,2,4,1,5,6] => [6,4,1,2,3,8,7,5] => 1100011
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [2,3,4,1,5,8,7,6] => [8,7,2,3,4,1,5,6] => [6,1,2,3,4,8,7,5] => 1000011
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [2,3,4,1,5,7,8,6] => [7,2,3,4,1,5,8,6] => [6,2,3,4,7,8,1,5] => 1000010
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,3,4,2,5,8,7,6] => [8,7,3,1,4,2,5,6] => [5,6,1,2,3,8,7,4] => 0100011
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,3,4,2,5,7,8,6] => [7,3,1,4,2,5,8,6] => [5,6,2,3,7,8,1,4] => 0100010
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,2,4,3,5,8,7,6] => [8,7,4,1,2,3,5,6] => [1,2,6,3,4,8,7,5] => 0010011
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [8,7,3,2,1,4,5,6] => [5,4,1,2,3,8,7,6] => 1100011
[[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [2,3,1,4,5,8,7,6] => [8,7,2,3,1,4,5,6] => [5,1,2,3,4,8,7,6] => 1000011
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [2,1,3,4,5,8,7,6] => [8,7,2,1,3,4,5,6] => [4,1,2,3,5,8,7,6] => 1000011
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,8,7,6] => 0000011
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => [7,1,2,3,4,5,8,6] => [2,3,4,5,7,8,1,6] => 0000010
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [8,6,5,4,3,2,1,7] => [7,6,5,4,3,1,8,2] => 1111101
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [5,6,4,3,2,1,8,7] => [8,5,6,4,3,2,1,7] => [7,6,5,4,1,2,8,3] => 1111001
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [4,6,5,3,2,1,8,7] => [8,6,4,5,3,2,1,7] => [7,6,5,1,4,2,8,3] => 1110101
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [5,4,6,3,2,1,8,7] => [8,5,4,6,3,2,1,7] => [7,6,5,3,1,2,8,4] => 1111001
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => [8,4,5,6,3,2,1,7] => [7,6,5,1,2,3,8,4] => 1110001
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [3,6,5,4,2,1,8,7] => [8,6,5,3,4,2,1,7] => [7,6,1,5,4,2,8,3] => 1101101
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => [8,5,3,6,4,2,1,7] => [7,6,4,5,1,2,8,3] => 1101001
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [4,3,6,5,2,1,8,7] => [8,6,4,3,5,2,1,7] => [7,6,4,1,5,2,8,3] => 1110101
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [4,5,3,6,2,1,8,7] => [8,4,5,3,6,2,1,7] => [7,6,4,1,2,3,8,5] => 1110001
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [4,3,5,6,2,1,8,7] => [8,4,3,5,6,2,1,7] => [7,6,3,1,2,4,8,5] => 1110001
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [3,4,5,6,2,1,8,7] => [8,3,4,5,6,2,1,7] => [7,6,1,2,3,4,8,5] => 1100001
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [2,5,4,6,3,1,8,7] => [8,5,4,2,6,3,1,7] => [7,5,6,3,1,2,8,4] => 1011001
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [3,2,5,6,4,1,8,7] => [8,5,3,2,6,4,1,7] => [7,5,4,6,1,2,8,3] => 1101001
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [2,3,6,5,4,1,8,7] => [8,6,5,2,3,4,1,7] => [7,1,2,6,5,3,8,4] => 1001101
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [4,3,2,6,5,1,8,7] => [8,6,4,3,2,5,1,7] => [7,5,4,1,6,2,8,3] => 1110101
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => [8,6,4,2,3,5,1,7] => [7,1,5,2,6,3,8,4] => 1010101
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [3,2,4,6,5,1,8,7] => [8,6,3,2,4,5,1,7] => [7,4,1,2,6,3,8,5] => 1100101
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [8,4,3,5,2,6,1,7] => [7,5,3,1,2,4,8,6] => 1110001
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [8,5,3,2,4,6,1,7] => [7,4,1,5,2,3,8,6] => 1101001
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [3,4,2,5,6,1,8,7] => [8,3,4,2,5,6,1,7] => [7,4,1,2,3,5,8,6] => 1100001
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => [8,2,3,4,5,6,1,7] => [7,1,2,3,4,5,8,6] => 1000001
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => [8,6,5,4,3,1,2,7] => [1,7,6,5,4,2,8,3] => 0111101
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => [8,5,6,4,1,3,2,7] => [2,7,6,5,1,3,8,4] => 0111001
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,3,5,6,4,2,8,7] => [8,5,3,1,6,4,2,7] => [6,7,4,5,1,2,8,3] => 0101001
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [8,6,5,4,2,1,3,7] => [6,1,7,5,4,2,8,3] => 1011101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [8,5,6,2,1,4,3,7] => [6,2,7,5,1,3,8,4] => 1011001
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,2,6,5,4,3,8,7] => [8,6,5,4,1,2,3,7] => [1,2,7,6,5,3,8,4] => 0011101
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,2,5,4,6,3,8,7] => [8,5,4,1,2,6,3,7] => [2,6,7,4,1,3,8,5] => 0011001
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,2,4,5,6,3,8,7] => [8,4,1,2,5,6,3,7] => [2,5,7,1,3,4,8,6] => 0010001
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [3,2,1,6,5,4,8,7] => [8,6,5,3,2,1,4,7] => [6,5,1,7,4,2,8,3] => 1101101
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [3,2,1,5,6,4,8,7] => [8,5,3,2,1,6,4,7] => [6,5,4,7,1,2,8,3] => 1101001
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [2,3,1,6,5,4,8,7] => [8,6,5,2,3,1,4,7] => [6,1,2,7,5,3,8,4] => 1001101
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,2,3,6,5,4,8,7] => [8,6,5,1,2,3,4,7] => [1,2,3,7,6,4,8,5] => 0001101
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [8,6,4,3,2,1,5,7] => [6,5,4,1,7,2,8,3] => 1110101
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => [8,6,3,4,2,1,5,7] => [6,5,1,2,7,3,8,4] => 1100101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => [8,6,4,2,3,1,5,7] => [6,1,5,2,7,3,8,4] => 1010101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [8,6,3,2,4,1,5,7] => [6,4,1,2,7,3,8,5] => 1100101
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => [8,6,2,3,4,1,5,7] => [6,1,2,3,7,4,8,5] => 1000101
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,4,3,2,6,5,8,7] => [8,6,4,3,1,2,5,7] => [1,6,5,2,7,3,8,4] => 0110101
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => [8,6,3,1,4,2,5,7] => [5,6,1,2,7,3,8,4] => 0100101
