Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00064: Permutations —reverse⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Images
[.,.] => [1] => [1] =>
[.,[.,.]] => [2,1] => [1,2] => 0
[[.,.],.] => [1,2] => [2,1] => 1
[.,[.,[.,.]]] => [3,2,1] => [1,2,3] => 00
[.,[[.,.],.]] => [2,3,1] => [1,3,2] => 01
[[.,.],[.,.]] => [1,3,2] => [2,3,1] => 10
[[.,[.,.]],.] => [2,1,3] => [3,1,2] => 10
[[[.,.],.],.] => [1,2,3] => [3,2,1] => 11
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,2,3,4] => 000
[.,[.,[[.,.],.]]] => [3,4,2,1] => [1,2,4,3] => 001
[.,[[.,.],[.,.]]] => [2,4,3,1] => [1,3,4,2] => 010
[.,[[.,[.,.]],.]] => [3,2,4,1] => [1,4,2,3] => 010
[.,[[[.,.],.],.]] => [2,3,4,1] => [1,4,3,2] => 011
[[.,.],[.,[.,.]]] => [1,4,3,2] => [2,3,4,1] => 100
[[.,.],[[.,.],.]] => [1,3,4,2] => [2,4,3,1] => 101
[[.,[.,.]],[.,.]] => [2,1,4,3] => [3,4,1,2] => 100
[[[.,.],.],[.,.]] => [1,2,4,3] => [3,4,2,1] => 110
[[.,[.,[.,.]]],.] => [3,2,1,4] => [4,1,2,3] => 100
[[.,[[.,.],.]],.] => [2,3,1,4] => [4,1,3,2] => 110
[[[.,.],[.,.]],.] => [1,3,2,4] => [4,2,3,1] => 110
[[[.,[.,.]],.],.] => [2,1,3,4] => [4,3,1,2] => 101
[[[[.,.],.],.],.] => [1,2,3,4] => [4,3,2,1] => 111
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,2,3,4,5] => 0000
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [1,2,3,5,4] => 0001
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [1,2,4,5,3] => 0010
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [1,2,5,3,4] => 0010
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [1,2,5,4,3] => 0011
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [1,3,4,5,2] => 0100
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [1,3,5,4,2] => 0101
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [1,4,5,2,3] => 0100
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [1,4,5,3,2] => 0110
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [1,5,2,3,4] => 0100
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [1,5,2,4,3] => 0110
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [1,5,3,4,2] => 0110
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [1,5,4,2,3] => 0101
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,5,4,3,2] => 0111
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [2,3,4,5,1] => 1000
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [2,3,5,4,1] => 1001
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [2,4,5,3,1] => 1010
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [2,5,3,4,1] => 1010
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [2,5,4,3,1] => 1011
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [3,4,5,1,2] => 1000
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [3,5,4,1,2] => 1001
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [3,4,5,2,1] => 1100
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [3,5,4,2,1] => 1101
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [4,5,1,2,3] => 1000
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [4,5,1,3,2] => 1100
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [4,5,2,3,1] => 1100
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [4,5,3,1,2] => 1010
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [4,5,3,2,1] => 1110
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [5,1,2,3,4] => 1000
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [5,1,2,4,3] => 1010
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [5,1,3,4,2] => 1100
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [5,1,4,2,3] => 1100
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [5,1,4,3,2] => 1110
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [5,2,3,4,1] => 1100
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [5,2,4,3,1] => 1110
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [5,3,4,1,2] => 1010
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [5,3,4,2,1] => 1110
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [5,4,1,2,3] => 1001
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [5,4,1,3,2] => 1101
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [5,4,2,3,1] => 1101
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [5,4,3,1,2] => 1011
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [5,4,3,2,1] => 1111
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => 00000
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [1,2,3,4,6,5] => 00001
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [1,2,3,5,6,4] => 00010
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [1,2,3,6,4,5] => 00010
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => 00011
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [1,2,4,5,6,3] => 00100
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [1,2,4,6,5,3] => 00101
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [1,2,5,6,3,4] => 00100
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [1,2,5,6,4,3] => 00110
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [1,2,6,3,4,5] => 00100
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [1,2,6,3,5,4] => 00110
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [1,2,6,4,5,3] => 00110
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [1,2,6,5,3,4] => 00101
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [1,2,6,5,4,3] => 00111
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [1,3,4,5,6,2] => 01000
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [1,3,4,6,5,2] => 01001
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [1,3,5,6,4,2] => 01010
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [1,3,6,4,5,2] => 01010
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [1,3,6,5,4,2] => 01011
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [1,4,5,6,2,3] => 01000
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [1,4,6,5,2,3] => 01001
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [1,4,5,6,3,2] => 01100
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [1,4,6,5,3,2] => 01101
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [1,5,6,2,3,4] => 01000
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [1,5,6,2,4,3] => 01100
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [1,5,6,3,4,2] => 01100
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [1,5,6,4,2,3] => 01010
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [1,5,6,4,3,2] => 01110
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [1,6,2,3,4,5] => 01000
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [1,6,2,3,5,4] => 01010
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [1,6,2,4,5,3] => 01100
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [1,6,2,5,3,4] => 01100
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [1,6,2,5,4,3] => 01110
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [1,6,3,4,5,2] => 01100
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [1,6,3,5,4,2] => 01110
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [1,6,4,5,2,3] => 01010
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [1,6,4,5,3,2] => 01110
>>> Load all 1931 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [1,6,5,2,3,4] => 01001
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [1,6,5,2,4,3] => 01101
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [1,6,5,3,4,2] => 01101
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [1,6,5,4,2,3] => 01011
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => 01111
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [2,3,4,5,6,1] => 10000
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [2,3,4,6,5,1] => 10001
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [2,3,5,6,4,1] => 10010
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [2,3,6,4,5,1] => 10010
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [2,3,6,5,4,1] => 10011
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [2,4,5,6,3,1] => 10100
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [2,4,6,5,3,1] => 10101
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [2,5,6,3,4,1] => 10100
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [2,5,6,4,3,1] => 10110
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [2,6,3,4,5,1] => 10100
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [2,6,3,5,4,1] => 10110
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [2,6,4,5,3,1] => 10110
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [2,6,5,3,4,1] => 10101
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [2,6,5,4,3,1] => 10111
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => 10000
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [3,4,6,5,1,2] => 10001
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [3,5,6,4,1,2] => 10010
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [3,6,4,5,1,2] => 10010
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [3,6,5,4,1,2] => 10011
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [3,4,5,6,2,1] => 11000
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [3,4,6,5,2,1] => 11001
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [3,5,6,4,2,1] => 11010
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [3,6,4,5,2,1] => 11010
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [3,6,5,4,2,1] => 11011
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [4,5,6,1,2,3] => 10000
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [4,6,5,1,2,3] => 10001
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [4,5,6,1,3,2] => 11000
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [4,6,5,1,3,2] => 11001
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [4,5,6,2,3,1] => 11000
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [4,6,5,2,3,1] => 11001
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [4,5,6,3,1,2] => 10100
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [4,6,5,3,1,2] => 10101
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [4,5,6,3,2,1] => 11100
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [4,6,5,3,2,1] => 11101
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [5,6,1,2,3,4] => 10000
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [5,6,1,2,4,3] => 10100
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [5,6,1,3,4,2] => 11000
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [5,6,1,4,2,3] => 11000
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [5,6,1,4,3,2] => 11100
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [5,6,2,3,4,1] => 11000
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [5,6,2,4,3,1] => 11100
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => 10100
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => 11100
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [5,6,4,1,2,3] => 10010
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [5,6,4,1,3,2] => 11010
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 11010
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => 10110
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 11110
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => 10000
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [6,1,2,3,5,4] => 10010
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [6,1,2,4,5,3] => 10100
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [6,1,2,5,3,4] => 10100
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [6,1,2,5,4,3] => 10110
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [6,1,3,4,5,2] => 11000
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [6,1,3,5,4,2] => 11010
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [6,1,4,5,2,3] => 11000
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [6,1,4,5,3,2] => 11100
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [6,1,5,2,3,4] => 11000
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [6,1,5,2,4,3] => 11100
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [6,1,5,3,4,2] => 11100
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [6,1,5,4,2,3] => 11010
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => 11110
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [6,2,3,4,5,1] => 11000
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [6,2,3,5,4,1] => 11010
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [6,2,4,5,3,1] => 11100
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [6,2,5,3,4,1] => 11100
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [6,2,5,4,3,1] => 11110
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [6,3,4,5,1,2] => 10100
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [6,3,5,4,1,2] => 10110
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [6,3,4,5,2,1] => 11100
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [6,3,5,4,2,1] => 11110
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [6,4,5,1,2,3] => 10010
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [6,4,5,1,3,2] => 11010
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => 11010
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [6,4,5,3,1,2] => 10110
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 11110
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => 10001
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [6,5,1,2,4,3] => 10101
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [6,5,1,3,4,2] => 11001
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [6,5,1,4,2,3] => 11001
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => 11101
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [6,5,2,3,4,1] => 11001
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [6,5,2,4,3,1] => 11101
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [6,5,3,4,1,2] => 10101
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 11101
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => 10011
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => 11011
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 11011
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => 10111
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 000000
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [1,2,3,4,5,7,6] => 000001
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [1,2,3,4,6,7,5] => 000010
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [1,2,3,4,7,5,6] => 000010
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [1,2,3,4,7,6,5] => 000011
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [1,2,3,5,6,7,4] => 000100
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [1,2,3,5,7,6,4] => 000101
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [1,2,3,6,7,4,5] => 000100
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [1,2,3,6,7,5,4] => 000110
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [1,2,3,7,4,5,6] => 000100
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [1,2,3,7,4,6,5] => 000110
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [1,2,3,7,5,6,4] => 000110
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [1,2,3,7,6,4,5] => 000101
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => 000111
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [1,2,4,5,6,7,3] => 001000
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [1,2,4,5,7,6,3] => 001001
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [1,2,4,6,7,5,3] => 001010
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [1,2,4,7,5,6,3] => 001010
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [1,2,4,7,6,5,3] => 001011
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [1,2,5,6,7,3,4] => 001000
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [1,2,5,7,6,3,4] => 001001
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [1,2,5,6,7,4,3] => 001100
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [1,2,5,7,6,4,3] => 001101
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [1,2,6,7,3,4,5] => 001000
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [1,2,6,7,3,5,4] => 001100
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [1,2,6,7,4,5,3] => 001100
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [1,2,6,7,5,3,4] => 001010
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [1,2,6,7,5,4,3] => 001110
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [1,2,7,3,4,5,6] => 001000
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [1,2,7,3,4,6,5] => 001010
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [1,2,7,3,5,6,4] => 001100
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [1,2,7,3,6,4,5] => 001100
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [1,2,7,3,6,5,4] => 001110
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [1,2,7,4,5,6,3] => 001100
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [1,2,7,4,6,5,3] => 001110
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [1,2,7,5,6,3,4] => 001010
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [1,2,7,5,6,4,3] => 001110
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [1,2,7,6,3,4,5] => 001001
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [1,2,7,6,3,5,4] => 001101
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [1,2,7,6,4,5,3] => 001101
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [1,2,7,6,5,3,4] => 001011
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [1,2,7,6,5,4,3] => 001111
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [1,3,4,5,6,7,2] => 010000
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [1,3,4,5,7,6,2] => 010001
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [1,3,4,6,7,5,2] => 010010
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [1,3,4,7,5,6,2] => 010010
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [1,3,4,7,6,5,2] => 010011
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [1,3,5,6,7,4,2] => 010100
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [1,3,5,7,6,4,2] => 010101
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [1,3,6,7,4,5,2] => 010100
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [1,3,6,7,5,4,2] => 010110
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [1,3,7,4,5,6,2] => 010100
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [1,3,7,4,6,5,2] => 010110
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [1,3,7,5,6,4,2] => 010110
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [1,3,7,6,4,5,2] => 010101
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [1,3,7,6,5,4,2] => 010111
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [1,4,5,6,7,2,3] => 010000
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [1,4,5,7,6,2,3] => 010001
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [1,4,6,7,5,2,3] => 010010
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [1,4,7,5,6,2,3] => 010010
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [1,4,7,6,5,2,3] => 010011
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [1,4,5,6,7,3,2] => 011000
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [1,4,5,7,6,3,2] => 011001
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [1,4,6,7,5,3,2] => 011010
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [1,4,7,5,6,3,2] => 011010
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [1,4,7,6,5,3,2] => 011011
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [1,5,6,7,2,3,4] => 010000
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => [1,5,7,6,2,3,4] => 010001
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [1,5,6,7,2,4,3] => 011000
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [1,5,7,6,2,4,3] => 011001
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [1,5,6,7,3,4,2] => 011000
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [1,5,7,6,3,4,2] => 011001
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [1,5,6,7,4,2,3] => 010100
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [1,5,7,6,4,2,3] => 010101
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [1,5,6,7,4,3,2] => 011100
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [1,5,7,6,4,3,2] => 011101
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [1,6,7,2,3,4,5] => 010000
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [1,6,7,2,3,5,4] => 010100
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [1,6,7,2,4,5,3] => 011000
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => [1,6,7,2,5,3,4] => 011000
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [1,6,7,2,5,4,3] => 011100
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [1,6,7,3,4,5,2] => 011000
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [1,6,7,3,5,4,2] => 011100
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [1,6,7,4,5,2,3] => 010100
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [1,6,7,4,5,3,2] => 011100
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [1,6,7,5,2,3,4] => 010010
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [1,6,7,5,2,4,3] => 011010
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [1,6,7,5,3,4,2] => 011010
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [1,6,7,5,4,2,3] => 010110
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [1,6,7,5,4,3,2] => 011110
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [1,7,2,3,4,5,6] => 010000
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [1,7,2,3,4,6,5] => 010010
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [1,7,2,3,5,6,4] => 010100
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [1,7,2,3,6,4,5] => 010100
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [1,7,2,3,6,5,4] => 010110
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => [1,7,2,4,5,6,3] => 011000
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [1,7,2,4,6,5,3] => 011010
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [1,7,2,5,6,3,4] => 011000
