Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00131: Permutations —descent bottoms⟶ Binary words
Images
[.,.] => [1] =>
[.,[.,.]] => [2,1] => 1
[[.,.],.] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => 11
[.,[[.,.],.]] => [2,3,1] => 10
[[.,.],[.,.]] => [3,1,2] => 10
[[.,[.,.]],.] => [2,1,3] => 10
[[[.,.],.],.] => [1,2,3] => 00
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 111
[.,[.,[[.,.],.]]] => [3,4,2,1] => 110
[.,[[.,.],[.,.]]] => [4,2,3,1] => 110
[.,[[.,[.,.]],.]] => [3,2,4,1] => 110
[.,[[[.,.],.],.]] => [2,3,4,1] => 100
[[.,.],[.,[.,.]]] => [4,3,1,2] => 101
[[.,.],[[.,.],.]] => [3,4,1,2] => 100
[[.,[.,.]],[.,.]] => [4,2,1,3] => 110
[[[.,.],.],[.,.]] => [4,1,2,3] => 100
[[.,[.,[.,.]]],.] => [3,2,1,4] => 110
[[.,[[.,.],.]],.] => [2,3,1,4] => 100
[[[.,.],[.,.]],.] => [3,1,2,4] => 100
[[[.,[.,.]],.],.] => [2,1,3,4] => 100
[[[[.,.],.],.],.] => [1,2,3,4] => 000
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 1111
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 1110
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => 1110
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1110
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 1100
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => 1101
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => 1100
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => 1110
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => 1100
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 1110
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 1100
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => 1100
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 1100
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 1000
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 1011
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 1010
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 1010
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 1010
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 1000
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 1101
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 1100
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 1001
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 1000
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 1110
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 1100
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 1010
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 1100
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 1000
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1110
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 1100
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => 1100
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 1100
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 1000
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => 1010
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 1000
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 1100
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 1000
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 1100
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 1000
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => 1000
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1000
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0000
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 11110
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => 11110
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 11110
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 11100
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => 11101
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => 11100
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => 11110
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => 11100
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 11110
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 11100
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => 11100
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 11100
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 11000
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => 11011
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => 11010
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 11010
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => 11010
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 11000
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 11101
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 11100
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 11001
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 11000
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 11110
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 11100
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 11010
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 11100
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 11000
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 11110
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 11100
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => 11100
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 11100
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 11000
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => 11010
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => 11000
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => 11100
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => 11000
>>> Load all 1941 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 11100
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 11000
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => 11000
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 11000
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 10000
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 10111
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 10110
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 10110
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 10110
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 10100
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 10101
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 10100
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 10110
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 10100
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 10110
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 10100
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 10100
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 10100
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 10000
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 11011
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 11010
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 11010
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 11010
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 11000
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 10011
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 10010
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 10010
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 10010
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 10000
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 11101
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 11100
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 11001
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 11000
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 10101
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 10100
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 11001
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 11000
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 10001
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 10000
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 11110
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 11100
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 11010
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 11100
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 11000
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 10110
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 10100
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 11010
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 10010
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 11100
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 11000
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 10100
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 11000
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 10000
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 11110
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 11100
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => 11100
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 11100
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 11000
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => 11010
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => 11000
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => 11100
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => 11000
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 11100
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 11000
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => 11000
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 11000
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 10000
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 10110
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 10100
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 10100
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 10100
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 10000
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 11010
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 11000
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 10010
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 10000
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 11100
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 11000
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 10100
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 11000
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 10000
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 11100
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 11000
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => 11000
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 11000
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 10000
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => 10100
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 10000
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 11000
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 10000
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 11000
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 10000
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => 10000
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 10000
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => 111110
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => 111110
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => 111110
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => 111100
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => 111101
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => 111100
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => 111110
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => 111100
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => 111110
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => 111100
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => 111100
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => 111100
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => 111000
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => 111011
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => 111010
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => 111010
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => 111010
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => 111000
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => 111101
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => 111100
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => 111001
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => 111000
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => 111110
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => 111100
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => 111010
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => 111100
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => 111000