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [8,6,4,2,1,3,5,7] => [5,1,6,2,7,3,8,4] => 1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => [8,6,4,1,2,3,5,7] => [1,2,6,3,7,4,8,5] => 0010101
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [3,2,1,4,6,5,8,7] => [8,6,3,2,1,4,5,7] => [5,4,1,2,7,3,8,6] => 1100101
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => [8,6,1,2,3,4,5,7] => [1,2,3,4,7,5,8,6] => 0000101
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => [8,5,4,3,2,1,6,7] => [6,5,4,3,1,2,8,7] => 1111001
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [3,4,5,2,1,6,8,7] => [8,3,4,5,2,1,6,7] => [6,5,1,2,3,4,8,7] => 1100001
[[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [2,4,5,3,1,6,8,7] => [8,4,2,5,3,1,6,7] => [6,4,5,1,2,3,8,7] => 1010001
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [2,4,3,5,1,6,8,7] => [8,4,2,3,5,1,6,7] => [6,1,4,2,3,5,8,7] => 1010001
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [2,3,4,5,1,6,8,7] => [8,2,3,4,5,1,6,7] => [6,1,2,3,4,5,8,7] => 1000001
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,4,5,3,2,6,8,7] => [8,4,5,1,3,2,6,7] => [2,6,5,1,3,4,8,7] => 0110001
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => [8,5,4,2,1,3,6,7] => [5,1,6,4,2,3,8,7] => 1011001
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => [8,4,2,1,5,3,6,7] => [5,4,6,1,2,3,8,7] => 1010001
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,2,4,5,3,6,8,7] => [8,4,1,2,5,3,6,7] => [2,5,6,1,3,4,8,7] => 0010001
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [3,2,1,5,4,6,8,7] => [8,5,3,2,1,4,6,7] => [5,4,1,6,2,3,8,7] => 1101001
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,3,2,5,4,6,8,7] => [8,5,3,1,2,4,6,7] => [1,5,2,6,3,4,8,7] => 0101001
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [2,1,3,5,4,6,8,7] => [8,5,2,1,3,4,6,7] => [4,1,2,6,3,5,8,7] => 1001001
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => [8,5,1,2,3,4,6,7] => [1,2,3,6,4,5,8,7] => 0001001
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [2,3,4,1,5,6,8,7] => [8,2,3,4,1,5,6,7] => [5,1,2,3,4,6,8,7] => 1000001
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => [8,4,1,2,3,5,6,7] => [1,2,5,3,4,6,8,7] => 0010001
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [3,2,1,4,5,6,8,7] => [8,3,2,1,4,5,6,7] => [4,3,1,2,5,6,8,7] => 1100001
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [2,3,1,4,5,6,8,7] => [8,2,3,1,4,5,6,7] => [4,1,2,3,5,6,8,7] => 1000001
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => [8,3,1,2,4,5,6,7] => [1,4,2,3,5,6,8,7] => 0100001
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [8,2,1,3,4,5,6,7] => [3,1,2,4,5,6,8,7] => 1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => [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] => [7,6,5,4,3,2,1,8] => 1111110
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1,8] => [7,6,5,4,3,1,2,8] => 1111100
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => [7,5,6,4,3,2,1,8] => [7,6,5,4,1,3,2,8] => 1111010
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [6,5,7,4,3,2,1,8] => [7,6,5,4,2,1,3,8] => 1111100
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1,8] => [7,6,5,4,1,2,3,8] => 1111000
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => [7,6,4,5,3,2,1,8] => [7,6,5,1,4,3,2,8] => 1110110
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [4,6,7,5,3,2,1,8] => [6,4,7,5,3,2,1,8] => [7,6,5,3,4,1,2,8] => 1110100
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [5,4,7,6,3,2,1,8] => [7,5,4,6,3,2,1,8] => [7,6,5,3,1,4,2,8] => 1111010
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [4,5,7,6,3,2,1,8] => [7,4,5,6,3,2,1,8] => [7,6,5,1,2,4,3,8] => 1110010
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1,8] => [7,6,5,3,2,1,4,8] => 1111100
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => [5,4,6,7,3,2,1,8] => [7,6,5,2,1,3,4,8] => 1111000
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => [4,5,6,7,3,2,1,8] => [7,6,5,1,2,3,4,8] => 1110000
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => [7,6,3,4,5,2,1,8] => [7,6,1,2,5,4,3,8] => 1100110
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [5,4,3,7,6,2,1,8] => [7,5,4,3,6,2,1,8] => [7,6,4,3,1,5,2,8] => 1111010
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [4,5,3,7,6,2,1,8] => [7,4,5,3,6,2,1,8] => [7,6,4,1,2,5,3,8] => 1110010
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => [6,5,4,3,7,2,1,8] => [7,6,4,3,2,1,5,8] => 1111100
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => [5,6,4,3,7,2,1,8] => [7,6,4,3,1,2,5,8] => 1111000
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => [5,4,6,3,7,2,1,8] => [7,6,4,2,1,3,5,8] => 1111000
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => [5,4,3,6,7,2,1,8] => [7,6,3,2,1,4,5,8] => 1111000
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => [3,4,5,6,7,2,1,8] => [7,6,1,2,3,4,5,8] => 1100000
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => [7,6,5,4,2,3,1,8] => [7,1,6,5,4,3,2,8] => 1011110
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.] => [2,6,5,7,4,3,1,8] => [6,5,7,2,4,3,1,8] => [7,2,6,5,3,1,4,8] => 1011100
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [2,5,6,7,4,3,1,8] => [5,6,2,7,4,3,1,8] => [7,5,6,4,1,2,3,8] => 1011000
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [2,4,7,6,5,3,1,8] => [7,6,4,2,5,3,1,8] => [7,5,6,1,4,3,2,8] => 1010110
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => [6,4,2,7,5,3,1,8] => [7,5,6,3,4,1,2,8] => 1010100
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [2,4,5,7,6,3,1,8] => [7,4,2,5,6,3,1,8] => [7,4,6,1,2,5,3,8] => 1010010
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => [7,6,5,3,2,4,1,8] => [7,5,1,6,4,3,2,8] => 1101110
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [3,2,6,5,7,4,1,8] => [6,5,3,2,7,4,1,8] => [7,5,4,6,2,1,3,8] => 1101100
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [3,2,5,6,7,4,1,8] => [5,3,2,6,7,4,1,8] => [7,4,3,6,1,2,5,8] => 1101000
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [2,3,7,6,5,4,1,8] => [7,6,5,2,3,4,1,8] => [7,1,2,6,5,4,3,8] => 1001110