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [1,7,2,5,6,4,3] => 011100
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [1,7,2,6,3,4,5] => 011000
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [1,7,2,6,3,5,4] => 011100
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [1,7,2,6,4,5,3] => 011100
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [1,7,2,6,5,3,4] => 011010
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [1,7,2,6,5,4,3] => 011110
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [1,7,3,4,5,6,2] => 011000
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [1,7,3,4,6,5,2] => 011010
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [1,7,3,5,6,4,2] => 011100
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [1,7,3,6,4,5,2] => 011100
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [1,7,3,6,5,4,2] => 011110
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [1,7,4,5,6,2,3] => 010100
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [1,7,4,6,5,2,3] => 010110
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [1,7,4,5,6,3,2] => 011100
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [1,7,4,6,5,3,2] => 011110
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => [1,7,5,6,2,3,4] => 010010
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [1,7,5,6,2,4,3] => 011010
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [1,7,5,6,3,4,2] => 011010
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [1,7,5,6,4,2,3] => 010110
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [1,7,5,6,4,3,2] => 011110
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [1,7,6,2,3,4,5] => 010001
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [1,7,6,2,3,5,4] => 010101
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [1,7,6,2,4,5,3] => 011001
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [1,7,6,2,5,3,4] => 011001
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [1,7,6,2,5,4,3] => 011101
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [1,7,6,3,4,5,2] => 011001
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [1,7,6,3,5,4,2] => 011101
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [1,7,6,4,5,2,3] => 010101
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [1,7,6,4,5,3,2] => 011101
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [1,7,6,5,2,3,4] => 010011
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [1,7,6,5,2,4,3] => 011011
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [1,7,6,5,3,4,2] => 011011
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [1,7,6,5,4,2,3] => 010111
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => 011111
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [2,3,4,5,6,7,1] => 100000
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [2,3,4,5,7,6,1] => 100001
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [2,3,4,6,7,5,1] => 100010
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [2,3,4,7,5,6,1] => 100010
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [2,3,4,7,6,5,1] => 100011
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [2,3,5,6,7,4,1] => 100100
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [2,3,5,7,6,4,1] => 100101
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [2,3,6,7,4,5,1] => 100100
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [2,3,6,7,5,4,1] => 100110
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [2,3,7,4,5,6,1] => 100100
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [2,3,7,4,6,5,1] => 100110
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [2,3,7,5,6,4,1] => 100110
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [2,3,7,6,4,5,1] => 100101
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [2,3,7,6,5,4,1] => 100111
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [2,4,5,6,7,3,1] => 101000
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [2,4,5,7,6,3,1] => 101001
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [2,4,6,7,5,3,1] => 101010
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [2,4,7,5,6,3,1] => 101010
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [2,4,7,6,5,3,1] => 101011
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [2,5,6,7,3,4,1] => 101000
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [2,5,7,6,3,4,1] => 101001
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [2,5,6,7,4,3,1] => 101100
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [2,5,7,6,4,3,1] => 101101
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [2,6,7,3,4,5,1] => 101000
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [2,6,7,3,5,4,1] => 101100
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [2,6,7,4,5,3,1] => 101100
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [2,6,7,5,3,4,1] => 101010
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [2,6,7,5,4,3,1] => 101110
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [2,7,3,4,5,6,1] => 101000
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [2,7,3,4,6,5,1] => 101010
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [2,7,3,5,6,4,1] => 101100
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [2,7,3,6,4,5,1] => 101100
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [2,7,3,6,5,4,1] => 101110
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [2,7,4,5,6,3,1] => 101100
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [2,7,4,6,5,3,1] => 101110
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [2,7,5,6,3,4,1] => 101010
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [2,7,5,6,4,3,1] => 101110
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [2,7,6,3,4,5,1] => 101001
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [2,7,6,3,5,4,1] => 101101
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [2,7,6,4,5,3,1] => 101101
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [2,7,6,5,3,4,1] => 101011
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [2,7,6,5,4,3,1] => 101111
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [3,4,5,6,7,1,2] => 100000
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [3,4,5,7,6,1,2] => 100001
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [3,4,6,7,5,1,2] => 100010
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [3,4,7,5,6,1,2] => 100010
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [3,4,7,6,5,1,2] => 100011
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [3,5,6,7,4,1,2] => 100100
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [3,5,7,6,4,1,2] => 100101
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [3,6,7,4,5,1,2] => 100100
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [3,6,7,5,4,1,2] => 100110
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [3,7,4,5,6,1,2] => 100100
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [3,7,4,6,5,1,2] => 100110
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [3,7,5,6,4,1,2] => 100110
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [3,7,6,4,5,1,2] => 100101
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [3,7,6,5,4,1,2] => 100111
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [3,4,5,6,7,2,1] => 110000
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [3,4,5,7,6,2,1] => 110001
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [3,4,6,7,5,2,1] => 110010
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [3,4,7,5,6,2,1] => 110010
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [3,4,7,6,5,2,1] => 110011
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [3,5,6,7,4,2,1] => 110100
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [3,5,7,6,4,2,1] => 110101
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [3,6,7,4,5,2,1] => 110100
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [3,6,7,5,4,2,1] => 110110
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [3,7,4,5,6,2,1] => 110100
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [3,7,4,6,5,2,1] => 110110
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [3,7,5,6,4,2,1] => 110110
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [3,7,6,4,5,2,1] => 110101
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [3,7,6,5,4,2,1] => 110111
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [4,5,6,7,1,2,3] => 100000
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [4,5,7,6,1,2,3] => 100001
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [4,6,7,5,1,2,3] => 100010
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [4,7,5,6,1,2,3] => 100010
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [4,7,6,5,1,2,3] => 100011
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [4,5,6,7,1,3,2] => 110000
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [4,5,7,6,1,3,2] => 110001
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [4,6,7,5,1,3,2] => 110010
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [4,7,5,6,1,3,2] => 110010
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [4,7,6,5,1,3,2] => 110011
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [4,5,6,7,2,3,1] => 110000
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [4,5,7,6,2,3,1] => 110001
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [4,6,7,5,2,3,1] => 110010
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [4,7,5,6,2,3,1] => 110010
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [4,7,6,5,2,3,1] => 110011
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [4,5,6,7,3,1,2] => 101000
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [4,5,7,6,3,1,2] => 101001
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [4,6,7,5,3,1,2] => 101010
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [4,7,5,6,3,1,2] => 101010
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [4,7,6,5,3,1,2] => 101011
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => 111000
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [4,5,7,6,3,2,1] => 111001
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [4,6,7,5,3,2,1] => 111010
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [4,7,5,6,3,2,1] => 111010
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [4,7,6,5,3,2,1] => 111011
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [5,6,7,1,2,3,4] => 100000
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [5,7,6,1,2,3,4] => 100001
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [5,6,7,1,2,4,3] => 101000
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [5,7,6,1,2,4,3] => 101001
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [5,6,7,1,3,4,2] => 110000
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [5,7,6,1,3,4,2] => 110001
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [5,6,7,1,4,2,3] => 110000
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [5,7,6,1,4,2,3] => 110001
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [5,6,7,1,4,3,2] => 111000
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [5,7,6,1,4,3,2] => 111001
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [5,6,7,2,3,4,1] => 110000
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [5,7,6,2,3,4,1] => 110001
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [5,6,7,2,4,3,1] => 111000
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [5,7,6,2,4,3,1] => 111001
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [5,6,7,3,4,1,2] => 101000
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [5,7,6,3,4,1,2] => 101001
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [5,6,7,3,4,2,1] => 111000
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [5,7,6,3,4,2,1] => 111001
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [5,6,7,4,1,2,3] => 100100
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [5,7,6,4,1,2,3] => 100101
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [5,6,7,4,1,3,2] => 110100
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [5,7,6,4,1,3,2] => 110101
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [5,6,7,4,2,3,1] => 110100
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [5,7,6,4,2,3,1] => 110101
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [5,6,7,4,3,1,2] => 101100
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [5,7,6,4,3,1,2] => 101101
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => 111100
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [5,7,6,4,3,2,1] => 111101
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [6,7,1,2,3,4,5] => 100000
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [6,7,1,2,3,5,4] => 100100
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [6,7,1,2,4,5,3] => 101000
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [6,7,1,2,5,3,4] => 101000
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [6,7,1,2,5,4,3] => 101100
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [6,7,1,3,4,5,2] => 110000
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [6,7,1,3,5,4,2] => 110100
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [6,7,1,4,5,2,3] => 110000
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [6,7,1,4,5,3,2] => 111000
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [6,7,1,5,2,3,4] => 110000
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [6,7,1,5,2,4,3] => 111000
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [6,7,1,5,3,4,2] => 111000
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [6,7,1,5,4,2,3] => 110100
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [6,7,1,5,4,3,2] => 111100
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [6,7,2,3,4,5,1] => 110000
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [6,7,2,3,5,4,1] => 110100
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [6,7,2,4,5,3,1] => 111000
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [6,7,2,5,3,4,1] => 111000
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [6,7,2,5,4,3,1] => 111100
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [6,7,3,4,5,1,2] => 101000
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [6,7,3,5,4,1,2] => 101100
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [6,7,3,4,5,2,1] => 111000
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [6,7,3,5,4,2,1] => 111100
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [6,7,4,5,1,2,3] => 100100
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [6,7,4,5,1,3,2] => 110100
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [6,7,4,5,2,3,1] => 110100
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [6,7,4,5,3,1,2] => 101100
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => 111100
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [6,7,5,1,2,3,4] => 100010
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [6,7,5,1,2,4,3] => 101010
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [6,7,5,1,3,4,2] => 110010
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [6,7,5,1,4,2,3] => 110010
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [6,7,5,1,4,3,2] => 111010
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [6,7,5,2,3,4,1] => 110010
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [6,7,5,2,4,3,1] => 111010
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [6,7,5,3,4,1,2] => 101010
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [6,7,5,3,4,2,1] => 111010
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [6,7,5,4,1,2,3] => 100110
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [6,7,5,4,1,3,2] => 110110
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [6,7,5,4,2,3,1] => 110110
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [6,7,5,4,3,1,2] => 101110
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => 111110
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [7,1,2,3,4,5,6] => 100000
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [7,1,2,3,4,6,5] => 100010
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [7,1,2,3,5,6,4] => 100100
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [7,1,2,3,6,4,5] => 100100
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [7,1,2,3,6,5,4] => 100110
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [7,1,2,4,5,6,3] => 101000
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [7,1,2,4,6,5,3] => 101010
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [7,1,2,5,6,3,4] => 101000
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [7,1,2,5,6,4,3] => 101100
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [7,1,2,6,3,4,5] => 101000
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [7,1,2,6,3,5,4] => 101100
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [7,1,2,6,4,5,3] => 101100
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [7,1,2,6,5,3,4] => 101010
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [7,1,2,6,5,4,3] => 101110
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [7,1,3,4,5,6,2] => 110000
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [7,1,3,4,6,5,2] => 110010
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [7,1,3,5,6,4,2] => 110100
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [7,1,3,6,4,5,2] => 110100
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [7,1,3,6,5,4,2] => 110110
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [7,1,4,5,6,2,3] => 110000
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [7,1,4,6,5,2,3] => 110010
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [7,1,4,5,6,3,2] => 111000
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [7,1,4,6,5,3,2] => 111010
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [7,1,5,6,2,3,4] => 110000
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [7,1,5,6,2,4,3] => 111000
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [7,1,5,6,3,4,2] => 111000
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [7,1,5,6,4,2,3] => 110100
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [7,1,5,6,4,3,2] => 111100
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [7,1,6,2,3,4,5] => 110000
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [7,1,6,2,3,5,4] => 110100
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [7,1,6,2,4,5,3] => 111000
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [7,1,6,2,5,3,4] => 111000
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [7,1,6,2,5,4,3] => 111100
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [7,1,6,3,4,5,2] => 111000
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [7,1,6,3,5,4,2] => 111100
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [7,1,6,4,5,2,3] => 110100
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [7,1,6,4,5,3,2] => 111100
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [7,1,6,5,2,3,4] => 110010
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [7,1,6,5,2,4,3] => 111010
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [7,1,6,5,3,4,2] => 111010
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [7,1,6,5,4,2,3] => 110110
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [7,1,6,5,4,3,2] => 111110
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [7,2,3,4,5,6,1] => 110000
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [7,2,3,4,6,5,1] => 110010
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [7,2,3,5,6,4,1] => 110100
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [7,2,3,6,4,5,1] => 110100
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [7,2,3,6,5,4,1] => 110110
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [7,2,4,5,6,3,1] => 111000
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [7,2,4,6,5,3,1] => 111010
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [7,2,5,6,3,4,1] => 111000
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [7,2,5,6,4,3,1] => 111100
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [7,2,6,3,4,5,1] => 111000
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [7,2,6,3,5,4,1] => 111100
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [7,2,6,4,5,3,1] => 111100
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [7,2,6,5,3,4,1] => 111010
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [7,2,6,5,4,3,1] => 111110
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [7,3,4,5,6,1,2] => 101000
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [7,3,4,6,5,1,2] => 101010
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [7,3,5,6,4,1,2] => 101100
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [7,3,6,4,5,1,2] => 101100
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [7,3,6,5,4,1,2] => 101110
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [7,3,4,5,6,2,1] => 111000
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [7,3,4,6,5,2,1] => 111010
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [7,3,5,6,4,2,1] => 111100
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [7,3,6,4,5,2,1] => 111100
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [7,3,6,5,4,2,1] => 111110
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [7,4,5,6,1,2,3] => 100100
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [7,4,6,5,1,2,3] => 100110
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [7,4,5,6,1,3,2] => 110100
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [7,4,6,5,1,3,2] => 110110
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [7,4,5,6,2,3,1] => 110100
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [7,4,6,5,2,3,1] => 110110
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [7,4,5,6,3,1,2] => 101100
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [7,4,6,5,3,1,2] => 101110
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [7,4,5,6,3,2,1] => 111100