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => 111110
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => 111100
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => 111100
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => 111100
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => 111000
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => 111010
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => 111000
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => 111100
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => 111000
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => 111100
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => 111000
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => 111000
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => 111000
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => 110000
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => 110111
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => 110110
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => 110110
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => 110110
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => 110100
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => 110101
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => 110100
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => 110110
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => 110100
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => 110110
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => 110100
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => 110100
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => 110100
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => 110000
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => 111011
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => 111010
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => 111010
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => 111010
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => 111000
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => 110011
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => 110010
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => 110010
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => 110010
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => 110000
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => 111101
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => 111100
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => 111001
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => 111000
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => 110101
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => 110100
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => 111001
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => 111000
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => 110001
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => 110000
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => 111110
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => 111100
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => 111010
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => 111100
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => 111000
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => 110110
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => 110100
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => 111010
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => 110010
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => 111100
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => 111000
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => 110100
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => 111000
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => 110000
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => 111110
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => 111100
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => 111100
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => 111100
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => 111000
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => 111010
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => 111000
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => 111100
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => 111000
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => 111100
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => 111000
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => 111000
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => 111000
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 110000
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => 110110
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => 110100
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => 110100
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => 110100
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => 110000
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => 111010
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => 111000
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => 110010
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => 110000
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => 111100
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => 111000
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => 110100
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => 111000
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => 110000
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => 111100
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => 111000
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => 111000
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 111000
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 110000
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => 110100
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => 110000
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => 111000
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => 110000
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 111000
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 110000
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => 110000
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 110000
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 100000
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => 101111
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => 101110
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => 101110
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => 101110
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => 101100
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => 101101
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => 101100
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => 101110
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => 101100
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => 101110
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => 101100
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => 101100
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => 101100
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => 101000
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => 101011
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => 101010
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => 101010
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => 101010
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => 101000
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => 101101
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => 101100
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => 101001
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => 101000
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => 101110
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => 101100
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => 101010
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => 101100
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => 101000
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => 101110
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => 101100
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => 101100
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => 101100
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => 101000
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => 101010
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => 101000
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => 101100
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => 101000
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => 101100
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => 101000
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => 101000
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => 101000
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => 100000
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => 110111
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => 110110
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => 110110
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => 110110
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => 110100
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => 110101
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => 110100
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => 110110
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => 110100
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => 110110
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => 110100
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => 110100
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => 110100
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => 110000
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => 100111
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => 100110
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => 100110
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => 100110
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => 100100
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => 100101
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => 100100
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => 100110
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => 100100
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => 100110
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => 100100
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => 100100
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => 100100
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => 100000
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => 111011
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => 111010
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => 111010
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => 111010
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => 111000
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => 110011
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => 110010
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => 110010
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => 110010
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => 110000
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => 101011
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => 101010
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => 101010
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => 101010
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => 101000
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => 110011
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => 110010
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => 110010
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => 110010
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => 110000
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => 100011
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => 100010
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => 100010
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => 100010
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => 100000
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => 111101
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => 111100
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => 111001
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => 111000
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => 110101
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => 110100
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => 111001