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [4,3,2,7,6,5,1,8] => [7,6,4,3,2,5,1,8] => [7,5,4,1,6,3,2,8] => 1110110
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [2,4,3,7,6,5,1,8] => [7,6,4,2,3,5,1,8] => [7,1,5,2,6,4,3,8] => 1010110
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [3,2,4,7,6,5,1,8] => [7,6,3,2,4,5,1,8] => [7,4,1,2,6,5,3,8] => 1100110
[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [3,2,4,6,7,5,1,8] => [6,3,2,4,7,5,1,8] => [7,4,2,5,6,1,3,8] => 1100100
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [2,3,4,7,6,5,1,8] => [7,6,2,3,4,5,1,8] => [7,1,2,3,6,5,4,8] => 1000110
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [3,5,4,2,7,6,1,8] => [7,5,3,4,2,6,1,8] => [7,5,1,4,2,6,3,8] => 1101010
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [4,3,5,2,7,6,1,8] => [7,4,3,5,2,6,1,8] => [7,5,3,1,2,6,4,8] => 1110010
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [2,5,4,3,7,6,1,8] => [7,5,4,2,3,6,1,8] => [7,1,5,4,2,6,3,8] => 1011010
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => [7,5,3,2,4,6,1,8] => [7,4,1,5,2,6,3,8] => 1101010
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => [7,2,3,4,5,6,1,8] => [7,1,2,3,4,6,5,8] => 1000010
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => [6,5,4,3,2,7,1,8] => [7,5,4,3,2,1,6,8] => 1111100
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => [5,6,4,3,2,7,1,8] => [7,5,4,3,1,2,6,8] => 1111000
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [3,5,6,4,2,7,1,8] => [5,3,6,4,2,7,1,8] => [7,5,3,4,1,2,6,8] => 1101000
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [3,4,6,5,2,7,1,8] => [6,3,4,5,2,7,1,8] => [7,5,1,2,4,3,6,8] => 1100100
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [5,4,3,6,2,7,1,8] => [7,5,3,2,1,4,6,8] => 1111000
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [4,5,3,6,2,7,1,8] => [7,5,3,1,2,4,6,8] => 1110000
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => [5,3,4,6,2,7,1,8] => [7,5,1,3,2,4,6,8] => 1101000
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [3,4,5,6,2,7,1,8] => [7,5,1,2,3,4,6,8] => 1100000
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [2,5,4,6,3,7,1,8] => [5,4,2,6,3,7,1,8] => [7,4,5,2,1,3,6,8] => 1011000
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [3,2,6,5,4,7,1,8] => [6,5,3,2,4,7,1,8] => [7,4,1,5,3,2,6,8] => 1101100
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [2,4,3,6,5,7,1,8] => [6,4,2,3,5,7,1,8] => [7,1,4,2,5,3,6,8] => 1010100
[[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [3,2,4,6,5,7,1,8] => [6,3,2,4,5,7,1,8] => [7,3,1,2,5,4,6,8] => 1100100
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => [6,2,3,4,5,7,1,8] => [7,1,2,3,5,4,6,8] => 1000100
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1,8] => [7,4,3,2,1,5,6,8] => 1111000
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => [3,4,5,2,6,7,1,8] => [7,4,1,2,3,5,6,8] => 1100000
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [2,5,4,3,6,7,1,8] => [5,4,2,3,6,7,1,8] => [7,1,4,3,2,5,6,8] => 1011000
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [2,3,5,4,6,7,1,8] => [5,2,3,4,6,7,1,8] => [7,1,2,4,3,5,6,8] => 1001000
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => [4,3,2,5,6,7,1,8] => [7,3,2,1,4,5,6,8] => 1110000
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => [3,4,2,5,6,7,1,8] => [7,3,1,2,4,5,6,8] => 1100000
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [2,4,3,5,6,7,1,8] => [4,2,3,5,6,7,1,8] => [7,1,3,2,4,5,6,8] => 1010000
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1,8] => [7,2,1,3,4,5,6,8] => 1100000
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8] => 1000000
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => [7,6,5,4,3,1,2,8] => [1,7,6,5,4,3,2,8] => 0111110
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => [6,7,5,4,1,3,2,8] => [2,7,6,5,4,1,3,8] => 0111100
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,5,7,6,4,3,2,8] => [7,5,6,4,1,3,2,8] => [2,7,6,5,1,4,3,8] => 0111010
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,6,5,7,4,3,2,8] => [6,5,7,4,1,3,2,8] => [2,7,6,5,3,1,4,8] => 0111100
[[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,4,6,7,5,3,2,8] => [6,4,7,1,5,3,2,8] => [3,7,6,4,5,1,2,8] => 0110100
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,3,5,7,6,4,2,8] => [7,5,3,1,6,4,2,8] => [6,7,4,5,1,3,2,8] => 0101010
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,3,5,4,7,6,2,8] => [7,5,3,1,4,6,2,8] => [5,7,1,4,2,6,3,8] => 0101010
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,4,3,5,7,6,2,8] => [7,4,3,1,5,6,2,8] => [5,7,3,1,2,6,4,8] => 0110010
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,4,5,6,3,7,2,8] => [4,5,1,6,3,7,2,8] => [5,7,4,1,2,3,6,8] => 0110000
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,3,6,5,4,7,2,8] => [6,5,3,1,4,7,2,8] => [5,7,1,4,3,2,6,8] => 0101100
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => [5,3,1,6,4,7,2,8] => [5,7,3,4,1,2,6,8] => 0101000
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,4,3,6,5,7,2,8] => [6,4,3,1,5,7,2,8] => [5,7,3,1,4,2,6,8] => 0110100
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,5,4,3,6,7,2,8] => [5,4,3,1,6,7,2,8] => [5,7,3,2,1,4,6,8] => 0111000
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,3,4,5,6,7,2,8] => [3,1,4,5,6,7,2,8] => [3,7,1,2,4,5,6,8] => 0100000
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [2,1,4,7,6,5,3,8] => [7,6,4,2,1,5,3,8] => [6,5,7,1,4,3,2,8] => 1010110
[[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [2,1,4,6,5,7,3,8] => [6,4,2,1,5,7,3,8] => [5,4,7,1,3,2,6,8] => 1010100
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8] => [7,6,5,4,1,2,3,8] => [1,2,7,6,5,4,3,8] => 0011110
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,2,4,5,7,6,3,8] => [7,4,1,2,5,6,3,8] => [2,5,7,1,3,6,4,8] => 0010010
[[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,2,4,6,5,7,3,8] => [6,4,1,2,5,7,3,8] => [2,5,7,1,4,3,6,8] => 0010100