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [7,4,6,5,3,2,1] => 111110
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [7,5,6,1,2,3,4] => 100010
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [7,5,6,1,2,4,3] => 101010
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [7,5,6,1,3,4,2] => 110010
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [7,5,6,1,4,2,3] => 110010
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [7,5,6,1,4,3,2] => 111010
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [7,5,6,2,3,4,1] => 110010
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [7,5,6,2,4,3,1] => 111010
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [7,5,6,3,4,1,2] => 101010
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [7,5,6,3,4,2,1] => 111010
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [7,5,6,4,1,2,3] => 100110
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [7,5,6,4,1,3,2] => 110110
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [7,5,6,4,2,3,1] => 110110
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [7,5,6,4,3,1,2] => 101110
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [7,5,6,4,3,2,1] => 111110
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [7,6,1,2,3,4,5] => 100001
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [7,6,1,2,3,5,4] => 100101
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [7,6,1,2,4,5,3] => 101001
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [7,6,1,2,5,3,4] => 101001
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [7,6,1,2,5,4,3] => 101101
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [7,6,1,3,4,5,2] => 110001
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [7,6,1,3,5,4,2] => 110101
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [7,6,1,4,5,2,3] => 110001
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [7,6,1,4,5,3,2] => 111001
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [7,6,1,5,2,3,4] => 110001
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [7,6,1,5,2,4,3] => 111001
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [7,6,1,5,3,4,2] => 111001
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [7,6,1,5,4,2,3] => 110101
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [7,6,1,5,4,3,2] => 111101
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [7,6,2,3,4,5,1] => 110001
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [7,6,2,3,5,4,1] => 110101
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [7,6,2,4,5,3,1] => 111001
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [7,6,2,5,3,4,1] => 111001
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [7,6,2,5,4,3,1] => 111101
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [7,6,3,4,5,1,2] => 101001
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [7,6,3,5,4,1,2] => 101101
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [7,6,3,4,5,2,1] => 111001
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [7,6,3,5,4,2,1] => 111101
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [7,6,4,5,1,2,3] => 100101
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [7,6,4,5,1,3,2] => 110101
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [7,6,4,5,2,3,1] => 110101
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [7,6,4,5,3,1,2] => 101101
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [7,6,4,5,3,2,1] => 111101
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [7,6,5,1,2,3,4] => 100011
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [7,6,5,1,2,4,3] => 101011
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [7,6,5,1,3,4,2] => 110011
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [7,6,5,1,4,2,3] => 110011
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [7,6,5,1,4,3,2] => 111011
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [7,6,5,2,3,4,1] => 110011
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [7,6,5,2,4,3,1] => 111011
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [7,6,5,3,4,1,2] => 101011
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [7,6,5,3,4,2,1] => 111011
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [7,6,5,4,1,2,3] => 100111
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [7,6,5,4,1,3,2] => 110111
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [7,6,5,4,2,3,1] => 110111
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [7,6,5,4,3,1,2] => 101111
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 0000000
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,7] => 0000001
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [6,8,7,5,4,3,2,1] => [1,2,3,4,5,7,8,6] => 0000010
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [1,2,3,4,5,8,6,7] => 0000010
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [1,2,3,4,5,8,7,6] => 0000011
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [5,8,7,6,4,3,2,1] => [1,2,3,4,6,7,8,5] => 0000100
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [5,7,8,6,4,3,2,1] => [1,2,3,4,6,8,7,5] => 0000101
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => [1,2,3,4,7,8,5,6] => 0000100
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [5,6,8,7,4,3,2,1] => [1,2,3,4,7,8,6,5] => 0000110
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [1,2,3,4,8,5,6,7] => 0000100
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => [1,2,3,4,8,5,7,6] => 0000110
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => [1,2,3,4,8,6,7,5] => 0000110
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [1,2,3,4,8,7,5,6] => 0000101
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [1,2,3,4,8,7,6,5] => 0000111
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => [1,2,3,5,6,7,8,4] => 0001000
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [4,7,8,6,5,3,2,1] => [1,2,3,5,6,8,7,4] => 0001001
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => [1,2,3,5,7,8,6,4] => 0001010
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [4,7,6,8,5,3,2,1] => [1,2,3,5,8,6,7,4] => 0001010
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [4,6,7,8,5,3,2,1] => [1,2,3,5,8,7,6,4] => 0001011
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [5,4,8,7,6,3,2,1] => [1,2,3,6,7,8,4,5] => 0001000
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [5,4,7,8,6,3,2,1] => [1,2,3,6,8,7,4,5] => 0001001
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [4,5,8,7,6,3,2,1] => [1,2,3,6,7,8,5,4] => 0001100
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [4,5,7,8,6,3,2,1] => [1,2,3,6,8,7,5,4] => 0001101
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [6,5,4,8,7,3,2,1] => [1,2,3,7,8,4,5,6] => 0001000
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [5,6,4,8,7,3,2,1] => [1,2,3,7,8,4,6,5] => 0001100
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [4,6,5,8,7,3,2,1] => [1,2,3,7,8,5,6,4] => 0001100
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [5,4,6,8,7,3,2,1] => [1,2,3,7,8,6,4,5] => 0001010
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => [1,2,3,7,8,6,5,4] => 0001110
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [1,2,3,8,4,5,6,7] => 0001000
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => [1,2,3,8,4,5,7,6] => 0001010
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [5,7,6,4,8,3,2,1] => [1,2,3,8,4,6,7,5] => 0001100
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [1,2,3,8,4,7,5,6] => 0001100
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => [1,2,3,8,4,7,6,5] => 0001110
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1] => [1,2,3,8,5,6,7,4] => 0001100
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [4,6,7,5,8,3,2,1] => [1,2,3,8,5,7,6,4] => 0001110
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [5,4,7,6,8,3,2,1] => [1,2,3,8,6,7,4,5] => 0001010
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [4,5,7,6,8,3,2,1] => [1,2,3,8,6,7,5,4] => 0001110
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => [1,2,3,8,7,4,5,6] => 0001001
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => [1,2,3,8,7,4,6,5] => 0001101
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [4,6,5,7,8,3,2,1] => [1,2,3,8,7,5,6,4] => 0001101
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => [1,2,3,8,7,6,4,5] => 0001011
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [1,2,3,8,7,6,5,4] => 0001111
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [3,8,7,6,5,4,2,1] => [1,2,4,5,6,7,8,3] => 0010000
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [3,7,8,6,5,4,2,1] => [1,2,4,5,6,8,7,3] => 0010001
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [3,6,8,7,5,4,2,1] => [1,2,4,5,7,8,6,3] => 0010010
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [3,7,6,8,5,4,2,1] => [1,2,4,5,8,6,7,3] => 0010010
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [3,6,7,8,5,4,2,1] => [1,2,4,5,8,7,6,3] => 0010011
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => [1,2,4,6,7,8,5,3] => 0010100
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => [1,2,4,6,8,7,5,3] => 0010101
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [3,6,5,8,7,4,2,1] => [1,2,4,7,8,5,6,3] => 0010100
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [3,5,6,8,7,4,2,1] => [1,2,4,7,8,6,5,3] => 0010110
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [3,7,6,5,8,4,2,1] => [1,2,4,8,5,6,7,3] => 0010100
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [3,5,6,7,8,4,2,1] => [1,2,4,8,7,6,5,3] => 0010111
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => [1,2,5,6,7,8,3,4] => 0010000
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [4,3,7,8,6,5,2,1] => [1,2,5,6,8,7,3,4] => 0010001
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [4,3,6,8,7,5,2,1] => [1,2,5,7,8,6,3,4] => 0010010
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [4,3,7,6,8,5,2,1] => [1,2,5,8,6,7,3,4] => 0010010
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [4,3,6,7,8,5,2,1] => [1,2,5,8,7,6,3,4] => 0010011
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [3,4,8,7,6,5,2,1] => [1,2,5,6,7,8,4,3] => 0011000
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [3,4,7,8,6,5,2,1] => [1,2,5,6,8,7,4,3] => 0011001
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [3,4,7,6,8,5,2,1] => [1,2,5,8,6,7,4,3] => 0011010
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => [1,2,5,8,7,6,4,3] => 0011011
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [5,4,3,8,7,6,2,1] => [1,2,6,7,8,3,4,5] => 0010000
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [5,4,3,7,8,6,2,1] => [1,2,6,8,7,3,4,5] => 0010001
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [4,5,3,8,7,6,2,1] => [1,2,6,7,8,3,5,4] => 0011000
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [4,5,3,7,8,6,2,1] => [1,2,6,8,7,3,5,4] => 0011001
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [3,5,4,8,7,6,2,1] => [1,2,6,7,8,4,5,3] => 0011000
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [3,5,4,7,8,6,2,1] => [1,2,6,8,7,4,5,3] => 0011001
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [4,3,5,8,7,6,2,1] => [1,2,6,7,8,5,3,4] => 0010100
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [4,3,5,7,8,6,2,1] => [1,2,6,8,7,5,3,4] => 0010101
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [3,4,5,8,7,6,2,1] => [1,2,6,7,8,5,4,3] => 0011100
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [6,5,4,3,8,7,2,1] => [1,2,7,8,3,4,5,6] => 0010000
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [5,6,4,3,8,7,2,1] => [1,2,7,8,3,4,6,5] => 0010100
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [4,6,5,3,8,7,2,1] => [1,2,7,8,3,5,6,4] => 0011000
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [5,4,6,3,8,7,2,1] => [1,2,7,8,3,6,4,5] => 0011000
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [4,5,6,3,8,7,2,1] => [1,2,7,8,3,6,5,4] => 0011100
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [3,6,5,4,8,7,2,1] => [1,2,7,8,4,5,6,3] => 0011000
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => [1,2,7,8,5,6,3,4] => 0010100
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [3,4,6,5,8,7,2,1] => [1,2,7,8,5,6,4,3] => 0011100
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [5,4,3,6,8,7,2,1] => [1,2,7,8,6,3,4,5] => 0010010
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [4,5,3,6,8,7,2,1] => [1,2,7,8,6,3,5,4] => 0011010
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [3,5,4,6,8,7,2,1] => [1,2,7,8,6,4,5,3] => 0011010
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [4,3,5,6,8,7,2,1] => [1,2,7,8,6,5,3,4] => 0010110
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [3,4,5,6,8,7,2,1] => [1,2,7,8,6,5,4,3] => 0011110
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [1,2,8,3,4,5,6,7] => 0010000
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => [1,2,8,3,4,5,7,6] => 0010010
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [5,7,6,4,3,8,2,1] => [1,2,8,3,4,6,7,5] => 0010100
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => [1,2,8,3,4,7,6,5] => 0010110
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [4,7,6,5,3,8,2,1] => [1,2,8,3,5,6,7,4] => 0011000
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [4,6,7,5,3,8,2,1] => [1,2,8,3,5,7,6,4] => 0011010
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [5,4,7,6,3,8,2,1] => [1,2,8,3,6,7,4,5] => 0011000
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => [1,2,8,3,7,4,5,6] => 0011000
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [5,6,4,7,3,8,2,1] => [1,2,8,3,7,4,6,5] => 0011100
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [1,2,8,3,7,6,4,5] => 0011010
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => [1,2,8,3,7,6,5,4] => 0011110
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [3,7,6,5,4,8,2,1] => [1,2,8,4,5,6,7,3] => 0011000
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [3,5,7,6,4,8,2,1] => [1,2,8,4,6,7,5,3] => 0011100
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [3,5,6,7,4,8,2,1] => [1,2,8,4,7,6,5,3] => 0011110
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [4,3,7,6,5,8,2,1] => [1,2,8,5,6,7,3,4] => 0010100
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [3,4,7,6,5,8,2,1] => [1,2,8,5,6,7,4,3] => 0011100
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [4,5,3,7,6,8,2,1] => [1,2,8,6,7,3,5,4] => 0011010
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [4,3,5,7,6,8,2,1] => [1,2,8,6,7,5,3,4] => 0010110
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [3,4,5,7,6,8,2,1] => [1,2,8,6,7,5,4,3] => 0011110
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => [1,2,8,7,3,4,5,6] => 0010001
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => [5,6,4,3,7,8,2,1] => [1,2,8,7,3,4,6,5] => 0010101
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => [1,2,8,7,3,6,5,4] => 0011101
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [3,6,5,4,7,8,2,1] => [1,2,8,7,4,5,6,3] => 0011001
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [3,5,6,4,7,8,2,1] => [1,2,8,7,4,6,5,3] => 0011101
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [4,3,6,5,7,8,2,1] => [1,2,8,7,5,6,3,4] => 0010101
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [3,4,6,5,7,8,2,1] => [1,2,8,7,5,6,4,3] => 0011101
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => [1,2,8,7,6,3,4,5] => 0010011
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [4,5,3,6,7,8,2,1] => [1,2,8,7,6,3,5,4] => 0011011
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [1,2,8,7,6,5,3,4] => 0010111
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [1,2,8,7,6,5,4,3] => 0011111
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => [1,3,4,5,6,7,8,2] => 0100000
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [2,7,8,6,5,4,3,1] => [1,3,4,5,6,8,7,2] => 0100001
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => [1,3,4,5,7,8,6,2] => 0100010
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [2,7,6,8,5,4,3,1] => [1,3,4,5,8,6,7,2] => 0100010
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [2,6,7,8,5,4,3,1] => [1,3,4,5,8,7,6,2] => 0100011
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [2,5,8,7,6,4,3,1] => [1,3,4,6,7,8,5,2] => 0100100
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [2,7,6,5,8,4,3,1] => [1,3,4,8,5,6,7,2] => 0100100
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [2,5,7,6,8,4,3,1] => [1,3,4,8,6,7,5,2] => 0100110
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [2,5,6,7,8,4,3,1] => [1,3,4,8,7,6,5,2] => 0100111
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [2,4,8,7,6,5,3,1] => [1,3,5,6,7,8,4,2] => 0101000
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [2,4,7,8,6,5,3,1] => [1,3,5,6,8,7,4,2] => 0101001
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => [1,3,5,7,8,6,4,2] => 0101010
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [2,4,6,7,8,5,3,1] => [1,3,5,8,7,6,4,2] => 0101011
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [2,5,4,7,8,6,3,1] => [1,3,6,8,7,4,5,2] => 0101001
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [2,4,5,8,7,6,3,1] => [1,3,6,7,8,5,4,2] => 0101100
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [2,4,5,7,8,6,3,1] => [1,3,6,8,7,5,4,2] => 0101101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [2,6,5,4,8,7,3,1] => [1,3,7,8,4,5,6,2] => 0101000
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [2,5,6,4,8,7,3,1] => [1,3,7,8,4,6,5,2] => 0101100
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [2,4,6,5,8,7,3,1] => [1,3,7,8,5,6,4,2] => 0101100
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [2,4,5,6,8,7,3,1] => [1,3,7,8,6,5,4,2] => 0101110
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [2,7,6,5,4,8,3,1] => [1,3,8,4,5,6,7,2] => 0101000
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [2,5,7,6,4,8,3,1] => [1,3,8,4,6,7,5,2] => 0101100
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [2,4,7,6,5,8,3,1] => [1,3,8,5,6,7,4,2] => 0101100
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [2,4,6,7,5,8,3,1] => [1,3,8,5,7,6,4,2] => 0101110
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [2,5,4,7,6,8,3,1] => [1,3,8,6,7,4,5,2] => 0101010
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [2,6,5,4,7,8,3,1] => [1,3,8,7,4,5,6,2] => 0101001
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [2,5,6,4,7,8,3,1] => [1,3,8,7,4,6,5,2] => 0101101
[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [2,4,6,5,7,8,3,1] => [1,3,8,7,5,6,4,2] => 0101101
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [2,4,5,6,7,8,3,1] => [1,3,8,7,6,5,4,2] => 0101111
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => [1,4,5,6,7,8,2,3] => 0100000
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [3,2,7,8,6,5,4,1] => [1,4,5,6,8,7,2,3] => 0100001
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [3,2,6,7,8,5,4,1] => [1,4,5,8,7,6,2,3] => 0100011
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [3,2,6,5,8,7,4,1] => [1,4,7,8,5,6,2,3] => 0100100
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [3,2,7,6,5,8,4,1] => [1,4,8,5,6,7,2,3] => 0100100
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [3,2,6,7,5,8,4,1] => [1,4,8,5,7,6,2,3] => 0100110
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [3,2,5,7,6,8,4,1] => [1,4,8,6,7,5,2,3] => 0100110
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => [1,4,5,6,7,8,3,2] => 0110000
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [2,3,6,8,7,5,4,1] => [1,4,5,7,8,6,3,2] => 0110010
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [2,3,7,6,8,5,4,1] => [1,4,5,8,6,7,3,2] => 0110010
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [2,3,6,7,8,5,4,1] => [1,4,5,8,7,6,3,2] => 0110011
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [2,3,5,8,7,6,4,1] => [1,4,6,7,8,5,3,2] => 0110100
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [2,3,5,7,8,6,4,1] => [1,4,6,8,7,5,3,2] => 0110101
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [2,3,6,5,8,7,4,1] => [1,4,7,8,5,6,3,2] => 0110100
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => [1,4,7,8,6,5,3,2] => 0110110
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [2,3,7,6,5,8,4,1] => [1,4,8,5,6,7,3,2] => 0110100
[.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [2,3,6,7,5,8,4,1] => [1,4,8,5,7,6,3,2] => 0110110
[.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [2,3,5,7,6,8,4,1] => [1,4,8,6,7,5,3,2] => 0110110
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [2,3,5,6,7,8,4,1] => [1,4,8,7,6,5,3,2] => 0110111
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => [1,5,6,7,8,2,3,4] => 0100000
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [4,3,2,7,8,6,5,1] => [1,5,6,8,7,2,3,4] => 0100001
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [4,3,2,6,8,7,5,1] => [1,5,7,8,6,2,3,4] => 0100010
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [4,3,2,6,7,8,5,1] => [1,5,8,7,6,2,3,4] => 0100011
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => [1,5,6,7,8,2,4,3] => 0110000
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [3,4,2,6,8,7,5,1] => [1,5,7,8,6,2,4,3] => 0110010
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [3,4,2,6,7,8,5,1] => [1,5,8,7,6,2,4,3] => 0110011
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [2,4,3,8,7,6,5,1] => [1,5,6,7,8,3,4,2] => 0110000
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [2,4,3,6,8,7,5,1] => [1,5,7,8,6,3,4,2] => 0110010
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [2,4,3,7,6,8,5,1] => [1,5,8,6,7,3,4,2] => 0110010
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [2,4,3,6,7,8,5,1] => [1,5,8,7,6,3,4,2] => 0110011
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [3,2,4,8,7,6,5,1] => [1,5,6,7,8,4,2,3] => 0101000
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [3,2,4,7,8,6,5,1] => [1,5,6,8,7,4,2,3] => 0101001