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => 111000
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => 110001
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => 110000
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => 101101
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => 101100
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => 101001
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => 101000
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => 110101
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => 110100
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => 100101
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => 100100
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => 111001
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => 111000
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => 110001
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => 110000
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => 101001
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => 101000
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => 110001
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => 110000
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => 100001
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => 100000
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => 111110
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => 111100
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => 111010
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => 111100
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => 111000
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => 110110
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => 110100
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => 111010
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => 110010
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => 111100
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => 111000
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => 110100
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => 111000
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => 110000
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => 101110
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => 101100
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => 101010
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => 101100
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => 101000
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => 110110
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => 110100
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => 100110
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => 100100
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => 111010
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => 110010
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => 101010
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => 110010
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => 100010
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => 111100
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => 111000
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => 110100
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => 111000
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => 110000
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => 101100
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => 101000
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => 110100
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => 100100
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => 111000
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => 110000
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => 101000
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => 110000
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => 100000
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 111110
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 111100
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => 111100
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 111100
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 111000
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => 111010
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => 111000
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => 111100
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => 111000
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 111100
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 111000
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => 111000
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => 111000
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => 110000
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => 110110
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => 110100
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => 110100
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => 110100
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => 110000
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => 111010
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => 111000
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => 110010
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => 110000
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => 111100
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => 111000
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => 110100
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => 111000
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => 110000
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 111100
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => 111000
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => 111000
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => 111000
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => 110000
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => 110100
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => 110000
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => 111000
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => 110000
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => 111000
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => 110000
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => 110000
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => 110000
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 100000
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => 101110
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => 101100
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => 101100
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => 101100
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => 101000
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => 101010
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => 101000
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => 101100
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => 101000
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => 101100
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => 101000
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => 101000
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => 101000
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => 100000
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => 110110
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => 110100
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => 110100
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => 110100
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => 110000
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => 100110
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => 100100
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => 100100
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => 100100
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => 100000
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => 111010
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => 111000
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => 110010
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => 110000
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => 101010
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => 101000
[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => 110010
[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => 110000
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => 100010
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => 100000
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => 111100
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => 111000
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => 110100
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => 111000
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => 110000
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => 101100
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => 101000
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => 110100
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => 100100
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => 111000
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => 110000
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => 101000
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => 110000
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => 100000
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 111100
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => 111000
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => 111000
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => 111000
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => 110000
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => 110100
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => 110000
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => 111000
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => 110000
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => 111000
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => 110000
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => 110000
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => 110000
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 100000
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => 101100
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => 101000
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => 101000
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => 101000
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => 100000
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => 110100
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => 110000
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => 100100
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => 100000
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => 111000
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => 110000
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => 101000
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => 110000
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => 100000
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 111000
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => 110000
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => 110000
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => 110000
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 100000
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => 101000
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => 100000
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => 110000
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => 100000
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 110000
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 100000
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => 100000
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 100000
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => 1111110
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [8,6,7,5,4,3,2,1] => 1111110
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 1111110
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => 1111100
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [8,7,5,6,4,3,2,1] => 1111101
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => 1111100
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [8,6,5,7,4,3,2,1] => 1111110
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [8,5,6,7,4,3,2,1] => 1111100
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => 1111110
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => 1111100
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => 1111100