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,2,5,4,6,7,3,8] => [5,4,1,2,6,7,3,8] => [2,5,7,3,1,4,6,8] => 0011000
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => [7,6,5,3,2,1,4,8] => [6,5,1,7,4,3,2,8] => 1101110
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [3,2,1,5,6,7,4,8] => [5,3,2,1,6,7,4,8] => [5,4,3,7,1,2,6,8] => 1101000
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [2,3,1,7,6,5,4,8] => [7,6,5,2,3,1,4,8] => [6,1,2,7,5,4,3,8] => 1001110
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [2,3,1,6,7,5,4,8] => [6,7,2,3,1,5,4,8] => [6,2,3,7,5,1,4,8] => 1001100
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,3,2,5,7,6,4,8] => [7,5,3,1,2,6,4,8] => [2,6,5,7,1,4,3,8] => 0101010
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,3,2,6,5,7,4,8] => [6,5,3,1,2,7,4,8] => [2,6,5,7,3,1,4,8] => 0101100
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => [7,6,5,1,2,3,4,8] => [1,2,3,7,6,5,4,8] => 0001110
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => [5,1,2,3,6,7,4,8] => [2,3,5,7,1,4,6,8] => 0001000
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => [6,4,3,2,1,7,5,8] => [6,5,4,3,7,1,2,8] => 1110100
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8] => [7,6,2,3,4,1,5,8] => [6,1,2,3,7,5,4,8] => 1000110
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [7,6,4,3,1,2,5,8] => [1,6,5,2,7,4,3,8] => 0110110
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,4,3,2,6,7,5,8] => [6,4,3,1,2,7,5,8] => [2,6,5,4,7,1,3,8] => 0110100
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [2,1,4,3,7,6,5,8] => [7,6,4,2,1,3,5,8] => [5,1,6,2,7,4,3,8] => 1010110
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => [7,6,3,2,1,4,5,8] => [5,4,1,2,7,6,3,8] => 1100110
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [3,2,1,4,6,7,5,8] => [6,3,2,1,4,7,5,8] => [5,4,2,6,7,1,3,8] => 1100100
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => [7,6,1,2,3,4,5,8] => [1,2,3,4,7,6,5,8] => 0000110
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => [6,1,2,3,4,7,5,8] => [2,3,4,6,7,1,5,8] => 0000100
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [4,3,5,2,1,7,6,8] => [7,4,3,5,2,1,6,8] => [6,5,3,1,2,7,4,8] => 1110010
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [2,5,4,3,1,7,6,8] => [7,5,4,2,3,1,6,8] => [6,1,5,4,2,7,3,8] => 1011010
[[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [2,4,5,3,1,7,6,8] => [7,4,2,5,3,1,6,8] => [6,4,5,1,2,7,3,8] => 1010010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [3,2,5,4,1,7,6,8] => [7,5,3,2,4,1,6,8] => [6,4,1,5,2,7,3,8] => 1101010
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [2,3,4,5,1,7,6,8] => [7,2,3,4,5,1,6,8] => [6,1,2,3,4,7,5,8] => 1000010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => [7,5,3,1,4,2,6,8] => [5,6,1,4,2,7,3,8] => 0101010
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => [7,3,1,4,5,2,6,8] => [4,6,1,2,3,7,5,8] => 0100010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => [7,5,3,2,1,4,6,8] => [5,4,1,6,2,7,3,8] => 1101010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => [7,5,2,3,1,4,6,8] => [5,1,2,6,3,7,4,8] => 1001010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [7,5,3,1,2,4,6,8] => [1,5,2,6,3,7,4,8] => 0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [7,5,1,2,3,4,6,8] => [1,2,3,6,4,7,5,8] => 0001010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => [7,4,3,2,1,5,6,8] => [5,4,3,1,2,7,6,8] => 1110010
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => [7,4,3,1,2,5,6,8] => [1,5,4,2,3,7,6,8] => 0110010
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => [7,4,1,2,3,5,6,8] => [1,2,5,3,4,7,6,8] => 0010010
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [3,2,1,4,5,7,6,8] => [7,3,2,1,4,5,6,8] => [4,3,1,2,5,7,6,8] => 1100010
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8] => [7,2,3,1,4,5,6,8] => [4,1,2,3,5,7,6,8] => 1000010
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [7,3,1,2,4,5,6,8] => [1,4,2,3,5,7,6,8] => 0100010
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => [7,2,1,3,4,5,6,8] => [3,1,2,4,5,7,6,8] => 1000010
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => [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] => [6,5,4,3,2,1,7,8] => 1111100
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => [5,6,4,3,2,1,7,8] => [6,5,4,3,1,2,7,8] => 1111000
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => [5,4,6,3,2,1,7,8] => [6,5,4,2,1,3,7,8] => 1111000
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => [4,5,6,3,2,1,7,8] => [6,5,4,1,2,3,7,8] => 1110000
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [3,6,5,4,2,1,7,8] => [6,5,3,4,2,1,7,8] => [6,5,1,4,3,2,7,8] => 1101100
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => [5,4,3,6,2,1,7,8] => [6,5,3,2,1,4,7,8] => 1111000
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [2,5,4,6,3,1,7,8] => [5,4,2,6,3,1,7,8] => [6,4,5,2,1,3,7,8] => 1011000
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [4,3,2,6,5,1,7,8] => [6,4,3,2,5,1,7,8] => [6,4,3,1,5,2,7,8] => 1110100
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => [6,2,3,4,5,1,7,8] => [6,1,2,3,5,4,7,8] => 1000100
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7,8] => [6,4,3,2,1,5,7,8] => 1111000
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => [4,5,3,2,6,1,7,8] => [6,4,3,1,2,5,7,8] => 1110000
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [4,3,5,2,6,1,7,8] => [6,4,2,1,3,5,7,8] => 1110000
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => [3,4,5,2,6,1,7,8] => [6,4,1,2,3,5,7,8] => 1100000
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => [5,2,3,4,6,1,7,8] => [6,1,2,4,3,5,7,8] => 1001000
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => [4,3,2,5,6,1,7,8] => [6,3,2,1,4,5,7,8] => 1110000
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => [3,2,4,5,6,1,7,8] => [6,2,1,3,4,5,7,8] => 1100000
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7,8] => [6,1,2,3,4,5,7,8] => 1000000