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [3,2,4,6,8,7,5,1] => [1,5,7,8,6,4,2,3] => 0101010
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [3,2,4,7,6,8,5,1] => [1,5,8,6,7,4,2,3] => 0101010
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => [1,5,6,7,8,4,3,2] => 0111000
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [2,3,4,6,7,8,5,1] => [1,5,8,7,6,4,3,2] => 0111011
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [5,4,3,2,8,7,6,1] => [1,6,7,8,2,3,4,5] => 0100000
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [5,4,3,2,7,8,6,1] => [1,6,8,7,2,3,4,5] => 0100001
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [4,5,3,2,8,7,6,1] => [1,6,7,8,2,3,5,4] => 0101000
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [4,5,3,2,7,8,6,1] => [1,6,8,7,2,3,5,4] => 0101001
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [3,5,4,2,8,7,6,1] => [1,6,7,8,2,4,5,3] => 0110000
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [4,3,5,2,8,7,6,1] => [1,6,7,8,2,5,3,4] => 0110000
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [4,3,5,2,7,8,6,1] => [1,6,8,7,2,5,3,4] => 0110001
[.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [3,4,5,2,7,8,6,1] => [1,6,8,7,2,5,4,3] => 0111001
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => [1,6,7,8,3,4,5,2] => 0110000
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [2,5,4,3,7,8,6,1] => [1,6,8,7,3,4,5,2] => 0110001
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [2,4,5,3,8,7,6,1] => [1,6,7,8,3,5,4,2] => 0111000
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [2,4,5,3,7,8,6,1] => [1,6,8,7,3,5,4,2] => 0111001
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [2,3,5,4,8,7,6,1] => [1,6,7,8,4,5,3,2] => 0111000
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [2,3,5,4,7,8,6,1] => [1,6,8,7,4,5,3,2] => 0111001
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [4,3,2,5,8,7,6,1] => [1,6,7,8,5,2,3,4] => 0100100
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [4,3,2,5,7,8,6,1] => [1,6,8,7,5,2,3,4] => 0100101
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [3,4,2,5,7,8,6,1] => [1,6,8,7,5,2,4,3] => 0110101
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [2,4,3,5,8,7,6,1] => [1,6,7,8,5,3,4,2] => 0110100
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [2,4,3,5,7,8,6,1] => [1,6,8,7,5,3,4,2] => 0110101
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [2,3,4,5,8,7,6,1] => [1,6,7,8,5,4,3,2] => 0111100
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [2,3,4,5,7,8,6,1] => [1,6,8,7,5,4,3,2] => 0111101
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [6,5,4,3,2,8,7,1] => [1,7,8,2,3,4,5,6] => 0100000
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [4,6,5,3,2,8,7,1] => [1,7,8,2,3,5,6,4] => 0101000
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [5,4,6,3,2,8,7,1] => [1,7,8,2,3,6,4,5] => 0101000
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [4,5,6,3,2,8,7,1] => [1,7,8,2,3,6,5,4] => 0101100
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [3,6,5,4,2,8,7,1] => [1,7,8,2,4,5,6,3] => 0110000
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [3,5,6,4,2,8,7,1] => [1,7,8,2,4,6,5,3] => 0110100
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [4,3,6,5,2,8,7,1] => [1,7,8,2,5,6,3,4] => 0110000
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [3,5,4,6,2,8,7,1] => [1,7,8,2,6,4,5,3] => 0111000
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [2,6,5,4,3,8,7,1] => [1,7,8,3,4,5,6,2] => 0110000
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [2,4,6,5,3,8,7,1] => [1,7,8,3,5,6,4,2] => 0111000
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [2,5,4,6,3,8,7,1] => [1,7,8,3,6,4,5,2] => 0111000
[.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [2,4,5,6,3,8,7,1] => [1,7,8,3,6,5,4,2] => 0111100
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => [1,7,8,4,5,6,2,3] => 0101000
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [3,2,5,6,4,8,7,1] => [1,7,8,4,6,5,2,3] => 0101100
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => [1,7,8,5,6,3,4,2] => 0110100
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [3,2,4,6,5,8,7,1] => [1,7,8,5,6,4,2,3] => 0101100
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [2,3,4,6,5,8,7,1] => [1,7,8,5,6,4,3,2] => 0111100
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [5,4,3,2,6,8,7,1] => [1,7,8,6,2,3,4,5] => 0100010
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [4,5,3,2,6,8,7,1] => [1,7,8,6,2,3,5,4] => 0101010
[.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [3,4,5,2,6,8,7,1] => [1,7,8,6,2,5,4,3] => 0111010
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [2,5,4,3,6,8,7,1] => [1,7,8,6,3,4,5,2] => 0110010
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [2,4,5,3,6,8,7,1] => [1,7,8,6,3,5,4,2] => 0111010
[.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [2,3,5,4,6,8,7,1] => [1,7,8,6,4,5,3,2] => 0111010
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [3,4,2,5,6,8,7,1] => [1,7,8,6,5,2,4,3] => 0110110
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => [1,7,8,6,5,3,4,2] => 0110110
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [3,2,4,5,6,8,7,1] => [1,7,8,6,5,4,2,3] => 0101110
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => [1,7,8,6,5,4,3,2] => 0111110
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [1,8,2,3,4,5,6,7] => 0100000
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [1,8,2,3,4,5,7,6] => 0100010
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [5,7,6,4,3,2,8,1] => [1,8,2,3,4,6,7,5] => 0100100
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [1,8,2,3,4,7,5,6] => 0100100
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => [1,8,2,3,4,7,6,5] => 0100110
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [4,7,6,5,3,2,8,1] => [1,8,2,3,5,6,7,4] => 0101000
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [4,5,7,6,3,2,8,1] => [1,8,2,3,6,7,5,4] => 0101100
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [4,6,5,7,3,2,8,1] => [1,8,2,3,7,5,6,4] => 0101100
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => [5,4,6,7,3,2,8,1] => [1,8,2,3,7,6,4,5] => 0101010
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => [1,8,2,3,7,6,5,4] => 0101110
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [3,7,6,5,4,2,8,1] => [1,8,2,4,5,6,7,3] => 0110000
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => [3,6,7,5,4,2,8,1] => [1,8,2,4,5,7,6,3] => 0110010
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [3,5,7,6,4,2,8,1] => [1,8,2,4,6,7,5,3] => 0110100
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [3,6,5,7,4,2,8,1] => [1,8,2,4,7,5,6,3] => 0110100
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [3,5,6,7,4,2,8,1] => [1,8,2,4,7,6,5,3] => 0110110
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [4,3,7,6,5,2,8,1] => [1,8,2,5,6,7,3,4] => 0110000
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [4,3,6,7,5,2,8,1] => [1,8,2,5,7,6,3,4] => 0110010
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [3,4,7,6,5,2,8,1] => [1,8,2,5,6,7,4,3] => 0111000
[.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [3,4,6,7,5,2,8,1] => [1,8,2,5,7,6,4,3] => 0111010
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [5,4,3,7,6,2,8,1] => [1,8,2,6,7,3,4,5] => 0110000
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [3,5,4,7,6,2,8,1] => [1,8,2,6,7,4,5,3] => 0111000
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [3,4,5,7,6,2,8,1] => [1,8,2,6,7,5,4,3] => 0111100
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [1,8,2,7,3,4,5,6] => 0110000
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [5,6,4,3,7,2,8,1] => [1,8,2,7,3,4,6,5] => 0110100
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [4,6,5,3,7,2,8,1] => [1,8,2,7,3,5,6,4] => 0111000
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [1,8,2,7,3,6,4,5] => 0111000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => [1,8,2,7,3,6,5,4] => 0111100
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [3,6,5,4,7,2,8,1] => [1,8,2,7,4,5,6,3] => 0111000
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => [1,8,2,7,4,6,5,3] => 0111100
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => [1,8,2,7,5,6,3,4] => 0110100
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => [1,8,2,7,6,3,4,5] => 0110010
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => [1,8,2,7,6,3,5,4] => 0111010
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [3,5,4,6,7,2,8,1] => [1,8,2,7,6,4,5,3] => 0111010
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => [1,8,2,7,6,5,4,3] => 0111110
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1] => [1,8,3,4,5,6,7,2] => 0110000
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [2,5,7,6,4,3,8,1] => [1,8,3,4,6,7,5,2] => 0110100
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [2,5,6,7,4,3,8,1] => [1,8,3,4,7,6,5,2] => 0110110
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [2,4,7,6,5,3,8,1] => [1,8,3,5,6,7,4,2] => 0111000
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [2,4,6,7,5,3,8,1] => [1,8,3,5,7,6,4,2] => 0111010
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [2,5,4,7,6,3,8,1] => [1,8,3,6,7,4,5,2] => 0111000
[.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [2,4,5,7,6,3,8,1] => [1,8,3,6,7,5,4,2] => 0111100
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [2,5,6,4,7,3,8,1] => [1,8,3,7,4,6,5,2] => 0111100
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => [1,8,3,7,5,6,4,2] => 0111100
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [2,5,4,6,7,3,8,1] => [1,8,3,7,6,4,5,2] => 0111010
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [2,4,5,6,7,3,8,1] => [1,8,3,7,6,5,4,2] => 0111110
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [3,2,7,6,5,4,8,1] => [1,8,4,5,6,7,2,3] => 0101000
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [3,2,6,7,5,4,8,1] => [1,8,4,5,7,6,2,3] => 0101010
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [3,2,5,7,6,4,8,1] => [1,8,4,6,7,5,2,3] => 0101100
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => [1,8,4,7,5,6,2,3] => 0101100
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [3,2,5,6,7,4,8,1] => [1,8,4,7,6,5,2,3] => 0101110
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [2,3,7,6,5,4,8,1] => [1,8,4,5,6,7,3,2] => 0111000
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [2,3,5,7,6,4,8,1] => [1,8,4,6,7,5,3,2] => 0111100
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [2,3,5,6,7,4,8,1] => [1,8,4,7,6,5,3,2] => 0111110
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1] => [1,8,5,6,7,2,3,4] => 0100100
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [4,3,2,6,7,5,8,1] => [1,8,5,7,6,2,3,4] => 0100110
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [3,4,2,7,6,5,8,1] => [1,8,5,6,7,2,4,3] => 0110100
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [3,4,2,6,7,5,8,1] => [1,8,5,7,6,2,4,3] => 0110110
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [2,4,3,7,6,5,8,1] => [1,8,5,6,7,3,4,2] => 0110100
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [3,2,4,7,6,5,8,1] => [1,8,5,6,7,4,2,3] => 0101100
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [2,3,4,7,6,5,8,1] => [1,8,5,6,7,4,3,2] => 0111100
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [2,3,4,6,7,5,8,1] => [1,8,5,7,6,4,3,2] => 0111110
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [5,4,3,2,7,6,8,1] => [1,8,6,7,2,3,4,5] => 0100010
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => [1,8,6,7,2,5,3,4] => 0110010
[.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [3,4,5,2,7,6,8,1] => [1,8,6,7,2,5,4,3] => 0111010
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [2,5,4,3,7,6,8,1] => [1,8,6,7,3,4,5,2] => 0110010
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => [1,8,6,7,4,5,2,3] => 0101010
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [2,3,5,4,7,6,8,1] => [1,8,6,7,4,5,3,2] => 0111010
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [4,3,2,5,7,6,8,1] => [1,8,6,7,5,2,3,4] => 0100110
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [2,4,3,5,7,6,8,1] => [1,8,6,7,5,3,4,2] => 0110110
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1] => [1,8,6,7,5,4,2,3] => 0101110
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => [1,8,6,7,5,4,3,2] => 0111110
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => [1,8,7,2,3,4,5,6] => 0100001
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [5,6,4,3,2,7,8,1] => [1,8,7,2,3,4,6,5] => 0100101
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => [4,6,5,3,2,7,8,1] => [1,8,7,2,3,5,6,4] => 0101001
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => [1,8,7,2,3,6,4,5] => 0101001
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => [1,8,7,2,3,6,5,4] => 0101101
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [3,6,5,4,2,7,8,1] => [1,8,7,2,4,5,6,3] => 0110001
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [4,3,6,5,2,7,8,1] => [1,8,7,2,5,6,3,4] => 0110001
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [3,4,6,5,2,7,8,1] => [1,8,7,2,5,6,4,3] => 0111001
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => [1,8,7,2,6,3,4,5] => 0110001
[.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [4,5,3,6,2,7,8,1] => [1,8,7,2,6,3,5,4] => 0111001
[.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [3,5,4,6,2,7,8,1] => [1,8,7,2,6,4,5,3] => 0111001
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => [1,8,7,2,6,5,3,4] => 0110101
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => [1,8,7,2,6,5,4,3] => 0111101
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [2,6,5,4,3,7,8,1] => [1,8,7,3,4,5,6,2] => 0110001
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [2,5,6,4,3,7,8,1] => [1,8,7,3,4,6,5,2] => 0110101
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [2,5,4,6,3,7,8,1] => [1,8,7,3,6,4,5,2] => 0111001
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [2,4,5,6,3,7,8,1] => [1,8,7,3,6,5,4,2] => 0111101
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [3,2,6,5,4,7,8,1] => [1,8,7,4,5,6,2,3] => 0101001
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [2,3,6,5,4,7,8,1] => [1,8,7,4,5,6,3,2] => 0111001
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [2,3,5,6,4,7,8,1] => [1,8,7,4,6,5,3,2] => 0111101
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [4,3,2,6,5,7,8,1] => [1,8,7,5,6,2,3,4] => 0100101
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [2,4,3,6,5,7,8,1] => [1,8,7,5,6,3,4,2] => 0110101
[.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [3,2,4,6,5,7,8,1] => [1,8,7,5,6,4,2,3] => 0101101
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [2,3,4,6,5,7,8,1] => [1,8,7,5,6,4,3,2] => 0111101
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [1,8,7,6,2,3,4,5] => 0100011
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [3,5,4,2,6,7,8,1] => [1,8,7,6,2,4,5,3] => 0110011
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [1,8,7,6,2,5,4,3] => 0111011
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1] => [1,8,7,6,3,4,5,2] => 0110011
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [2,4,5,3,6,7,8,1] => [1,8,7,6,3,5,4,2] => 0111011
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [3,2,5,4,6,7,8,1] => [1,8,7,6,4,5,2,3] => 0101011
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1] => [1,8,7,6,4,5,3,2] => 0111011
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [1,8,7,6,5,2,3,4] => 0100111
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [1,8,7,6,5,2,4,3] => 0110111
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [2,4,3,5,6,7,8,1] => [1,8,7,6,5,3,4,2] => 0110111
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [1,8,7,6,5,4,2,3] => 0101111
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2] => 0111111
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [2,3,4,5,6,7,8,1] => 1000000
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => [2,3,4,5,6,8,7,1] => 1000001
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => [2,3,4,5,7,8,6,1] => 1000010
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => [2,3,4,5,8,6,7,1] => 1000010
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => [2,3,4,5,8,7,6,1] => 1000011
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => [2,3,4,6,7,8,5,1] => 1000100
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,5,7,8,6,4,3,2] => [2,3,4,6,8,7,5,1] => 1000101
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,6,5,8,7,4,3,2] => [2,3,4,7,8,5,6,1] => 1000100
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,5,6,8,7,4,3,2] => [2,3,4,7,8,6,5,1] => 1000110
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => [2,3,4,8,5,6,7,1] => 1000100
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => [2,3,4,8,5,7,6,1] => 1000110
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,5,7,6,8,4,3,2] => [2,3,4,8,6,7,5,1] => 1000110
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,6,5,7,8,4,3,2] => [2,3,4,8,7,5,6,1] => 1000101
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => [2,3,4,8,7,6,5,1] => 1000111
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => [2,3,5,6,7,8,4,1] => 1001000
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => [2,3,5,6,8,7,4,1] => 1001001
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => [2,3,5,7,8,6,4,1] => 1001010
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,4,7,6,8,5,3,2] => [2,3,5,8,6,7,4,1] => 1001010
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,4,6,7,8,5,3,2] => [2,3,5,8,7,6,4,1] => 1001011
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,5,4,7,8,6,3,2] => [2,3,6,8,7,4,5,1] => 1001001
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,4,5,8,7,6,3,2] => [2,3,6,7,8,5,4,1] => 1001100
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,6,5,4,8,7,3,2] => [2,3,7,8,4,5,6,1] => 1001000
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,5,4,6,8,7,3,2] => [2,3,7,8,6,4,5,1] => 1001010
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => [2,3,8,4,5,6,7,1] => 1001000
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,5,7,6,4,8,3,2] => [2,3,8,4,6,7,5,1] => 1001100
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,6,5,7,4,8,3,2] => [2,3,8,4,7,5,6,1] => 1001100
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,4,7,6,5,8,3,2] => [2,3,8,5,6,7,4,1] => 1001100
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,4,6,7,5,8,3,2] => [2,3,8,5,7,6,4,1] => 1001110
[[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,4,5,7,6,8,3,2] => [2,3,8,6,7,5,4,1] => 1001110
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,6,5,4,7,8,3,2] => [2,3,8,7,4,5,6,1] => 1001001
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,4,5,6,7,8,3,2] => [2,3,8,7,6,5,4,1] => 1001111
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => [2,4,5,6,7,8,3,1] => 1010000
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,3,7,8,6,5,4,2] => [2,4,5,6,8,7,3,1] => 1010001
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,3,6,8,7,5,4,2] => [2,4,5,7,8,6,3,1] => 1010010
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,3,5,8,7,6,4,2] => [2,4,6,7,8,5,3,1] => 1010100
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => [2,4,6,8,7,5,3,1] => 1010101
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,3,6,5,8,7,4,2] => [2,4,7,8,5,6,3,1] => 1010100
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,3,5,6,8,7,4,2] => [2,4,7,8,6,5,3,1] => 1010110
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,3,7,6,5,8,4,2] => [2,4,8,5,6,7,3,1] => 1010100
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,3,6,7,5,8,4,2] => [2,4,8,5,7,6,3,1] => 1010110
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,3,5,7,6,8,4,2] => [2,4,8,6,7,5,3,1] => 1010110
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => [2,4,8,7,5,6,3,1] => 1010101
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => [2,4,8,7,6,5,3,1] => 1010111
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => [2,5,6,7,8,3,4,1] => 1010000
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => [2,5,6,8,7,3,4,1] => 1010001
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,4,3,6,8,7,5,2] => [2,5,7,8,6,3,4,1] => 1010010
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,4,3,7,6,8,5,2] => [2,5,8,6,7,3,4,1] => 1010010
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => [2,5,6,7,8,4,3,1] => 1011000
[[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,3,4,7,6,8,5,2] => [2,5,8,6,7,4,3,1] => 1011010
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,3,4,6,7,8,5,2] => [2,5,8,7,6,4,3,1] => 1011011
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,5,4,3,7,8,6,2] => [2,6,8,7,3,4,5,1] => 1010001
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,3,5,4,8,7,6,2] => [2,6,7,8,4,5,3,1] => 1011000
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,3,5,4,7,8,6,2] => [2,6,8,7,4,5,3,1] => 1011001
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,4,3,5,8,7,6,2] => [2,6,7,8,5,3,4,1] => 1010100
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,4,3,5,7,8,6,2] => [2,6,8,7,5,3,4,1] => 1010101
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,3,4,5,8,7,6,2] => [2,6,7,8,5,4,3,1] => 1011100
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => [2,6,8,7,5,4,3,1] => 1011101
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => [2,7,8,3,4,5,6,1] => 1010000
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => [2,7,8,3,4,6,5,1] => 1010100
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,5,4,6,3,8,7,2] => [2,7,8,3,6,4,5,1] => 1011000
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,3,6,5,4,8,7,2] => [2,7,8,4,5,6,3,1] => 1011000
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => [2,7,8,5,6,3,4,1] => 1010100
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,4,5,3,6,8,7,2] => [2,7,8,6,3,5,4,1] => 1011010