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => [6,5,4,3,1,2,7,8] => [1,6,5,4,3,2,7,8] => 0111100
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,3,6,5,4,2,7,8] => [6,5,3,1,4,2,7,8] => [5,6,1,4,3,2,7,8] => 0101100
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => [5,3,1,6,4,2,7,8] => [5,6,3,4,1,2,7,8] => 0101000
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,4,3,6,5,2,7,8] => [6,4,3,1,5,2,7,8] => [5,6,3,1,4,2,7,8] => 0110100
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,5,4,3,6,2,7,8] => [5,4,3,1,6,2,7,8] => [5,6,3,2,1,4,7,8] => 0111000
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => [3,1,4,5,6,2,7,8] => [3,6,1,2,4,5,7,8] => 0100000
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [2,1,5,6,4,3,7,8] => [5,6,2,1,4,3,7,8] => [5,2,6,4,1,3,7,8] => 1011000
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [2,1,4,6,5,3,7,8] => [6,4,2,1,5,3,7,8] => [5,4,6,1,3,2,7,8] => 1010100
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => [6,5,4,1,2,3,7,8] => [1,2,6,5,4,3,7,8] => 0011100
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,2,4,6,5,3,7,8] => [6,4,1,2,5,3,7,8] => [2,5,6,1,4,3,7,8] => 0010100
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => [4,1,2,5,6,3,7,8] => [2,4,6,1,3,5,7,8] => 0010000
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [3,2,1,6,5,4,7,8] => [6,5,3,2,1,4,7,8] => [5,4,1,6,3,2,7,8] => 1101100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [3,2,1,5,6,4,7,8] => [5,3,2,1,6,4,7,8] => [5,4,3,6,1,2,7,8] => 1101000
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => [6,5,1,2,3,4,7,8] => [1,2,3,6,5,4,7,8] => 0001100
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,2,3,5,6,4,7,8] => [5,1,2,3,6,4,7,8] => [2,3,5,6,1,4,7,8] => 0001000
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => [6,4,3,2,1,5,7,8] => [5,4,3,1,6,2,7,8] => 1110100
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,4,3,2,6,5,7,8] => [6,4,3,1,2,5,7,8] => [1,5,4,2,6,3,7,8] => 0110100
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => [6,4,2,1,3,5,7,8] => [4,1,5,2,6,3,7,8] => 1010100
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [6,4,1,2,3,5,7,8] => [1,2,5,3,6,4,7,8] => 0010100
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [3,2,1,4,6,5,7,8] => [6,3,2,1,4,5,7,8] => [4,3,1,2,6,5,7,8] => 1100100
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => [6,3,1,2,4,5,7,8] => [1,4,2,3,6,5,7,8] => 0100100
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => [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] => [5,4,3,2,1,6,7,8] => 1111000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => [4,5,3,2,1,6,7,8] => [5,4,3,1,2,6,7,8] => 1110000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [3,5,4,2,1,6,7,8] => [5,3,4,2,1,6,7,8] => [5,4,1,3,2,6,7,8] => 1101000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => [4,3,5,2,1,6,7,8] => [5,4,2,1,3,6,7,8] => 1110000
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => [3,4,5,2,1,6,7,8] => [5,4,1,2,3,6,7,8] => 1100000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [2,5,4,3,1,6,7,8] => [5,4,2,3,1,6,7,8] => [5,1,4,3,2,6,7,8] => 1011000
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => [4,2,5,3,1,6,7,8] => [5,3,4,1,2,6,7,8] => 1010000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [3,2,5,4,1,6,7,8] => [5,3,2,4,1,6,7,8] => [5,3,1,4,2,6,7,8] => 1101000
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [2,3,5,4,1,6,7,8] => [5,2,3,4,1,6,7,8] => [5,1,2,4,3,6,7,8] => 1001000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => [4,3,2,5,1,6,7,8] => [5,3,2,1,4,6,7,8] => 1110000
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [3,4,2,5,1,6,7,8] => [5,3,1,2,4,6,7,8] => 1100000
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => [4,2,3,5,1,6,7,8] => [5,1,3,2,4,6,7,8] => 1010000
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => [3,2,4,5,1,6,7,8] => [5,2,1,3,4,6,7,8] => 1100000
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7,8] => [5,1,2,3,4,6,7,8] => 1000000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => [5,4,3,1,2,6,7,8] => [1,5,4,3,2,6,7,8] => 0111000
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,4,5,3,2,6,7,8] => [4,5,1,3,2,6,7,8] => [2,5,4,1,3,6,7,8] => 0110000
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,3,5,4,2,6,7,8] => [5,3,1,4,2,6,7,8] => [4,5,1,3,2,6,7,8] => 0101000
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => [3,1,4,5,2,6,7,8] => [3,5,1,2,4,6,7,8] => 0100000
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => [4,2,1,5,3,6,7,8] => [4,3,5,1,2,6,7,8] => 1010000
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => [5,4,1,2,3,6,7,8] => [1,2,5,4,3,6,7,8] => 0011000
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,2,4,5,3,6,7,8] => [4,1,2,5,3,6,7,8] => [2,4,5,1,3,6,7,8] => 0010000
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [2,3,1,5,4,6,7,8] => [5,2,3,1,4,6,7,8] => [4,1,2,5,3,6,7,8] => 1001000
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [5,3,1,2,4,6,7,8] => [1,4,2,5,3,6,7,8] => 0101000
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => [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] => [4,3,2,1,5,6,7,8] => 1110000
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => [3,4,2,1,5,6,7,8] => [4,3,1,2,5,6,7,8] => 1100000
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [4,1,3,2,5,6,7,8] => 1010000
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [4,2,1,3,5,6,7,8] => 1100000
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => 1000000
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => [4,3,1,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => 0110000
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => [3,1,4,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => 0100000
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => [4,2,1,3,5,6,7,8] => [3,1,4,2,5,6,7,8] => 1010000
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => [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] => [3,2,1,4,5,6,7,8] => 1100000
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => 1000000
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [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] => [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] => [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] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [8,9,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1,2] => 11111110
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [7,8,9,6,5,4,3,2,1] => [9,8,7,6,5,4,1,2,3] => 11111100
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => [6,7,8,9,5,4,3,2,1] => [9,8,7,6,5,1,2,3,4] => 11111000
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => [5,6,7,8,9,4,3,2,1] => [9,8,7,6,1,2,3,4,5] => 11110000
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => [4,5,6,7,8,9,3,2,1] => [9,8,7,1,2,3,4,5,6] => 11100000
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => [3,4,5,6,7,8,9,2,1] => [9,8,1,2,3,4,5,6,7] => 11000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => 10000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [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] => [10,9,8,7,6,5,4,3,2,1] => 111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [9,10,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,1,2] => 111111110
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [7,9,8,6,5,4,3,2,1] => [9,7,8,6,5,4,3,2,1] => [9,8,7,6,5,4,1,3,2] => 11111101
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => [8,9,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,1,2,3] => 111111100
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [6,8,9,7,5,4,3,2,1] => [8,6,9,7,5,4,3,2,1] => [9,8,7,6,5,3,4,1,2] => 11111010
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => [7,8,9,10,6,5,4,3,2,1] => [10,9,8,7,6,5,1,2,3,4] => 111111000
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [6,7,8,9,10,5,4,3,2,1] => [10,9,8,7,6,1,2,3,4,5] => 111110000
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => [5,6,7,8,9,10,4,3,2,1] => [10,9,8,7,1,2,3,4,5,6] => 111100000
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => [4,5,6,7,8,9,10,3,2,1] => [10,9,8,1,2,3,4,5,6,7] => 111000000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [2,4,5,6,7,8,9,3,1] => [4,2,5,6,7,8,9,3,1] => [9,3,8,1,2,4,5,6,7] => 10100000
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => [3,4,5,6,7,8,9,10,2,1] => [10,9,1,2,3,4,5,6,7,8] => 110000000
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,2] => [3,1,4,5,6,7,8,9,2] => [3,9,1,2,4,5,6,7,8] => 01000000
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => 100000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [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] => [8,7,9,6,5,4,3,2,1] => [9,8,7,6,5,4,2,1,3] => 11111110
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [8,7,6,9,5,4,3,2,1] => [9,8,7,6,5,3,2,1,4] => 11111110
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [8,7,6,5,9,4,3,2,1] => [9,8,7,6,4,3,2,1,5] => 11111110
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [8,7,6,5,4,9,3,2,1] => [9,8,7,5,4,3,2,1,6] => 11111110
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [8,7,6,5,4,3,9,2,1] => [9,8,6,5,4,3,2,1,7] => 11111110
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,9,1] => [9,7,6,5,4,3,2,1,8] => 11111110
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [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] => [9,8,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,2,1,3] => 111111110
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [9,8,7,10,6,5,4,3,2,1] => [10,9,8,7,6,5,3,2,1,4] => 111111110
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [9,8,7,6,10,5,4,3,2,1] => [10,9,8,7,6,4,3,2,1,5] => 111111110
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [9,8,7,6,5,10,4,3,2,1] => [10,9,8,7,5,4,3,2,1,6] => 111111110
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [9,8,7,6,5,4,10,3,2,1] => [10,9,8,6,5,4,3,2,1,7] => 111111110
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [9,8,7,6,5,4,3,10,2,1] => [10,9,7,6,5,4,3,2,1,8] => 111111110
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,8,7,6,5,4,3,2,9] => [8,7,6,5,4,3,1,2,9] => [1,8,7,6,5,4,3,2,9] => 01111110
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [9,8,7,6,5,4,3,2,10,1] => [10,8,7,6,5,4,3,2,1,9] => 111111110
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => 111111110
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,3,5,7,9,10,8,6,4,2] => [9,7,5,3,1,10,8,6,4,2] => [9,10,7,8,5,6,3,4,1,2] => 010101010
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => [5,6,4,7,3,8,2,9,1,10] => [9,7,5,3,1,2,4,6,8,10] => 111100000
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [1,3,5,7,9,11,12,10,8,6,4,2] => [11,9,7,5,3,1,12,10,8,6,4,2] => [11,12,9,10,7,8,5,6,3,4,1,2] => 01010101010
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => [10,8,6,4,2,1,3,5,7,9] => [6,1,7,2,8,3,9,4,10,5] => 101010101
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => [12,10,8,6,4,2,1,3,5,7,9,11] => [7,1,8,2,9,3,10,4,11,5,12,6] => 10101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,9,8] => 00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,10,9] => 000000001
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,9,8] => [9,2,1,3,4,5,6,7,8] => [3,1,2,4,5,6,7,9,8] => 10000001
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,9,1] => [9,2,1,3,4,5,6,7,8] => 11000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => [11,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [2,4,3,5,6,7,8,9,1] => [4,2,3,5,6,7,8,9,1] => [9,1,3,2,4,5,6,7,8] => 10100000
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => [3,4,2,5,6,7,8,9,1] => [9,3,1,2,4,5,6,7,8] => 11000000
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => [3,2,4,5,6,7,8,9,10,1] => [10,2,1,3,4,5,6,7,8,9] => 110000000
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => 1000000000