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => [2,7,8,6,5,4,3,1] => 1011110
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => [2,8,3,4,5,6,7,1] => 1010000
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,6,7,5,4,3,8,2] => [2,8,3,4,5,7,6,1] => 1010010
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,6,5,7,4,3,8,2] => [2,8,3,4,7,5,6,1] => 1010100
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,4,7,6,5,3,8,2] => [2,8,3,5,6,7,4,1] => 1011000
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => [2,8,3,5,7,6,4,1] => 1011010
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,5,4,7,6,3,8,2] => [2,8,3,6,7,4,5,1] => 1011000
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,4,5,7,6,3,8,2] => [2,8,3,6,7,5,4,1] => 1011100
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,6,5,4,7,3,8,2] => [2,8,3,7,4,5,6,1] => 1011000
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => [2,8,3,7,4,6,5,1] => 1011100
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,4,6,5,7,3,8,2] => [2,8,3,7,5,6,4,1] => 1011100
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => [2,8,3,7,6,5,4,1] => 1011110
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,3,7,6,5,4,8,2] => [2,8,4,5,6,7,3,1] => 1011000
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,3,5,7,6,4,8,2] => [2,8,4,6,7,5,3,1] => 1011100
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,3,5,6,7,4,8,2] => [2,8,4,7,6,5,3,1] => 1011110
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,4,3,6,7,5,8,2] => [2,8,5,7,6,3,4,1] => 1010110
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,3,4,7,6,5,8,2] => [2,8,5,6,7,4,3,1] => 1011100
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,3,4,6,7,5,8,2] => [2,8,5,7,6,4,3,1] => 1011110
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,3,5,4,7,6,8,2] => [2,8,6,7,4,5,3,1] => 1011010
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,4,3,5,7,6,8,2] => [2,8,6,7,5,3,4,1] => 1010110
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,3,4,5,7,6,8,2] => [2,8,6,7,5,4,3,1] => 1011110
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,6,5,4,3,7,8,2] => [2,8,7,3,4,5,6,1] => 1010001
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,5,6,4,3,7,8,2] => [2,8,7,3,4,6,5,1] => 1010101
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,3,6,5,4,7,8,2] => [2,8,7,4,5,6,3,1] => 1011001
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,3,5,6,4,7,8,2] => [2,8,7,4,6,5,3,1] => 1011101
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,4,3,6,5,7,8,2] => [2,8,7,5,6,3,4,1] => 1010101
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,3,4,6,5,7,8,2] => [2,8,7,5,6,4,3,1] => 1011101
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,5,4,3,6,7,8,2] => [2,8,7,6,3,4,5,1] => 1010011
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => [2,8,7,6,3,5,4,1] => 1011011
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,3,5,4,6,7,8,2] => [2,8,7,6,4,5,3,1] => 1011011
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => [2,8,7,6,5,3,4,1] => 1010111
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => [2,8,7,6,5,4,3,1] => 1011111
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [3,4,5,6,7,8,1,2] => 1000000
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [2,1,7,8,6,5,4,3] => [3,4,5,6,8,7,1,2] => 1000001
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [2,1,6,8,7,5,4,3] => [3,4,5,7,8,6,1,2] => 1000010
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => [3,4,5,8,6,7,1,2] => 1000010
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [3,4,5,8,7,6,1,2] => 1000011
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [2,1,5,8,7,6,4,3] => [3,4,6,7,8,5,1,2] => 1000100
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => [3,4,6,8,7,5,1,2] => 1000101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [2,1,6,5,8,7,4,3] => [3,4,7,8,5,6,1,2] => 1000100
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [2,1,5,6,8,7,4,3] => [3,4,7,8,6,5,1,2] => 1000110
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [2,1,7,6,5,8,4,3] => [3,4,8,5,6,7,1,2] => 1000100
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => [3,4,8,5,7,6,1,2] => 1000110
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => [3,4,8,7,5,6,1,2] => 1000101
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => [3,4,8,7,6,5,1,2] => 1000111
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => [3,5,6,7,8,4,1,2] => 1001000
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [2,1,4,7,8,6,5,3] => [3,5,6,8,7,4,1,2] => 1001001
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => [3,5,7,8,6,4,1,2] => 1001010
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [2,1,4,7,6,8,5,3] => [3,5,8,6,7,4,1,2] => 1001010
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [2,1,4,6,7,8,5,3] => [3,5,8,7,6,4,1,2] => 1001011
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [2,1,5,4,8,7,6,3] => [3,6,7,8,4,5,1,2] => 1001000
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => [3,6,7,8,5,4,1,2] => 1001100
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [2,1,6,5,4,8,7,3] => [3,7,8,4,5,6,1,2] => 1001000
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => [3,7,8,5,6,4,1,2] => 1001100
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => [3,8,4,7,5,6,1,2] => 1001100
[[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [2,1,5,6,7,4,8,3] => [3,8,4,7,6,5,1,2] => 1001110
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [2,1,4,7,6,5,8,3] => [3,8,5,6,7,4,1,2] => 1001100
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => [3,8,6,7,4,5,1,2] => 1001010
[[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [2,1,4,5,7,6,8,3] => [3,8,6,7,5,4,1,2] => 1001110
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [2,1,6,5,4,7,8,3] => [3,8,7,4,5,6,1,2] => 1001001
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [2,1,5,6,4,7,8,3] => [3,8,7,4,6,5,1,2] => 1001101
[[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [2,1,4,6,5,7,8,3] => [3,8,7,5,6,4,1,2] => 1001101
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [2,1,5,4,6,7,8,3] => [3,8,7,6,4,5,1,2] => 1001011
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => [3,8,7,6,5,4,1,2] => 1001111
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => [3,4,5,6,7,8,2,1] => 1100000
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => [3,4,5,6,8,7,2,1] => 1100001
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,2,6,8,7,5,4,3] => [3,4,5,7,8,6,2,1] => 1100010
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,2,7,6,8,5,4,3] => [3,4,5,8,6,7,2,1] => 1100010
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => [3,4,5,8,7,6,2,1] => 1100011
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,2,5,8,7,6,4,3] => [3,4,6,7,8,5,2,1] => 1100100
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => [3,4,8,5,6,7,2,1] => 1100100
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,2,6,5,7,8,4,3] => [3,4,8,7,5,6,2,1] => 1100101
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,2,5,6,7,8,4,3] => [3,4,8,7,6,5,2,1] => 1100111
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => [3,5,6,7,8,4,2,1] => 1101000
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,2,4,7,8,6,5,3] => [3,5,6,8,7,4,2,1] => 1101001
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,2,4,6,8,7,5,3] => [3,5,7,8,6,4,2,1] => 1101010
[[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,2,4,7,6,8,5,3] => [3,5,8,6,7,4,2,1] => 1101010
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => [3,5,8,7,6,4,2,1] => 1101011
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,2,5,4,8,7,6,3] => [3,6,7,8,4,5,2,1] => 1101000
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,2,4,5,7,8,6,3] => [3,6,8,7,5,4,2,1] => 1101101
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,2,6,5,4,8,7,3] => [3,7,8,4,5,6,2,1] => 1101000
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,2,4,6,5,8,7,3] => [3,7,8,5,6,4,2,1] => 1101100
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,2,4,5,6,8,7,3] => [3,7,8,6,5,4,2,1] => 1101110
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,2,7,6,5,4,8,3] => [3,8,4,5,6,7,2,1] => 1101000
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,2,6,5,7,4,8,3] => [3,8,4,7,5,6,2,1] => 1101100
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => [3,8,4,7,6,5,2,1] => 1101110
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,2,4,6,7,5,8,3] => [3,8,5,7,6,4,2,1] => 1101110
[[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,2,4,5,7,6,8,3] => [3,8,6,7,5,4,2,1] => 1101110
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,2,6,5,4,7,8,3] => [3,8,7,4,5,6,2,1] => 1101001
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,2,5,6,4,7,8,3] => [3,8,7,4,6,5,2,1] => 1101101
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,2,4,6,5,7,8,3] => [3,8,7,5,6,4,2,1] => 1101101
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => [3,8,7,6,4,5,2,1] => 1101011
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => [3,8,7,6,5,4,2,1] => 1101111
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => [4,5,6,7,8,1,2,3] => 1000000
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [3,2,1,7,8,6,5,4] => [4,5,6,8,7,1,2,3] => 1000001
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [3,2,1,6,8,7,5,4] => [4,5,7,8,6,1,2,3] => 1000010
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [3,2,1,7,6,8,5,4] => [4,5,8,6,7,1,2,3] => 1000010
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => [4,5,8,7,6,1,2,3] => 1000011
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => [4,6,7,8,5,1,2,3] => 1000100
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => [4,6,8,7,5,1,2,3] => 1000101
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => [4,7,8,5,6,1,2,3] => 1000100
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => [4,7,8,6,5,1,2,3] => 1000110
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => [4,8,5,6,7,1,2,3] => 1000100
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => [4,8,5,7,6,1,2,3] => 1000110
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [3,2,1,5,7,6,8,4] => [4,8,6,7,5,1,2,3] => 1000110
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [3,2,1,6,5,7,8,4] => [4,8,7,5,6,1,2,3] => 1000101
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => [4,8,7,6,5,1,2,3] => 1000111
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => [4,5,6,7,8,1,3,2] => 1100000
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [2,3,1,7,6,8,5,4] => [4,5,8,6,7,1,3,2] => 1100010
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [2,3,1,6,7,8,5,4] => [4,5,8,7,6,1,3,2] => 1100011
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [2,3,1,5,8,7,6,4] => [4,6,7,8,5,1,3,2] => 1100100
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [2,3,1,6,5,8,7,4] => [4,7,8,5,6,1,3,2] => 1100100
[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [2,3,1,5,6,8,7,4] => [4,7,8,6,5,1,3,2] => 1100110
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [2,3,1,7,6,5,8,4] => [4,8,5,6,7,1,3,2] => 1100100
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [2,3,1,6,7,5,8,4] => [4,8,5,7,6,1,3,2] => 1100110
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [2,3,1,5,7,6,8,4] => [4,8,6,7,5,1,3,2] => 1100110
[[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [2,3,1,6,5,7,8,4] => [4,8,7,5,6,1,3,2] => 1100101
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [2,3,1,5,6,7,8,4] => [4,8,7,6,5,1,3,2] => 1100111
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => [4,5,6,7,8,2,3,1] => 1100000
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,3,2,7,6,8,5,4] => [4,5,8,6,7,2,3,1] => 1100010
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,3,2,5,8,7,6,4] => [4,6,7,8,5,2,3,1] => 1100100
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,3,2,5,7,8,6,4] => [4,6,8,7,5,2,3,1] => 1100101
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,3,2,6,5,8,7,4] => [4,7,8,5,6,2,3,1] => 1100100
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,3,2,7,6,5,8,4] => [4,8,5,6,7,2,3,1] => 1100100
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,3,2,5,7,6,8,4] => [4,8,6,7,5,2,3,1] => 1100110
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,3,2,6,5,7,8,4] => [4,8,7,5,6,2,3,1] => 1100101
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,3,2,5,6,7,8,4] => [4,8,7,6,5,2,3,1] => 1100111
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => [4,5,6,7,8,3,1,2] => 1010000
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [2,1,3,7,8,6,5,4] => [4,5,6,8,7,3,1,2] => 1010001
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [2,1,3,6,8,7,5,4] => [4,5,7,8,6,3,1,2] => 1010010
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [2,1,3,6,7,8,5,4] => [4,5,8,7,6,3,1,2] => 1010011
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [2,1,3,5,7,8,6,4] => [4,6,8,7,5,3,1,2] => 1010101
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [2,1,3,7,6,5,8,4] => [4,8,5,6,7,3,1,2] => 1010100
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [2,1,3,6,7,5,8,4] => [4,8,5,7,6,3,1,2] => 1010110
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [2,1,3,5,7,6,8,4] => [4,8,6,7,5,3,1,2] => 1010110
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [2,1,3,6,5,7,8,4] => [4,8,7,5,6,3,1,2] => 1010101
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [2,1,3,5,6,7,8,4] => [4,8,7,6,5,3,1,2] => 1010111
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => [4,5,6,7,8,3,2,1] => 1110000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => [4,5,6,8,7,3,2,1] => 1110001
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => [4,5,7,8,6,3,2,1] => 1110010
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => [4,5,8,6,7,3,2,1] => 1110010
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => [4,5,8,7,6,3,2,1] => 1110011
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => [4,6,7,8,5,3,2,1] => 1110100
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => [4,6,8,7,5,3,2,1] => 1110101
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => [4,7,8,5,6,3,2,1] => 1110100
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => [4,7,8,6,5,3,2,1] => 1110110
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => [4,8,5,6,7,3,2,1] => 1110100
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => [4,8,5,7,6,3,2,1] => 1110110
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => [4,8,6,7,5,3,2,1] => 1110110
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => [4,8,7,5,6,3,2,1] => 1110101
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => [4,8,7,6,5,3,2,1] => 1110111
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [5,6,7,8,1,2,3,4] => 1000000
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => [5,6,8,7,1,2,3,4] => 1000001
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => [5,7,8,6,1,2,3,4] => 1000010
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => [5,8,6,7,1,2,3,4] => 1000010
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => [5,8,7,6,1,2,3,4] => 1000011
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => [5,6,7,8,1,2,4,3] => 1010000
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => [5,6,8,7,1,2,4,3] => 1010001
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => [5,7,8,6,1,2,4,3] => 1010010
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => [5,8,6,7,1,2,4,3] => 1010010
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [3,4,2,1,6,7,8,5] => [5,8,7,6,1,2,4,3] => 1010011
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => [5,6,7,8,1,3,4,2] => 1100000
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [2,4,3,1,7,8,6,5] => [5,6,8,7,1,3,4,2] => 1100001
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => [5,7,8,6,1,3,4,2] => 1100010
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => [5,8,6,7,1,3,4,2] => 1100010
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [2,4,3,1,6,7,8,5] => [5,8,7,6,1,3,4,2] => 1100011
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => [5,6,7,8,1,4,2,3] => 1100000
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => [5,6,8,7,1,4,2,3] => 1100001
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => [5,7,8,6,1,4,2,3] => 1100010
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => [5,8,6,7,1,4,2,3] => 1100010
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [3,2,4,1,6,7,8,5] => [5,8,7,6,1,4,2,3] => 1100011
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => [5,6,7,8,1,4,3,2] => 1110000
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [2,3,4,1,7,8,6,5] => [5,6,8,7,1,4,3,2] => 1110001
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [2,3,4,1,6,8,7,5] => [5,7,8,6,1,4,3,2] => 1110010
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => [5,8,6,7,1,4,3,2] => 1110010
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => [5,8,7,6,1,4,3,2] => 1110011
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => [5,6,7,8,2,3,4,1] => 1100000
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,4,3,2,6,8,7,5] => [5,7,8,6,2,3,4,1] => 1100010
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => [5,8,6,7,2,3,4,1] => 1100010
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => [5,8,7,6,2,3,4,1] => 1100011
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => [5,6,7,8,2,4,3,1] => 1110000
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,3,4,2,7,8,6,5] => [5,6,8,7,2,4,3,1] => 1110001
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => [5,8,6,7,2,4,3,1] => 1110010
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,3,4,2,6,7,8,5] => [5,8,7,6,2,4,3,1] => 1110011
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [5,6,7,8,3,4,1,2] => 1010000
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [5,6,8,7,3,4,1,2] => 1010001
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => [5,7,8,6,3,4,1,2] => 1010010
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [5,8,6,7,3,4,1,2] => 1010010
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => [5,8,7,6,3,4,1,2] => 1010011
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => [5,6,7,8,3,4,2,1] => 1110000
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => [5,7,8,6,3,4,2,1] => 1110010
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => [5,8,6,7,3,4,2,1] => 1110010
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => [5,8,7,6,3,4,2,1] => 1110011
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => [5,6,7,8,4,1,2,3] => 1001000
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [3,2,1,4,7,8,6,5] => [5,6,8,7,4,1,2,3] => 1001001
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [3,2,1,4,6,8,7,5] => [5,7,8,6,4,1,2,3] => 1001010
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [3,2,1,4,7,6,8,5] => [5,8,6,7,4,1,2,3] => 1001010
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [3,2,1,4,6,7,8,5] => [5,8,7,6,4,1,2,3] => 1001011
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => [5,6,7,8,4,1,3,2] => 1101000
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => [5,8,6,7,4,1,3,2] => 1101010
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [2,3,1,4,6,7,8,5] => [5,8,7,6,4,1,3,2] => 1101011
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => [5,6,7,8,4,2,3,1] => 1101000
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,3,2,4,6,8,7,5] => [5,7,8,6,4,2,3,1] => 1101010
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => [5,8,6,7,4,2,3,1] => 1101010
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,3,2,4,6,7,8,5] => [5,8,7,6,4,2,3,1] => 1101011
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => [5,6,7,8,4,3,1,2] => 1011000
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [2,1,3,4,7,8,6,5] => [5,6,8,7,4,3,1,2] => 1011001
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => [5,8,6,7,4,3,1,2] => 1011010
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => [5,8,7,6,4,3,1,2] => 1011011
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => [5,6,7,8,4,3,2,1] => 1111000
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => [5,6,8,7,4,3,2,1] => 1111001
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => [5,7,8,6,4,3,2,1] => 1111010
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => [5,8,6,7,4,3,2,1] => 1111010
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => [5,8,7,6,4,3,2,1] => 1111011
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => [6,7,8,1,2,3,4,5] => 1000000
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => [6,8,7,1,2,3,4,5] => 1000001
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [4,5,3,2,1,8,7,6] => [6,7,8,1,2,3,5,4] => 1001000
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [3,5,4,2,1,8,7,6] => [6,7,8,1,2,4,5,3] => 1010000
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [4,3,5,2,1,8,7,6] => [6,7,8,1,2,5,3,4] => 1010000
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [3,4,5,2,1,8,7,6] => [6,7,8,1,2,5,4,3] => 1011000
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [2,5,4,3,1,8,7,6] => [6,7,8,1,3,4,5,2] => 1100000
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [2,5,4,3,1,7,8,6] => [6,8,7,1,3,4,5,2] => 1100001
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [2,4,5,3,1,8,7,6] => [6,7,8,1,3,5,4,2] => 1101000
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [2,4,5,3,1,7,8,6] => [6,8,7,1,3,5,4,2] => 1101001
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => [6,7,8,1,4,5,2,3] => 1100000
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [3,2,5,4,1,7,8,6] => [6,8,7,1,4,5,2,3] => 1100001
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [2,3,5,4,1,8,7,6] => [6,7,8,1,4,5,3,2] => 1110000
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => [6,7,8,1,5,2,3,4] => 1100000
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [4,3,2,5,1,7,8,6] => [6,8,7,1,5,2,3,4] => 1100001
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => [6,7,8,1,5,2,4,3] => 1110000
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [2,4,3,5,1,8,7,6] => [6,7,8,1,5,3,4,2] => 1110000
[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [2,4,3,5,1,7,8,6] => [6,8,7,1,5,3,4,2] => 1110001
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [3,2,4,5,1,8,7,6] => [6,7,8,1,5,4,2,3] => 1101000
[[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [3,2,4,5,1,7,8,6] => [6,8,7,1,5,4,2,3] => 1101001
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [2,3,4,5,1,8,7,6] => [6,7,8,1,5,4,3,2] => 1111000
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => [6,8,7,1,5,4,3,2] => 1111001
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => [6,7,8,2,3,4,5,1] => 1100000
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,5,4,3,2,7,8,6] => [6,8,7,2,3,4,5,1] => 1100001
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,4,5,3,2,8,7,6] => [6,7,8,2,3,5,4,1] => 1101000
[[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,4,5,3,2,7,8,6] => [6,8,7,2,3,5,4,1] => 1101001
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,3,5,4,2,8,7,6] => [6,7,8,2,4,5,3,1] => 1110000
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,3,5,4,2,7,8,6] => [6,8,7,2,4,5,3,1] => 1110001
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,3,4,5,2,8,7,6] => [6,7,8,2,5,4,3,1] => 1111000
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,3,4,5,2,7,8,6] => [6,8,7,2,5,4,3,1] => 1111001
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [2,1,5,4,3,8,7,6] => [6,7,8,3,4,5,1,2] => 1010000
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [2,1,5,4,3,7,8,6] => [6,8,7,3,4,5,1,2] => 1010001
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => [6,7,8,3,4,5,2,1] => 1110000
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,2,5,4,3,7,8,6] => [6,8,7,3,4,5,2,1] => 1110001
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => [6,7,8,3,5,4,2,1] => 1111000
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,2,4,5,3,7,8,6] => [6,8,7,3,5,4,2,1] => 1111001
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [3,2,1,5,4,8,7,6] => [6,7,8,4,5,1,2,3] => 1001000
[[[.,[[.,.],.]],[.,.]],[[.,.],.]] => [2,3,1,5,4,7,8,6] => [6,8,7,4,5,1,3,2] => 1101001
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => [6,7,8,4,5,2,3,1] => 1101000
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,3,2,5,4,7,8,6] => [6,8,7,4,5,2,3,1] => 1101001
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [2,1,3,5,4,8,7,6] => [6,7,8,4,5,3,1,2] => 1011000
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [2,1,3,5,4,7,8,6] => [6,8,7,4,5,3,1,2] => 1011001
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => [6,7,8,4,5,3,2,1] => 1111000
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,2,3,5,4,7,8,6] => [6,8,7,4,5,3,2,1] => 1111001
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => [6,7,8,5,1,2,3,4] => 1000100
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => [6,8,7,5,1,2,3,4] => 1000101
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [3,4,2,1,5,8,7,6] => [6,7,8,5,1,2,4,3] => 1010100
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [3,4,2,1,5,7,8,6] => [6,8,7,5,1,2,4,3] => 1010101
[[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [2,4,3,1,5,7,8,6] => [6,8,7,5,1,3,4,2] => 1100101
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => [6,7,8,5,1,4,2,3] => 1100100
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => [6,8,7,5,1,4,2,3] => 1100101
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [2,3,4,1,5,8,7,6] => [6,7,8,5,1,4,3,2] => 1110100
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [2,3,4,1,5,7,8,6] => [6,8,7,5,1,4,3,2] => 1110101
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => [6,7,8,5,2,3,4,1] => 1100100
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,3,4,2,5,7,8,6] => [6,8,7,5,2,4,3,1] => 1110101
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [2,1,4,3,5,8,7,6] => [6,7,8,5,3,4,1,2] => 1010100
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [2,1,4,3,5,7,8,6] => [6,8,7,5,3,4,1,2] => 1010101
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,2,4,3,5,7,8,6] => [6,8,7,5,3,4,2,1] => 1110101
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [6,7,8,5,4,1,2,3] => 1001100
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [3,2,1,4,5,7,8,6] => [6,8,7,5,4,1,2,3] => 1001101
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => [6,8,7,5,4,1,3,2] => 1101101
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,3,2,4,5,7,8,6] => [6,8,7,5,4,2,3,1] => 1101101
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [2,1,3,4,5,8,7,6] => [6,7,8,5,4,3,1,2] => 1011100
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [2,1,3,4,5,7,8,6] => [6,8,7,5,4,3,1,2] => 1011101
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [6,7,8,5,4,3,2,1] => 1111100
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => [6,8,7,5,4,3,2,1] => 1111101
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [7,8,1,2,3,4,5,6] => 1000000
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [5,6,4,3,2,1,8,7] => [7,8,1,2,3,4,6,5] => 1000100
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [4,6,5,3,2,1,8,7] => [7,8,1,2,3,5,6,4] => 1001000
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [5,4,6,3,2,1,8,7] => [7,8,1,2,3,6,4,5] => 1001000
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => [7,8,1,2,3,6,5,4] => 1001100
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [3,6,5,4,2,1,8,7] => [7,8,1,2,4,5,6,3] => 1010000
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => [7,8,1,2,4,6,5,3] => 1010100
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [4,3,6,5,2,1,8,7] => [7,8,1,2,5,6,3,4] => 1010000
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [3,4,6,5,2,1,8,7] => [7,8,1,2,5,6,4,3] => 1011000
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [5,4,3,6,2,1,8,7] => [7,8,1,2,6,3,4,5] => 1010000
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [4,5,3,6,2,1,8,7] => [7,8,1,2,6,3,5,4] => 1011000
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [4,3,5,6,2,1,8,7] => [7,8,1,2,6,5,3,4] => 1010100
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [3,4,5,6,2,1,8,7] => [7,8,1,2,6,5,4,3] => 1011100
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [2,6,5,4,3,1,8,7] => [7,8,1,3,4,5,6,2] => 1100000
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [2,4,6,5,3,1,8,7] => [7,8,1,3,5,6,4,2] => 1101000
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [2,5,4,6,3,1,8,7] => [7,8,1,3,6,4,5,2] => 1101000
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [3,2,6,5,4,1,8,7] => [7,8,1,4,5,6,2,3] => 1100000
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [2,3,6,5,4,1,8,7] => [7,8,1,4,5,6,3,2] => 1110000
[[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [2,3,5,6,4,1,8,7] => [7,8,1,4,6,5,3,2] => 1110100
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [4,3,2,6,5,1,8,7] => [7,8,1,5,6,2,3,4] => 1100000
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => [7,8,1,5,6,3,4,2] => 1110000
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [3,2,4,6,5,1,8,7] => [7,8,1,5,6,4,2,3] => 1101000
[[.,[[[[.,.],.],.],[.,.]]],[.,.]] => [2,3,4,6,5,1,8,7] => [7,8,1,5,6,4,3,2] => 1111000
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [5,4,3,2,6,1,8,7] => [7,8,1,6,2,3,4,5] => 1100000
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [4,5,3,2,6,1,8,7] => [7,8,1,6,2,3,5,4] => 1101000
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [3,5,4,2,6,1,8,7] => [7,8,1,6,2,4,5,3] => 1110000
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [7,8,1,6,2,5,3,4] => 1110000
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [3,4,5,2,6,1,8,7] => [7,8,1,6,2,5,4,3] => 1111000
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [2,5,4,3,6,1,8,7] => [7,8,1,6,3,4,5,2] => 1110000
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [2,4,5,3,6,1,8,7] => [7,8,1,6,3,5,4,2] => 1111000
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [7,8,1,6,4,5,2,3] => 1101000
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [4,3,2,5,6,1,8,7] => [7,8,1,6,5,2,3,4] => 1100100
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [3,4,2,5,6,1,8,7] => [7,8,1,6,5,2,4,3] => 1110100
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [2,4,3,5,6,1,8,7] => [7,8,1,6,5,3,4,2] => 1110100
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => [7,8,1,6,5,4,3,2] => 1111100
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => [7,8,2,3,4,5,6,1] => 1100000
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => [7,8,2,3,4,6,5,1] => 1100100
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,5,4,6,3,2,8,7] => [7,8,2,3,6,4,5,1] => 1101000
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,4,5,3,6,2,8,7] => [7,8,2,6,3,5,4,1] => 1111000
[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,3,5,4,6,2,8,7] => [7,8,2,6,4,5,3,1] => 1111000
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,3,4,5,6,2,8,7] => [7,8,2,6,5,4,3,1] => 1111100
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [7,8,3,4,5,6,1,2] => 1010000
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [7,8,3,4,6,5,1,2] => 1010100
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => [7,8,3,5,6,4,1,2] => 1011000
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [7,8,3,6,4,5,1,2] => 1011000
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => [7,8,3,6,5,4,1,2] => 1011100
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,2,6,5,4,3,8,7] => [7,8,3,4,5,6,2,1] => 1110000
[[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,2,5,6,4,3,8,7] => [7,8,3,4,6,5,2,1] => 1110100
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [3,2,1,6,5,4,8,7] => [7,8,4,5,6,1,2,3] => 1001000
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [2,3,1,6,5,4,8,7] => [7,8,4,5,6,1,3,2] => 1101000
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,3,2,6,5,4,8,7] => [7,8,4,5,6,2,3,1] => 1101000
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [2,1,3,6,5,4,8,7] => [7,8,4,5,6,3,1,2] => 1011000
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [2,1,3,5,6,4,8,7] => [7,8,4,6,5,3,1,2] => 1011100
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [7,8,5,6,1,2,3,4] => 1000100
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => [7,8,5,6,1,2,4,3] => 1010100
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => [7,8,5,6,1,3,4,2] => 1100100
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [7,8,5,6,1,4,2,3] => 1100100
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => [7,8,5,6,1,4,3,2] => 1110100
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,4,3,2,6,5,8,7] => [7,8,5,6,2,3,4,1] => 1100100
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => [7,8,5,6,2,4,3,1] => 1110100
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => 1010100
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => [7,8,5,6,3,4,2,1] => 1110100
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [3,2,1,4,6,5,8,7] => [7,8,5,6,4,1,2,3] => 1001100
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [2,3,1,4,6,5,8,7] => [7,8,5,6,4,1,3,2] => 1101100
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [2,1,3,4,6,5,8,7] => [7,8,5,6,4,3,1,2] => 1011100
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => [7,8,5,6,4,3,2,1] => 1111100
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => [7,8,6,1,2,3,4,5] => 1000010
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => [3,5,4,2,1,6,8,7] => [7,8,6,1,2,4,5,3] => 1010010
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [2,5,4,3,1,6,8,7] => [7,8,6,1,3,4,5,2] => 1100010
[[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [2,4,5,3,1,6,8,7] => [7,8,6,1,3,5,4,2] => 1101010
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [3,2,5,4,1,6,8,7] => [7,8,6,1,4,5,2,3] => 1100010
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [2,3,5,4,1,6,8,7] => [7,8,6,1,4,5,3,2] => 1110010
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [4,3,2,5,1,6,8,7] => [7,8,6,1,5,2,3,4] => 1100010
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [2,4,3,5,1,6,8,7] => [7,8,6,1,5,3,4,2] => 1110010
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [2,3,4,5,1,6,8,7] => [7,8,6,1,5,4,3,2] => 1111010
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,5,4,3,2,6,8,7] => [7,8,6,2,3,4,5,1] => 1100010
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,4,5,3,2,6,8,7] => [7,8,6,2,3,5,4,1] => 1101010
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => [7,8,6,3,4,5,1,2] => 1010010
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,2,5,4,3,6,8,7] => [7,8,6,3,4,5,2,1] => 1110010
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,2,4,5,3,6,8,7] => [7,8,6,3,5,4,2,1] => 1111010
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [2,1,3,5,4,6,8,7] => [7,8,6,4,5,3,1,2] => 1011010
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => [7,8,6,4,5,3,2,1] => 1111010
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => [7,8,6,5,1,2,3,4] => 1000110
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [3,4,2,1,5,6,8,7] => [7,8,6,5,1,2,4,3] => 1010110
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => [7,8,6,5,1,4,2,3] => 1100110
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [2,3,4,1,5,6,8,7] => [7,8,6,5,1,4,3,2] => 1110110
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,3,4,2,5,6,8,7] => [7,8,6,5,2,4,3,1] => 1110110
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [2,1,4,3,5,6,8,7] => [7,8,6,5,3,4,1,2] => 1010110
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => [7,8,6,5,3,4,2,1] => 1110110
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [3,2,1,4,5,6,8,7] => [7,8,6,5,4,1,2,3] => 1001110
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [2,3,1,4,5,6,8,7] => [7,8,6,5,4,1,3,2] => 1101110
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => [7,8,6,5,4,2,3,1] => 1101110
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [7,8,6,5,4,3,1,2] => 1011110
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [7,8,6,5,4,3,2,1] => 1111110
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7] => 1000000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [8,1,2,3,4,5,7,6] => 1000010
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => [8,1,2,3,4,6,7,5] => 1000100
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [8,1,2,3,4,7,5,6] => 1000100
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [8,1,2,3,4,7,6,5] => 1000110
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => [8,1,2,3,5,6,7,4] => 1001000
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [4,6,7,5,3,2,1,8] => [8,1,2,3,5,7,6,4] => 1001010
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [5,4,7,6,3,2,1,8] => [8,1,2,3,6,7,4,5] => 1001000
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [4,5,7,6,3,2,1,8] => [8,1,2,3,6,7,5,4] => 1001100
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [8,1,2,3,7,4,5,6] => 1001000
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [4,6,5,7,3,2,1,8] => [8,1,2,3,7,5,6,4] => 1001100
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => [8,1,2,3,7,6,5,4] => 1001110
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [3,7,6,5,4,2,1,8] => [8,1,2,4,5,6,7,3] => 1010000
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [3,5,7,6,4,2,1,8] => [8,1,2,4,6,7,5,3] => 1010100
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [3,5,6,7,4,2,1,8] => [8,1,2,4,7,6,5,3] => 1010110
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [4,3,7,6,5,2,1,8] => [8,1,2,5,6,7,3,4] => 1010000
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => [8,1,2,5,6,7,4,3] => 1011000
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [4,5,3,7,6,2,1,8] => [8,1,2,6,7,3,5,4] => 1011000
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [3,5,4,7,6,2,1,8] => [8,1,2,6,7,4,5,3] => 1011000
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [4,3,5,7,6,2,1,8] => [8,1,2,6,7,5,3,4] => 1010100
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [3,4,5,7,6,2,1,8] => [8,1,2,6,7,5,4,3] => 1011100
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => [8,1,2,7,3,4,5,6] => 1010000
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => [8,1,2,7,3,4,6,5] => 1010100
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [4,6,5,3,7,2,1,8] => [8,1,2,7,3,5,6,4] => 1011000
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => [8,1,2,7,3,6,4,5] => 1011000
[[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [4,5,6,3,7,2,1,8] => [8,1,2,7,3,6,5,4] => 1011100
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [3,6,5,4,7,2,1,8] => [8,1,2,7,4,5,6,3] => 1011000
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [3,5,6,4,7,2,1,8] => [8,1,2,7,4,6,5,3] => 1011100
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [4,3,6,5,7,2,1,8] => [8,1,2,7,5,6,3,4] => 1010100
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => [8,1,2,7,6,3,4,5] => 1010010
[[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [4,5,3,6,7,2,1,8] => [8,1,2,7,6,3,5,4] => 1011010
[[.,[.,[[[[.,.],[.,.]],.],.]]],.] => [3,5,4,6,7,2,1,8] => [8,1,2,7,6,4,5,3] => 1011010
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => [8,1,2,7,6,5,4,3] => 1011110
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => [8,1,3,4,5,6,7,2] => 1100000
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [2,6,7,5,4,3,1,8] => [8,1,3,4,5,7,6,2] => 1100010
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [2,5,7,6,4,3,1,8] => [8,1,3,4,6,7,5,2] => 1100100
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [2,4,7,6,5,3,1,8] => [8,1,3,5,6,7,4,2] => 1101000
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => [8,1,3,5,7,6,4,2] => 1101010
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [2,5,4,7,6,3,1,8] => [8,1,3,6,7,4,5,2] => 1101000
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [2,4,5,7,6,3,1,8] => [8,1,3,6,7,5,4,2] => 1101100
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [2,6,5,4,7,3,1,8] => [8,1,3,7,4,5,6,2] => 1101000
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [2,5,6,4,7,3,1,8] => [8,1,3,7,4,6,5,2] => 1101100
[[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [2,4,6,5,7,3,1,8] => [8,1,3,7,5,6,4,2] => 1101100
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [2,5,4,6,7,3,1,8] => [8,1,3,7,6,4,5,2] => 1101010
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [2,4,5,6,7,3,1,8] => [8,1,3,7,6,5,4,2] => 1101110
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => [8,1,4,5,6,7,2,3] => 1100000
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [3,2,6,7,5,4,1,8] => [8,1,4,5,7,6,2,3] => 1100010
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [3,2,5,7,6,4,1,8] => [8,1,4,6,7,5,2,3] => 1100100
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [3,2,5,6,7,4,1,8] => [8,1,4,7,6,5,2,3] => 1100110
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [2,3,7,6,5,4,1,8] => [8,1,4,5,6,7,3,2] => 1110000
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [2,3,6,7,5,4,1,8] => [8,1,4,5,7,6,3,2] => 1110010
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [2,3,5,6,7,4,1,8] => [8,1,4,7,6,5,3,2] => 1110110
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [4,3,2,7,6,5,1,8] => [8,1,5,6,7,2,3,4] => 1100000
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [4,3,2,6,7,5,1,8] => [8,1,5,7,6,2,3,4] => 1100010
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [3,4,2,7,6,5,1,8] => [8,1,5,6,7,2,4,3] => 1110000
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [3,4,2,6,7,5,1,8] => [8,1,5,7,6,2,4,3] => 1110010
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [2,4,3,7,6,5,1,8] => [8,1,5,6,7,3,4,2] => 1110000
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [3,2,4,7,6,5,1,8] => [8,1,5,6,7,4,2,3] => 1101000
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [2,3,4,7,6,5,1,8] => [8,1,5,6,7,4,3,2] => 1111000
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => [8,1,6,7,2,3,4,5] => 1100000
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [4,5,3,2,7,6,1,8] => [8,1,6,7,2,3,5,4] => 1101000
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [3,5,4,2,7,6,1,8] => [8,1,6,7,2,4,5,3] => 1110000
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [4,3,5,2,7,6,1,8] => [8,1,6,7,2,5,3,4] => 1110000
[[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [3,4,5,2,7,6,1,8] => [8,1,6,7,2,5,4,3] => 1111000
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => [8,1,6,7,4,5,2,3] => 1101000
[[.,[[[[.,.],.],[.,.]],[.,.]]],.] => [2,3,5,4,7,6,1,8] => [8,1,6,7,4,5,3,2] => 1111000
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [4,3,2,5,7,6,1,8] => [8,1,6,7,5,2,3,4] => 1100100
[[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [3,4,2,5,7,6,1,8] => [8,1,6,7,5,2,4,3] => 1110100
[[.,[[[[.,.],[.,.]],.],[.,.]]],.] => [2,4,3,5,7,6,1,8] => [8,1,6,7,5,3,4,2] => 1110100
[[.,[[[[.,[.,.]],.],.],[.,.]]],.] => [3,2,4,5,7,6,1,8] => [8,1,6,7,5,4,2,3] => 1101100
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => [8,1,6,7,5,4,3,2] => 1111100
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => [8,1,7,2,3,4,5,6] => 1100000
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => [8,1,7,2,3,6,4,5] => 1101000
[[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [4,5,6,3,2,7,1,8] => [8,1,7,2,3,6,5,4] => 1101100
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [3,6,5,4,2,7,1,8] => [8,1,7,2,4,5,6,3] => 1110000
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [3,5,6,4,2,7,1,8] => [8,1,7,2,4,6,5,3] => 1110100
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [4,3,6,5,2,7,1,8] => [8,1,7,2,5,6,3,4] => 1110000
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [3,4,6,5,2,7,1,8] => [8,1,7,2,5,6,4,3] => 1111000
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [8,1,7,2,6,3,4,5] => 1110000
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [8,1,7,2,6,3,5,4] => 1111000
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => [8,1,7,2,6,4,5,3] => 1111000