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => [8,1,2,3,4,5,6,9,7] => [2,3,4,5,6,8,9,1,7] => 00000010
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,7,8,9,6] => [7,1,2,3,4,5,8,9,6] => [2,3,4,5,7,9,1,6,8] => 00000100
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => [9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,9,8,7] => 00000011
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,7,9,10,8] => [9,1,2,3,4,5,6,7,10,8] => [2,3,4,5,6,7,9,10,1,8] => 000000010
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => [9,8,7,6,5,4,3,1,2] => [1,9,8,7,6,5,4,3,2] => 01111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => [7,8,6,5,4,3,2,1,9] => [8,7,6,5,4,3,1,2,9] => 11111100
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => [8,9,7,6,5,4,1,3,2] => [2,9,8,7,6,5,4,1,3] => 01111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => [10,9,8,7,6,5,4,3,1,2] => [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] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => [8,9,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,1,2,10] => 111111100
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [7,6,8,5,4,3,2,1,9] => [8,7,6,5,4,2,1,3,9] => 11111100
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,9,10,8,7,6,5,4,3,2] => [9,10,8,7,6,5,4,1,3,2] => [2,10,9,8,7,6,5,4,1,3] => 011111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => [11,10,9,8,7,6,5,4,3,1,2] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => [6,5,7,4,8,3,9,2,10,1] => [10,8,6,4,2,1,3,5,7,9] => 111110000
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [7,6,8,5,9,4,10,3,11,2,12,1] => [7,6,8,5,9,4,10,3,11,2,12,1] => [12,10,8,6,4,2,1,3,5,7,9,11] => 11111100000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [2,1,9,8,7,6,5,4,3] => [9,8,7,6,5,4,2,1,3] => [8,1,9,7,6,5,4,3,2] => 10111111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [3,2,1,9,8,7,6,5,4] => [9,8,7,6,5,3,2,1,4] => [8,7,1,9,6,5,4,3,2] => 11011111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [4,3,2,1,9,8,7,6,5] => [9,8,7,6,4,3,2,1,5] => [8,7,6,1,9,5,4,3,2] => 11101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [5,4,3,2,1,9,8,7,6] => [9,8,7,5,4,3,2,1,6] => [8,7,6,5,1,9,4,3,2] => 11110111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [6,5,4,3,2,1,9,8,7] => [9,8,6,5,4,3,2,1,7] => [8,7,6,5,4,1,9,3,2] => 11111011
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [7,6,5,4,3,2,1,9,8] => [9,7,6,5,4,3,2,1,8] => [8,7,6,5,4,3,1,9,2] => 11111101
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,9,8,7,6,5,4,3] => [9,8,7,6,5,4,1,2,3] => [1,2,9,8,7,6,5,4,3] => 00111111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,4,2,1,3] => [9,1,10,8,7,6,5,4,3,2] => 101111111
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [2,3,1,9,8,7,6,5,4] => [9,8,7,6,5,2,3,1,4] => [8,1,2,9,7,6,5,4,3] => 10011111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [3,2,1,10,9,8,7,6,5,4] => [10,9,8,7,6,5,3,2,1,4] => [9,8,1,10,7,6,5,4,3,2] => 110111111
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]] => [3,4,2,1,9,8,7,6,5] => [9,8,7,6,3,4,2,1,5] => [8,7,1,2,9,6,5,4,3] => 11001111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [7,6,5,4,3,2,1,10,9,8] => [10,9,7,6,5,4,3,2,1,8] => [9,8,7,6,5,4,1,10,3,2] => 111111011
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => [10,8,7,6,5,4,3,2,1,9] => [9,8,7,6,5,4,3,1,10,2] => 111111101
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [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] => [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] => [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] => [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] => [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] => [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] => [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] => [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] => [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] => [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] => [4,3,2,1,5,6,7,8,9,10] => 111000000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [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] => [3,1,2,4,5,6,7,8,9] => [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] => [2,1,3,4,5,6,7,8,9,10] => 100000000
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [4,9,8,7,6,5,3,2,1] => [9,8,7,6,4,5,3,2,1] => [9,8,7,1,6,5,4,3,2] => 11101111
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [3,9,8,7,6,5,4,2,1] => [9,8,7,6,5,3,4,2,1] => [9,8,1,7,6,5,4,3,2] => 11011111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => [9,8,7,6,5,4,2,3,1] => [9,1,8,7,6,5,4,3,2] => 10111111
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [6,10,9,8,7,5,4,3,2,1] => [10,9,8,6,7,5,4,3,2,1] => [10,9,8,7,6,1,5,4,3,2] => 111110111
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,9,8,1] => [9,2,3,4,5,6,7,8,1] => [9,1,2,3,4,5,6,8,7] => 10000001
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,8,10,9,1] => [10,2,3,4,5,6,7,8,9,1] => [10,1,2,3,4,5,6,7,9,8] => 100000001
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => [3,4,5,6,7,8,2,9,1] => [9,7,1,2,3,4,5,6,8] => 11000000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9] => 10000000
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => 10000000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [2,3,4,5,6,7,1,8,9] => [7,1,2,3,4,5,6,8,9] => 10000000
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => 100000000
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [2,4,3,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [4,1,3,2,5,6,7,8,9] => 10100000
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [2,3,4,5,6,8,7,1,9] => [8,2,3,4,5,6,7,1,9] => [8,1,2,3,4,5,7,6,9] => 10000010
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10] => 100000000