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [8,1,7,2,6,5,4,3] => 1111100
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [2,6,5,4,3,7,1,8] => [8,1,7,3,4,5,6,2] => 1110000
[[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [2,4,6,5,3,7,1,8] => [8,1,7,3,5,6,4,2] => 1111000
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [2,5,4,6,3,7,1,8] => [8,1,7,3,6,4,5,2] => 1111000
[[.,[[[.,.],[[[.,.],.],.]],.]],.] => [2,4,5,6,3,7,1,8] => [8,1,7,3,6,5,4,2] => 1111100
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [3,2,6,5,4,7,1,8] => [8,1,7,4,5,6,2,3] => 1101000
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [2,3,5,6,4,7,1,8] => [8,1,7,4,6,5,3,2] => 1111100
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [4,3,2,6,5,7,1,8] => [8,1,7,5,6,2,3,4] => 1100100
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [3,4,2,6,5,7,1,8] => [8,1,7,5,6,2,4,3] => 1110100
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [2,4,3,6,5,7,1,8] => [8,1,7,5,6,3,4,2] => 1110100
[[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [3,2,4,6,5,7,1,8] => [8,1,7,5,6,4,2,3] => 1101100
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => [8,1,7,5,6,4,3,2] => 1111100
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [8,1,7,6,2,3,4,5] => 1100010
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [3,5,4,2,6,7,1,8] => [8,1,7,6,2,4,5,3] => 1110010
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => [8,1,7,6,2,5,4,3] => 1111010
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [2,5,4,3,6,7,1,8] => [8,1,7,6,3,4,5,2] => 1110010
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [2,4,5,3,6,7,1,8] => [8,1,7,6,3,5,4,2] => 1111010
[[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [3,2,5,4,6,7,1,8] => [8,1,7,6,4,5,2,3] => 1101010
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [2,3,5,4,6,7,1,8] => [8,1,7,6,4,5,3,2] => 1111010
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => [8,1,7,6,5,2,3,4] => 1100110
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => [8,1,7,6,5,2,4,3] => 1110110
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [2,4,3,5,6,7,1,8] => [8,1,7,6,5,3,4,2] => 1110110
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [8,1,7,6,5,4,2,3] => 1101110
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [8,1,7,6,5,4,3,2] => 1111110
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => [8,2,3,4,5,6,7,1] => 1100000
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => [8,2,3,4,5,7,6,1] => 1100010
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,5,6,7,4,3,2,8] => [8,2,3,4,7,6,5,1] => 1100110
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,4,7,6,5,3,2,8] => [8,2,3,5,6,7,4,1] => 1101000
[[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,4,6,7,5,3,2,8] => [8,2,3,5,7,6,4,1] => 1101010
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,5,4,7,6,3,2,8] => [8,2,3,6,7,4,5,1] => 1101000
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,6,5,4,7,3,2,8] => [8,2,3,7,4,5,6,1] => 1101000
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,4,6,5,7,3,2,8] => [8,2,3,7,5,6,4,1] => 1101100
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,5,4,6,7,3,2,8] => [8,2,3,7,6,4,5,1] => 1101010
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => [8,2,3,7,6,5,4,1] => 1101110
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,3,7,6,5,4,2,8] => [8,2,4,5,6,7,3,1] => 1110000
[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,3,6,7,5,4,2,8] => [8,2,4,5,7,6,3,1] => 1110010
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,3,5,7,6,4,2,8] => [8,2,4,6,7,5,3,1] => 1110100
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,3,6,5,7,4,2,8] => [8,2,4,7,5,6,3,1] => 1110100
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,3,5,6,7,4,2,8] => [8,2,4,7,6,5,3,1] => 1110110
[[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,3,4,7,6,5,2,8] => [8,2,5,6,7,4,3,1] => 1111000
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => [8,2,5,7,6,4,3,1] => 1111010
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,3,5,4,7,6,2,8] => [8,2,6,7,4,5,3,1] => 1111000
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,4,3,5,7,6,2,8] => [8,2,6,7,5,3,4,1] => 1110100
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,3,4,5,7,6,2,8] => [8,2,6,7,5,4,3,1] => 1111100
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,6,5,4,3,7,2,8] => [8,2,7,3,4,5,6,1] => 1110000
[[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [1,5,6,4,3,7,2,8] => [8,2,7,3,4,6,5,1] => 1110100
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,5,4,6,3,7,2,8] => [8,2,7,3,6,4,5,1] => 1111000
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,4,5,6,3,7,2,8] => [8,2,7,3,6,5,4,1] => 1111100
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,3,6,5,4,7,2,8] => [8,2,7,4,5,6,3,1] => 1111000
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => [8,2,7,4,6,5,3,1] => 1111100
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,4,3,6,5,7,2,8] => [8,2,7,5,6,3,4,1] => 1110100
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,3,4,6,5,7,2,8] => [8,2,7,5,6,4,3,1] => 1111100
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,5,4,3,6,7,2,8] => [8,2,7,6,3,4,5,1] => 1110010
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,4,5,3,6,7,2,8] => [8,2,7,6,3,5,4,1] => 1111010
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,3,5,4,6,7,2,8] => [8,2,7,6,4,5,3,1] => 1111010
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,4,3,5,6,7,2,8] => [8,2,7,6,5,3,4,1] => 1110110
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,3,4,5,6,7,2,8] => [8,2,7,6,5,4,3,1] => 1111110
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [2,1,7,6,5,4,3,8] => [8,3,4,5,6,7,1,2] => 1010000
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [2,1,6,7,5,4,3,8] => [8,3,4,5,7,6,1,2] => 1010010
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [2,1,5,7,6,4,3,8] => [8,3,4,6,7,5,1,2] => 1010100
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [2,1,6,5,4,7,3,8] => [8,3,7,4,5,6,1,2] => 1011000
[[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [2,1,5,6,4,7,3,8] => [8,3,7,4,6,5,1,2] => 1011100
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [2,1,5,4,6,7,3,8] => [8,3,7,6,4,5,1,2] => 1011010
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8] => [8,3,4,5,6,7,2,1] => 1110000
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,2,6,7,5,4,3,8] => [8,3,4,5,7,6,2,1] => 1110010
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,2,5,6,7,4,3,8] => [8,3,4,7,6,5,2,1] => 1110110
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,2,4,6,7,5,3,8] => [8,3,5,7,6,4,2,1] => 1111010
[[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,2,6,5,4,7,3,8] => [8,3,7,4,5,6,2,1] => 1111000
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,2,5,6,4,7,3,8] => [8,3,7,4,6,5,2,1] => 1111100
[[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,2,4,6,5,7,3,8] => [8,3,7,5,6,4,2,1] => 1111100
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,2,4,5,6,7,3,8] => [8,3,7,6,5,4,2,1] => 1111110
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => [8,4,5,6,7,1,2,3] => 1001000
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [3,2,1,6,7,5,4,8] => [8,4,5,7,6,1,2,3] => 1001010
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [3,2,1,5,7,6,4,8] => [8,4,6,7,5,1,2,3] => 1001100
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [3,2,1,5,6,7,4,8] => [8,4,7,6,5,1,2,3] => 1001110
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [2,3,1,6,7,5,4,8] => [8,4,5,7,6,1,3,2] => 1101010
[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [2,3,1,5,7,6,4,8] => [8,4,6,7,5,1,3,2] => 1101100
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [2,3,1,6,5,7,4,8] => [8,4,7,5,6,1,3,2] => 1101100
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => [8,4,7,6,5,1,3,2] => 1101110
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,3,2,7,6,5,4,8] => [8,4,5,6,7,2,3,1] => 1101000
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,3,2,6,7,5,4,8] => [8,4,5,7,6,2,3,1] => 1101010
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,3,2,5,7,6,4,8] => [8,4,6,7,5,2,3,1] => 1101100
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,3,2,6,5,7,4,8] => [8,4,7,5,6,2,3,1] => 1101100
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,3,2,5,6,7,4,8] => [8,4,7,6,5,2,3,1] => 1101110
[[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [2,1,3,5,7,6,4,8] => [8,4,6,7,5,3,1,2] => 1011100
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [2,1,3,5,6,7,4,8] => [8,4,7,6,5,3,1,2] => 1011110
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => [8,4,5,6,7,3,2,1] => 1111000
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => [8,4,5,7,6,3,2,1] => 1111010
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,2,3,5,7,6,4,8] => [8,4,6,7,5,3,2,1] => 1111100
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,2,3,6,5,7,4,8] => [8,4,7,5,6,3,2,1] => 1111100
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => [8,4,7,6,5,3,2,1] => 1111110
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => [8,5,6,7,1,2,3,4] => 1000100
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => [8,5,7,6,1,2,3,4] => 1000110
[[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [3,4,2,1,6,7,5,8] => [8,5,7,6,1,2,4,3] => 1010110
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8] => [8,5,6,7,1,4,2,3] => 1100100
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => [8,5,7,6,1,4,2,3] => 1100110
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8] => [8,5,6,7,1,4,3,2] => 1110100
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [2,3,4,1,6,7,5,8] => [8,5,7,6,1,4,3,2] => 1110110
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [8,5,6,7,2,3,4,1] => 1100100
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,4,3,2,6,7,5,8] => [8,5,7,6,2,3,4,1] => 1100110
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,3,4,2,7,6,5,8] => [8,5,6,7,2,4,3,1] => 1110100
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [8,5,7,6,2,4,3,1] => 1110110
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [2,1,4,3,7,6,5,8] => [8,5,6,7,3,4,1,2] => 1010100
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [2,1,4,3,6,7,5,8] => [8,5,7,6,3,4,1,2] => 1010110
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,2,4,3,7,6,5,8] => [8,5,6,7,3,4,2,1] => 1110100
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => [8,5,6,7,4,1,2,3] => 1001100
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [3,2,1,4,6,7,5,8] => [8,5,7,6,4,1,2,3] => 1001110
[[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [2,3,1,4,7,6,5,8] => [8,5,6,7,4,1,3,2] => 1101100
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => [8,5,7,6,4,1,3,2] => 1101110
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8] => [8,5,6,7,4,2,3,1] => 1101100
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,3,2,4,6,7,5,8] => [8,5,7,6,4,2,3,1] => 1101110
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [2,1,3,4,6,7,5,8] => [8,5,7,6,4,3,1,2] => 1011110
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => [8,5,6,7,4,3,2,1] => 1111100
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => [8,5,7,6,4,3,2,1] => 1111110
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8] => [8,6,7,1,2,3,4,5] => 1000010
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [4,3,5,2,1,7,6,8] => [8,6,7,1,2,5,3,4] => 1010010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [3,2,5,4,1,7,6,8] => [8,6,7,1,4,5,2,3] => 1100010
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [2,3,5,4,1,7,6,8] => [8,6,7,1,4,5,3,2] => 1110010
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [4,3,2,5,1,7,6,8] => [8,6,7,1,5,2,3,4] => 1100010
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [3,4,2,5,1,7,6,8] => [8,6,7,1,5,2,4,3] => 1110010
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8] => [8,6,7,1,5,3,4,2] => 1110010
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [2,3,4,5,1,7,6,8] => [8,6,7,1,5,4,3,2] => 1111010
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => [8,6,7,2,3,4,5,1] => 1100010
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,4,5,3,2,7,6,8] => [8,6,7,2,3,5,4,1] => 1101010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => [8,6,7,2,4,5,3,1] => 1110010
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,4,3,5,2,7,6,8] => [8,6,7,2,5,3,4,1] => 1110010
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => [8,6,7,2,5,4,3,1] => 1111010
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [2,1,5,4,3,7,6,8] => [8,6,7,3,4,5,1,2] => 1010010
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,2,5,4,3,7,6,8] => [8,6,7,3,4,5,2,1] => 1110010
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,2,4,5,3,7,6,8] => [8,6,7,3,5,4,2,1] => 1111010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => [8,6,7,4,5,1,2,3] => 1001010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => [8,6,7,4,5,1,3,2] => 1101010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [8,6,7,4,5,2,3,1] => 1101010
[[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [2,1,3,5,4,7,6,8] => [8,6,7,4,5,3,1,2] => 1011010
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [8,6,7,4,5,3,2,1] => 1111010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => [8,6,7,5,1,2,3,4] => 1000110
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => [8,6,7,5,1,4,2,3] => 1100110
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [2,3,4,1,5,7,6,8] => [8,6,7,5,1,4,3,2] => 1110110
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => [8,6,7,5,2,3,4,1] => 1100110
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,3,4,2,5,7,6,8] => [8,6,7,5,2,4,3,1] => 1110110
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => [8,6,7,5,3,4,2,1] => 1110110
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8] => [8,6,7,5,4,1,3,2] => 1101110
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [8,6,7,5,4,2,3,1] => 1101110
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => [8,6,7,5,4,3,1,2] => 1011110
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [8,6,7,5,4,3,2,1] => 1111110
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [8,7,1,2,3,4,5,6] => 1000001
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => [8,7,1,2,3,4,6,5] => 1000101
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => [8,7,1,2,3,6,4,5] => 1001001
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => [8,7,1,2,3,6,5,4] => 1001101
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [3,6,5,4,2,1,7,8] => [8,7,1,2,4,5,6,3] => 1010001
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [3,5,6,4,2,1,7,8] => [8,7,1,2,4,6,5,3] => 1010101
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => [8,7,1,2,6,3,4,5] => 1010001
[[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [4,3,5,6,2,1,7,8] => [8,7,1,2,6,5,3,4] => 1010101
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => [8,7,1,2,6,5,4,3] => 1011101
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [2,6,5,4,3,1,7,8] => [8,7,1,3,4,5,6,2] => 1100001
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [2,4,5,6,3,1,7,8] => [8,7,1,3,6,5,4,2] => 1101101
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [3,2,6,5,4,1,7,8] => [8,7,1,4,5,6,2,3] => 1100001
[[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [3,2,5,6,4,1,7,8] => [8,7,1,4,6,5,2,3] => 1100101
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [2,3,6,5,4,1,7,8] => [8,7,1,4,5,6,3,2] => 1110001
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [2,3,5,6,4,1,7,8] => [8,7,1,4,6,5,3,2] => 1110101
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [4,3,2,6,5,1,7,8] => [8,7,1,5,6,2,3,4] => 1100001
[[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [3,4,2,6,5,1,7,8] => [8,7,1,5,6,2,4,3] => 1110001
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => [8,7,1,5,6,4,3,2] => 1111001
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [8,7,1,6,2,3,4,5] => 1100001
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => [8,7,1,6,2,3,5,4] => 1101001
[[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [3,5,4,2,6,1,7,8] => [8,7,1,6,2,4,5,3] => 1110001
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [8,7,1,6,2,5,3,4] => 1110001
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => [8,7,1,6,2,5,4,3] => 1111001
[[[.,[[[.,.],[[.,.],.]],.]],.],.] => [2,4,5,3,6,1,7,8] => [8,7,1,6,3,5,4,2] => 1111001
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [3,2,5,4,6,1,7,8] => [8,7,1,6,4,5,2,3] => 1101001
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => [8,7,1,6,4,5,3,2] => 1111001
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => [8,7,1,6,5,2,3,4] => 1100101
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => [8,7,1,6,5,2,4,3] => 1110101
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [8,7,1,6,5,4,3,2] => 1111101
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => [8,7,2,3,4,5,6,1] => 1100001
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,4,5,6,3,2,7,8] => [8,7,2,3,6,5,4,1] => 1101101
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,3,6,5,4,2,7,8] => [8,7,2,4,5,6,3,1] => 1110001
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => [8,7,2,4,6,5,3,1] => 1110101
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,3,4,6,5,2,7,8] => [8,7,2,5,6,4,3,1] => 1111001
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,4,5,3,6,2,7,8] => [8,7,2,6,3,5,4,1] => 1111001
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,3,5,4,6,2,7,8] => [8,7,2,6,4,5,3,1] => 1111001
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => [8,7,2,6,5,4,3,1] => 1111101
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [2,1,6,5,4,3,7,8] => [8,7,3,4,5,6,1,2] => 1010001
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [2,1,5,6,4,3,7,8] => [8,7,3,4,6,5,1,2] => 1010101
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => [8,7,3,4,5,6,2,1] => 1110001
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => [8,7,3,4,6,5,2,1] => 1110101
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,2,4,6,5,3,7,8] => [8,7,3,5,6,4,2,1] => 1111001
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,2,5,4,6,3,7,8] => [8,7,3,6,4,5,2,1] => 1111001
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => [8,7,3,6,5,4,2,1] => 1111101
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [3,2,1,6,5,4,7,8] => [8,7,4,5,6,1,2,3] => 1001001
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [2,3,1,6,5,4,7,8] => [8,7,4,5,6,1,3,2] => 1101001
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [2,3,1,5,6,4,7,8] => [8,7,4,6,5,1,3,2] => 1101101
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => [8,7,4,5,6,2,3,1] => 1101001
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,3,2,5,6,4,7,8] => [8,7,4,6,5,2,3,1] => 1101101
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [2,1,3,5,6,4,7,8] => [8,7,4,6,5,3,1,2] => 1011101
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => [8,7,4,5,6,3,2,1] => 1111001
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,2,3,5,6,4,7,8] => [8,7,4,6,5,3,2,1] => 1111101
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => [8,7,5,6,1,2,3,4] => 1000101
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [3,4,2,1,6,5,7,8] => [8,7,5,6,1,2,4,3] => 1010101
[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [2,4,3,1,6,5,7,8] => [8,7,5,6,1,3,4,2] => 1100101
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => [8,7,5,6,1,4,2,3] => 1100101
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [2,3,4,1,6,5,7,8] => [8,7,5,6,1,4,3,2] => 1110101
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,4,3,2,6,5,7,8] => [8,7,5,6,2,3,4,1] => 1100101
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => [8,7,5,6,3,4,1,2] => 1010101
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [8,7,5,6,3,4,2,1] => 1110101
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [2,3,1,4,6,5,7,8] => [8,7,5,6,4,1,3,2] => 1101101
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => [8,7,5,6,4,2,3,1] => 1101101
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => [8,7,5,6,4,3,1,2] => 1011101
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => [8,7,5,6,4,3,2,1] => 1111101
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [8,7,6,1,2,3,4,5] => 1000011
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => [8,7,6,1,2,3,5,4] => 1001011
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [3,5,4,2,1,6,7,8] => [8,7,6,1,2,4,5,3] => 1010011
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => [8,7,6,1,2,5,3,4] => 1010011
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => [8,7,6,1,2,5,4,3] => 1011011
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [2,5,4,3,1,6,7,8] => [8,7,6,1,3,4,5,2] => 1100011
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => [8,7,6,1,3,5,4,2] => 1101011
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [3,2,5,4,1,6,7,8] => [8,7,6,1,4,5,2,3] => 1100011
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [2,3,5,4,1,6,7,8] => [8,7,6,1,4,5,3,2] => 1110011
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => [8,7,6,1,5,2,3,4] => 1100011
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [8,7,6,1,5,2,4,3] => 1110011
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => [8,7,6,1,5,3,4,2] => 1110011
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => [8,7,6,1,5,4,2,3] => 1101011
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [8,7,6,1,5,4,3,2] => 1111011
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => [8,7,6,2,3,4,5,1] => 1100011
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,4,5,3,2,6,7,8] => [8,7,6,2,3,5,4,1] => 1101011
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,3,5,4,2,6,7,8] => [8,7,6,2,4,5,3,1] => 1110011
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,4,3,5,2,6,7,8] => [8,7,6,2,5,3,4,1] => 1110011
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => [8,7,6,2,5,4,3,1] => 1111011
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8] => [8,7,6,3,4,5,1,2] => 1010011
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => [8,7,6,3,5,4,1,2] => 1011011
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => [8,7,6,3,4,5,2,1] => 1110011
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,2,4,5,3,6,7,8] => [8,7,6,3,5,4,2,1] => 1111011
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [3,2,1,5,4,6,7,8] => [8,7,6,4,5,1,2,3] => 1001011
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [2,3,1,5,4,6,7,8] => [8,7,6,4,5,1,3,2] => 1101011
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [8,7,6,4,5,2,3,1] => 1101011
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8] => [8,7,6,4,5,3,1,2] => 1011011
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [8,7,6,4,5,3,2,1] => 1111011
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [8,7,6,5,1,2,3,4] => 1000111
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => [8,7,6,5,1,2,4,3] => 1010111
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => [8,7,6,5,1,3,4,2] => 1100111
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [8,7,6,5,1,4,2,3] => 1100111
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [8,7,6,5,1,4,3,2] => 1110111
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => [8,7,6,5,2,3,4,1] => 1100111
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => [8,7,6,5,2,4,3,1] => 1110111
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => [8,7,6,5,3,4,1,2] => 1010111
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => [8,7,6,5,3,4,2,1] => 1110111
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [8,7,6,5,4,1,2,3] => 1001111
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [8,7,6,5,4,1,3,2] => 1101111
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [8,7,6,5,4,2,3,1] => 1101111
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [8,7,6,5,4,3,1,2] => 1011111
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => 00000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => 00000001
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [1,2,3,4,5,6,9,8,7] => 00000011
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => [1,2,3,4,5,9,8,7,6] => 00000111
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => [1,2,3,4,9,8,7,6,5] => 00001111
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => [1,2,3,9,8,7,6,5,4] => 00011111
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => [1,2,9,8,7,6,5,4,3] => 00111111
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,3,2] => 01111111
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 000000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,10,9] => 000000001
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [7,9,8,6,5,4,3,2,1] => [1,2,3,4,5,6,8,9,7] => 00000010
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,10,9,8] => 000000011
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [6,8,9,7,5,4,3,2,1] => [1,2,3,4,5,7,9,8,6] => 00000101
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => [1,2,3,4,5,6,10,9,8,7] => 000000111
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [5,7,8,9,6,4,3,2,1] => [1,2,3,4,6,9,8,7,5] => 00001011
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [1,2,3,4,5,10,9,8,7,6] => 000001111
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [4,6,7,8,9,5,3,2,1] => [1,2,3,5,9,8,7,6,4] => 00010111
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => [1,2,3,4,10,9,8,7,6,5] => 000011111
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [3,5,6,7,8,9,4,2,1] => [1,2,4,9,8,7,6,5,3] => 00101111
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => [1,2,3,10,9,8,7,6,5,4] => 000111111
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [2,4,5,6,7,8,9,3,1] => [1,3,9,8,7,6,5,4,2] => 01011111
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => [1,2,10,9,8,7,6,5,4,3] => 001111111
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,2] => [2,9,8,7,6,5,4,3,1] => 10111111
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,4,3,2] => 011111111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,2,1] => 111111111
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [1,2,3,4,5,6,9,7,8] => 00000010
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [1,2,3,4,5,9,6,7,8] => 00000100
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [1,2,3,4,9,5,6,7,8] => 00001000
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [1,2,3,9,4,5,6,7,8] => 00010000
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [1,2,9,3,4,5,6,7,8] => 00100000
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,7,8] => 01000000
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,7,8] => 10000000
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,10,8,9] => 000000010
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [6,8,7,9,5,4,3,2,1] => [1,2,3,4,5,9,7,8,6] => 00000110
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [1,2,3,4,5,6,10,7,8,9] => 000000100
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [5,8,7,6,9,4,3,2,1] => [1,2,3,4,9,6,7,8,5] => 00001100
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [1,2,3,4,5,10,6,7,8,9] => 000001000
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [4,8,7,6,5,9,3,2,1] => [1,2,3,9,5,6,7,8,4] => 00011000
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [1,2,3,4,10,5,6,7,8,9] => 000010000
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [3,8,7,6,5,4,9,2,1] => [1,2,9,4,5,6,7,8,3] => 00110000
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [1,2,3,10,4,5,6,7,8,9] => 000100000
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [2,8,7,6,5,4,3,9,1] => [1,9,3,4,5,6,7,8,2] => 01100000
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [1,2,10,3,4,5,6,7,8,9] => 001000000
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,8,7,6,5,4,3,2,9] => [9,2,3,4,5,6,7,8,1] => 11000000
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [1,10,2,3,4,5,6,7,8,9] => 010000000
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,8,9] => 100000000
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => [10,1,9,2,8,3,7,4,6,5] => 111110000
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,9,8,1,10] => [10,1,8,9,6,7,4,5,2,3] => 110101000
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => [9,10,7,8,5,6,3,4,1,2] => 101010100
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,6,3,4,1,2] => 10101010100
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => [8,9,7,6,5,4,3,2,1] => 11111110
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => [9,10,8,7,6,5,4,3,2,1] => 111111110
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,9,8] => [8,9,7,6,5,4,3,1,2] => 10111110
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,2,3] => 01011111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => [10,11,9,8,7,6,5,4,3,2,1] => 1111111110
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,8,10,9] => [9,10,8,7,6,5,4,3,1,2] => 101111110
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,3,2,4,5,6,7,9,8] => [8,9,7,6,5,4,2,3,1] => 11011110
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [2,3,1,4,5,6,7,9,8] => [8,9,7,6,5,4,1,3,2] => 11011110
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => [1,9,8,7,6,5,2,4,3] => 01101111
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,4,2,3] => 010111111
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => [7,9,8,6,5,4,3,2,1] => 11111101
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,7,8,9,6] => [6,9,8,7,5,4,3,2,1] => 11111011
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,6,7,8,9,5] => [5,9,8,7,6,4,3,2,1] => 11110111
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,5,6,7,8,9,4] => [4,9,8,7,6,5,3,2,1] => 11101111
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,3] => [3,9,8,7,6,5,4,2,1] => 11011111
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => [7,8,9,6,5,4,3,2,1] => 11111100
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,7,9,10,8] => [8,10,9,7,6,5,4,3,2,1] => 111111101
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,5,8,7,9,6] => [6,9,7,8,5,4,3,2,1] => 11111010
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,6,8,9,10,7] => [7,10,9,8,6,5,4,3,2,1] => 111111011
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,4,7,6,8,9,5] => [5,9,8,6,7,4,3,2,1] => 11110101
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,5,7,8,9,10,6] => [6,10,9,8,7,5,4,3,2,1] => 111110111
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [1,2,3,6,5,7,8,9,4] => [4,9,8,7,5,6,3,2,1] => 11101011
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,4,6,7,8,9,10,5] => [5,10,9,8,7,6,4,3,2,1] => 111101111
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [1,2,5,4,6,7,8,9,3] => [3,9,8,7,6,4,5,2,1] => 11010111
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,3,5,6,7,8,9,10,4] => [4,10,9,8,7,6,5,3,2,1] => 111011111
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,4,3,5,6,7,8,9,2] => [2,9,8,7,6,5,3,4,1] => 10101111
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,10,3] => [3,10,9,8,7,6,5,4,2,1] => 110111111
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,10,2] => [2,10,9,8,7,6,5,4,3,1] => 101111111
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => [2,3,4,5,6,7,8,9,1] => 10000000
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,8,7] => 10000010
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => [2,3,4,5,6,7,9,8,1] => 10000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => [2,3,4,5,6,7,8,9,10,1] => 100000000
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => [11,1,2,3,4,5,6,7,8,9,10] => 1000000000
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,9,8] => 100000010
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [9,1,2,3,4,5,8,6,7] => 10000100
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,8,7,9,6,5,4,3,2] => [2,3,4,5,6,9,7,8,1] => 10000010
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,9,10,8,7,6,5,4,3,2] => [2,3,4,5,6,7,8,10,9,1] => 100000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => [2,3,4,5,6,7,8,9,10,11,1] => 1000000000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [2,1,9,8,7,6,5,4,3] => [3,4,5,6,7,8,9,1,2] => 10000000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [3,2,1,9,8,7,6,5,4] => [4,5,6,7,8,9,1,2,3] => 10000000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [4,3,2,1,9,8,7,6,5] => [5,6,7,8,9,1,2,3,4] => 10000000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [5,4,3,2,1,9,8,7,6] => [6,7,8,9,1,2,3,4,5] => 10000000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [6,5,4,3,2,1,9,8,7] => [7,8,9,1,2,3,4,5,6] => 10000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [7,6,5,4,3,2,1,9,8] => [8,9,1,2,3,4,5,6,7] => 10000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,9,8,7,6,5,4,3] => [3,4,5,6,7,8,9,2,1] => 11000000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => [3,4,5,6,7,8,9,10,1,2] => 100000000
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [2,3,1,9,8,7,6,5,4] => [4,5,6,7,8,9,1,3,2] => 11000000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [3,2,1,10,9,8,7,6,5,4] => [4,5,6,7,8,9,10,1,2,3] => 100000000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => [5,6,7,8,9,10,1,2,3,4] => 100000000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [5,4,3,2,1,10,9,8,7,6] => [6,7,8,9,10,1,2,3,4,5] => 100000000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => [7,8,9,10,1,2,3,4,5,6] => 100000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [7,6,5,4,3,2,1,10,9,8] => [8,9,10,1,2,3,4,5,6,7] => 100000000
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => [9,10,1,2,3,4,5,6,7,8] => 100000000
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [9,8,1,2,3,4,5,6,7] => 10000001
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => [9,8,7,1,2,3,4,5,6] => 10000011
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => [9,8,7,6,1,2,3,4,5] => 10000111
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => [9,8,7,6,5,1,2,3,4] => 10001111
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [9,8,7,6,5,4,1,2,3] => 10011111
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,1,2] => 10111111
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => [10,9,1,2,3,4,5,6,7,8] => 100000001
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => [10,9,8,1,2,3,4,5,6,7] => 100000011
[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,7,6,5,4,3,2,8,9] => [9,8,2,3,4,5,6,7,1] => 11000001
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => [10,9,8,7,1,2,3,4,5,6] => 100000111
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => [10,9,8,7,6,1,2,3,4,5] => 100001111
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => [10,9,8,7,6,5,1,2,3,4] => 100011111
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,4,3,2,5,6,7,8,9] => [9,8,7,6,5,2,3,4,1] => 11001111
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,1,2,3] => 100111111
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9] => [9,8,7,6,5,4,2,3,1] => 11011111
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,1,2] => 101111111
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [4,9,8,7,6,5,3,2,1] => [1,2,3,5,6,7,8,9,4] => 00010000
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [3,9,8,7,6,5,4,2,1] => [1,2,4,5,6,7,8,9,3] => 00100000
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => [1,3,4,5,6,7,8,9,2] => 01000000
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [6,10,9,8,7,5,4,3,2,1] => [1,2,3,4,5,7,8,9,10,6] => 000001000
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [2,4,6,8,10,9,7,5,3,1] => [1,3,5,7,9,10,8,6,4,2] => 010101010
[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,8,7,1,10,9] => [9,10,1,7,8,5,6,3,4,2] => 111010000
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,9,8,1] => [1,8,9,7,6,5,4,3,2] => 01111110
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [11,10,9,8,7,6,5,4,3,1,2] => 1011111111
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [2,1,3,4,5,6,8,7,9] => [9,7,8,6,5,4,3,1,2] => 10111110
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [2,3,4,5,6,8,9,7,1] => [1,7,9,8,6,5,4,3,2] => 01111101
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,8,10,9,1] => [1,9,10,8,7,6,5,4,3,2] => 011111110
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [2,1,4,3,5,6,7,8,9] => [9,8,7,6,5,3,4,1,2] => 10101111
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [6,5,4,3,2,1,8,7,9] => [9,7,8,1,2,3,4,5,6] => 10000010
[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]] => [7,8,6,9,5,4,3,2,1] => [1,2,3,4,5,9,6,8,7] => 00000110
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => [1,9,2,8,7,6,5,4,3] => 01111110
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [9,1,8,7,6,5,4,3,2] => 11111110
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => [9,8,7,6,5,4,1,3,2] => 11011111
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [9,8,1,7,6,5,4,3,2] => 11111101
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,1,3,2] => 110111111
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [2,4,3,1,5,6,7,8,9] => [9,8,7,6,5,1,3,4,2] => 11001111
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [2,3,5,4,1,6,7,8,9] => [9,8,7,6,1,4,5,3,2] => 11100111
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [2,3,4,6,5,1,7,8,9] => [9,8,7,1,5,6,4,3,2] => 11110011
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [2,3,4,5,7,6,1,8,9] => [9,8,1,6,7,5,4,3,2] => 11111001
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [2,3,4,5,6,8,7,1,9] => [9,1,7,8,6,5,4,3,2] => 11111100
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [10,1,9,8,7,6,5,4,3,2] => 111111110
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9] => [9,8,7,6,5,3,4,2,1] => 11101111
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,2,3,5,4,6,7,8,9] => [9,8,7,6,4,5,3,2,1] => 11110111
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,6,5,7,8,9] => [9,8,7,5,6,4,3,2,1] => 11111011
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,8,7,9] => [9,7,8,6,5,4,3,2,1] => 11111110
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,2,3,1] => 110111111
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,2,3,4,6,5,7,8,9,10] => [10,9,8,7,5,6,4,3,2,1] => 111110111
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,5,7,6,8,9,10] => [10,9,8,6,7,5,4,3,2,1] => 111111011
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,9,8,10] => [10,8,9,7,6,5,4,3,2,1] => 111111110
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [1,3,4,5,6,7,9,8,2] => [2,8,9,7,6,5,4,3,1] => 10111110
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [7,6,5,4,3,2,9,8,1] => [1,8,9,2,3,4,5,6,7] => 01000000
[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,1] => [1,9,8,7,6,5,2,3,4] => 01001111
[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]] => [6,5,4,3,2,7,8,9,10,1] => [1,10,9,8,7,2,3,4,5,6] => 010000111
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,7,6,5,4,3,2,9,8] => [8,9,2,3,4,5,6,7,1] => 11000000
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => [11,10,9,8,7,6,5,4,3,2,1] => 1111111111
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,2,10,9,8,7,6,5,4,3] => [3,4,5,6,7,8,9,10,2,1] => 110000000
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,3,2,9,8,7,6,5,4] => [4,5,6,7,8,9,2,3,1] => 11000000
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [2,1,8,7,6,5,4,3,9] => [9,3,4,5,6,7,8,1,2] => 10100000
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,9,8,7,6,5,4,3,2,10] => [10,2,3,4,5,6,7,8,9,1] => 110000000
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [1,3,2,5,4,6,7,8,9] => [9,8,7,6,4,5,2,3,1] => 11010111
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [8,7,6,5,4,3,2,10,9,1] => [1,9,10,2,3,4,5,6,7,8] => 010000000
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [2,1,4,5,6,7,8,9,3] => [3,9,8,7,6,5,4,1,2] => 10011111
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,3,4,5,6,7,8,2,9] => [9,2,8,7,6,5,4,3,1] => 11111110
[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]] => [6,7,8,5,4,3,2,9,1] => [1,9,2,3,4,5,8,7,6] => 01000110
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,7,10,9,8] => [8,9,10,7,6,5,4,3,2,1] => 111111100
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => [9,1,2,3,4,5,8,7,6] => 10000110
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,9,8,7] => 100000110
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,9,8,7,6] => [6,7,8,9,5,4,3,2,1] => 11111000
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,9,8,7,6,5] => [5,6,7,8,9,4,3,2,1] => 11110000
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,9,8,7,6,5,4] => [4,5,6,7,8,9,3,2,1] => 11100000
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,7,6,9,8] => [8,9,6,7,5,4,3,2,1] => 11111100
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,6,10,9,8,7] => [7,8,9,10,6,5,4,3,2,1] => 111111000
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,5,10,9,8,7,6] => [6,7,8,9,10,5,4,3,2,1] => 111110000
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,4,10,9,8,7,6,5] => [5,6,7,8,9,10,4,3,2,1] => 111100000
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,3,10,9,8,7,6,5,4] => [4,5,6,7,8,9,10,3,2,1] => 111000000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,6,8,7,10,9] => [9,10,7,8,6,5,4,3,2,1] => 111111100
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,11,9,10] => 0000000010
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [1,9,8,10,7,6,5,4,3,2] => [2,3,4,5,6,7,10,8,9,1] => 100000010
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [2,8,9,7,6,5,4,3,1] => [1,3,4,5,6,7,9,8,2] => 01000001
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,8,7] => 01000010
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => [9,1,8,2,3,4,5,6,7] => 11000000
[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.] => [5,8,7,6,4,3,2,1,9] => [9,1,2,3,4,6,7,8,5] => 10001000
[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.] => [6,5,8,7,4,3,2,1,9] => [9,1,2,3,4,7,8,5,6] => 10001000
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => [7,6,5,8,4,3,2,1,9] => [9,1,2,3,4,8,5,6,7] => 10001000
[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]] => [4,3,2,9,8,7,6,5,1] => [1,5,6,7,8,9,2,3,4] => 01000000
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,5,8,7,6,9] => [9,6,7,8,5,4,3,2,1] => 11111100
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [5,4,3,2,1,8,7,6,9] => [9,6,7,8,1,2,3,4,5] => 10000100
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [2,3,9,8,7,6,5,4,1] => [1,4,5,6,7,8,9,3,2] => 01100000
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,8,7,6,5,4,3,9,2] => [2,9,3,4,5,6,7,8,1] => 10100000
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [2,8,7,6,5,4,3,1,9] => [9,1,3,4,5,6,7,8,2] => 11000000
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [2,3,4,5,6,7,1,9,8] => [8,9,1,7,6,5,4,3,2] => 11111100
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,3,4,2,5,6,7,8,9] => [9,8,7,6,5,2,4,3,1] => 11101111
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,2,8,7,6,5,4,3,9] => [9,3,4,5,6,7,8,2,1] => 11100000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,8,10,9,11] => [11,9,10,8,7,6,5,4,3,2,1] => 1111111110
[[[[[[.,[[.,.],.]],.],.],.],[.,.]],.] => [2,3,1,4,5,6,8,7,9] => [9,7,8,6,5,4,1,3,2] => 11011110
[[[[.,[.,.]],.],.],[[[[.,.],.],.],.]] => [2,1,3,4,6,7,8,9,5] => [5,9,8,7,6,4,3,1,2] => 10110111
[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => [9,10,11,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,11,10,9] => 0000000011
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
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
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