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => 00100000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,2,3,5,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => 00010000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,6,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => 00001000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,7,6,8,9] => [7,1,2,3,4,5,6,8,9] => [1,2,3,4,5,7,6,8,9] => 00000100
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => [1,2,3,4,5,6,8,7,9] => 00000010
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => 010000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => 001000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,2,3,5,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => 000100000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,2,3,4,6,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => 000010000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,5,7,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => 000001000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,6,8,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => 000000100
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => [1,2,3,4,5,6,7,9,8,10] => 000000010
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [7,6,5,4,3,2,9,8,1] => [9,7,6,5,4,3,2,8,1] => [9,7,6,5,4,3,1,8,2] => 11111101
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => [6,5,4,3,2,7,8,9,1] => [9,5,4,3,2,1,6,7,8] => 11111000
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => [7,6,5,4,3,2,8,9,1] => [7,6,5,4,3,2,8,9,1] => [9,6,5,4,3,2,1,7,8] => 11111100
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]] => [8,7,6,5,4,3,2,9,10,1] => [8,7,6,5,4,3,2,9,10,1] => [10,7,6,5,4,3,2,1,8,9] => 111111100
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [6,5,4,3,2,1,8,9,7] => [8,6,5,4,3,2,1,9,7] => [8,7,6,5,4,3,9,1,2] => 11111010
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => [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] => [10,9,8,7,6,5,4,1,2,3] => [1,2,10,9,8,7,6,5,4,3] => 001111111
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,9,8,7,6,5,4,3,2,10] => [9,8,7,6,5,4,3,1,2,10] => [1,9,8,7,6,5,4,3,2,10] => 011111110
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [2,1,4,5,3,6,7,8,9] => [4,2,1,5,3,6,7,8,9] => [4,3,5,1,2,6,7,8,9] => 10100000
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,7,10,9,8] => [10,9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,10,9,8] => 000000011
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => [6,7,8,5,4,3,2,1,9] => [8,7,6,5,4,1,2,3,9] => 11111000
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,9,8,7,6] => [9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,9,8,7,6] => 00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,9,8,7,6,5] => [9,8,7,6,1,2,3,4,5] => [1,2,3,4,9,8,7,6,5] => 00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,9,8,7,6,5,4] => [9,8,7,6,5,1,2,3,4] => [1,2,3,9,8,7,6,5,4] => 00011111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,7,6,9,8] => [9,7,1,2,3,4,5,6,8] => [1,2,3,4,5,8,6,9,7] => 00000101
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,6,10,9,8,7] => [10,9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,10,9,8,7] => 000000111
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,5,10,9,8,7,6] => [10,9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,10,9,8,7,6] => 000001111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,4,10,9,8,7,6,5] => [10,9,8,7,6,1,2,3,4,5] => [1,2,3,4,10,9,8,7,6,5] => 000011111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,3,10,9,8,7,6,5,4] => [10,9,8,7,6,5,1,2,3,4] => [1,2,3,10,9,8,7,6,5,4] => 000111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => [10,11,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,1,2] => 1111111110
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => [7,8,6,5,4,3,2,9,1] => [9,7,6,5,4,3,1,2,8] => 11111100
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => [3,4,2,1,5,6,7,8,9] => [4,3,1,2,5,6,7,8,9] => 11000000
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.] => [3,4,2,5,1,6,7,8,9] => [3,4,2,5,1,6,7,8,9] => [5,3,1,2,4,6,7,8,9] => 11000000
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => [7,6,5,4,3,2,8,1,9] => [8,6,5,4,3,2,1,7,9] => 11111100
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => [7,6,5,8,4,3,2,1,9] => [7,6,5,8,4,3,2,1,9] => [8,7,6,5,3,2,1,4,9] => 11111100
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => [4,5,3,2,1,6,7,8,9] => [5,4,3,1,2,6,7,8,9] => 11100000
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => [3,2,4,5,6,7,8,1,9] => [8,2,1,3,4,5,6,7,9] => 11000000
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [2,3,4,5,6,7,1,9,8] => [9,2,3,4,5,6,7,1,8] => [8,1,2,3,4,5,6,9,7] => 10000001
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,3,4,2,5,6,7,8,9] => [3,1,4,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => 01000000
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => [8,7,6,5,4,3,2,9,1,10] => [8,7,6,5,4,3,2,9,1,10] => [9,7,6,5,4,3,2,1,8,10] => 111111100
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,8,10,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.] => [5,6,4,3,2,1,7,8,9] => [5,6,4,3,2,1,7,8,9] => [6,5,4,3,1,2,7,8,9] => 11110000
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => [5,6,4,3,2,1,7,8,9,10] => [5,6,4,3,2,1,7,8,9,10] => [6,5,4,3,1,2,7,8,9,10] => 111100000
[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.] => [6,7,5,4,3,2,1,8,9,10,11] => [6,7,5,4,3,2,1,8,9,10,11] => [7,6,5,4,3,1,2,8,9,10,11] => 1111100000
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.] => [6,7,5,4,3,2,1,8,9,10] => [6,7,5,4,3,2,1,8,9,10] => [7,6,5,4,3,1,2,8,9,10] => 111110000
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.] => [5,6,4,3,2,7,1,8,9] => [5,6,4,3,2,7,1,8,9] => [7,5,4,3,1,2,6,8,9] => 11110000
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
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
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