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => 1111100
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => 1111000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => 1111011
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => 1111010
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => 1111010
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [7,6,8,4,5,3,2,1] => 1111010
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [6,7,8,4,5,3,2,1] => 1111000
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [8,7,5,4,6,3,2,1] => 1111101
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [8,7,4,5,6,3,2,1] => 1111001
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [8,6,5,4,7,3,2,1] => 1111110
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [8,5,6,4,7,3,2,1] => 1111100
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [8,6,4,5,7,3,2,1] => 1111010
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [8,5,4,6,7,3,2,1] => 1111100
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [8,4,5,6,7,3,2,1] => 1111000
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 1111110
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => 1111100
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [7,5,6,4,8,3,2,1] => 1111100
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 1111100
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => 1111000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => 1111010
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [6,7,4,5,8,3,2,1] => 1111000
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => 1111100
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => 1111000
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => 1111100
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => 1111000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [6,4,5,7,8,3,2,1] => 1111000
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => 1111000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => 1110000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => 1110111
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => 1110110
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => 1110110
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [7,6,8,5,3,4,2,1] => 1110110
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => 1110101
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [7,8,5,6,3,4,2,1] => 1110100
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [8,5,6,7,3,4,2,1] => 1110100
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [7,6,5,8,3,4,2,1] => 1110110
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [6,7,5,8,3,4,2,1] => 1110100
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [6,5,7,8,3,4,2,1] => 1110100
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => 1110000
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [8,7,6,4,3,5,2,1] => 1111011
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [7,8,6,4,3,5,2,1] => 1111010
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [8,6,7,4,3,5,2,1] => 1111010
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [7,6,8,4,3,5,2,1] => 1111010
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [6,7,8,4,3,5,2,1] => 1111000
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1] => 1110011
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [7,8,6,3,4,5,2,1] => 1110010
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [8,6,7,3,4,5,2,1] => 1110010
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [7,6,8,3,4,5,2,1] => 1110010
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => 1110000
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => 1111101
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [7,8,5,4,3,6,2,1] => 1111100
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [8,7,4,5,3,6,2,1] => 1111001
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [8,7,5,3,4,6,2,1] => 1110101
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [7,8,5,3,4,6,2,1] => 1110100
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [8,7,4,3,5,6,2,1] => 1111001
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [8,7,3,4,5,6,2,1] => 1110001
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [7,8,3,4,5,6,2,1] => 1110000
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [8,6,5,4,3,7,2,1] => 1111110
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [8,6,4,5,3,7,2,1] => 1111010
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [8,6,4,3,5,7,2,1] => 1111010
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [8,5,4,3,6,7,2,1] => 1111100
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [8,5,3,4,6,7,2,1] => 1110100
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [8,4,3,5,6,7,2,1] => 1111000
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [8,3,4,5,6,7,2,1] => 1110000
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => 1111110
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => 1111100
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [7,5,6,4,3,8,2,1] => 1111100
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [6,5,7,4,3,8,2,1] => 1111100
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => 1111000
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [6,7,4,5,3,8,2,1] => 1111000
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [7,5,4,6,3,8,2,1] => 1111100
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [7,4,5,6,3,8,2,1] => 1111000
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => 1111100
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [6,4,5,7,3,8,2,1] => 1111000
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => 1111000
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => 1110000
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => 1110110
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => 1111010
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => 1110010
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [7,5,4,3,6,8,2,1] => 1111100
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [7,5,3,4,6,8,2,1] => 1110100
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [7,3,4,5,6,8,2,1] => 1110000
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => 1111100
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => 1110000
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [6,5,3,4,7,8,2,1] => 1110100
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [6,3,4,5,7,8,2,1] => 1110000
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => 1111000
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [5,3,4,6,7,8,2,1] => 1110000
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => 1110000
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => 1100000
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => 1101111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => 1101110
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => 1101110
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,2,3,1] => 1101110
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => 1101101
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,2,3,1] => 1101110
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,2,3,1] => 1101100
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,2,3,1] => 1101110
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,2,3,1] => 1101100
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,2,3,1] => 1101100
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => 1101000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => 1101011
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => 1101010
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [7,6,8,4,5,2,3,1] => 1101010
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,2,3,1] => 1101000
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,2,3,1] => 1101101
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,2,3,1] => 1101001
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => 1101000
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [8,6,5,4,7,2,3,1] => 1101110
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,2,3,1] => 1101100
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,2,3,1] => 1101010
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [8,4,5,6,7,2,3,1] => 1101000
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,2,3,1] => 1101110
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,2,3,1] => 1101100
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,2,3,1] => 1101100
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,2,3,1] => 1101000
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => 1100000
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,2,4,1] => 1110111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,2,4,1] => 1110110
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [8,6,7,5,3,2,4,1] => 1110110
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,2,4,1] => 1110110
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,2,4,1] => 1110100
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,2,4,1] => 1110101
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => 1110110
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,2,4,1] => 1110100
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,2,4,1] => 1110110
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,2,4,1] => 1110100
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => 1110000
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => 1100111
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,2,3,4,1] => 1100110
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,2,3,4,1] => 1100110
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => 1100100
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,2,3,4,1] => 1100101
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [7,8,5,6,2,3,4,1] => 1100100
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [8,6,5,7,2,3,4,1] => 1100110
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => 1100100
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,2,3,4,1] => 1100110
[.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [6,7,5,8,2,3,4,1] => 1100100
[.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [6,5,7,8,2,3,4,1] => 1100100
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => 1100000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [8,7,6,4,3,2,5,1] => 1111011
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [7,8,6,4,3,2,5,1] => 1111010
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [8,6,7,4,3,2,5,1] => 1111010
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [7,6,8,4,3,2,5,1] => 1111010
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [6,7,8,4,3,2,5,1] => 1111000
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [8,7,6,3,4,2,5,1] => 1110011
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [7,8,6,3,4,2,5,1] => 1110010
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [8,6,7,3,4,2,5,1] => 1110010
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [7,6,8,3,4,2,5,1] => 1110010
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [6,7,8,3,4,2,5,1] => 1110000
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,2,3,5,1] => 1101011
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [8,6,7,4,2,3,5,1] => 1101010
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [7,6,8,4,2,3,5,1] => 1101010
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [6,7,8,4,2,3,5,1] => 1101000
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [8,7,6,3,2,4,5,1] => 1110011
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [7,8,6,3,2,4,5,1] => 1110010
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [8,6,7,3,2,4,5,1] => 1110010
[.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [6,7,8,3,2,4,5,1] => 1110000
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => 1100011
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [7,8,6,2,3,4,5,1] => 1100010
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [8,6,7,2,3,4,5,1] => 1100010
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [7,6,8,2,3,4,5,1] => 1100010
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [6,7,8,2,3,4,5,1] => 1100000
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [8,7,5,4,3,2,6,1] => 1111101
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [7,8,5,4,3,2,6,1] => 1111100
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [8,7,5,3,4,2,6,1] => 1110101
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [7,8,5,3,4,2,6,1] => 1110100
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [8,7,4,3,5,2,6,1] => 1111001
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [7,8,4,3,5,2,6,1] => 1111000
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,2,3,6,1] => 1101101
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [8,7,5,3,2,4,6,1] => 1110101
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [8,7,4,3,2,5,6,1] => 1111001
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [7,8,4,3,2,5,6,1] => 1111000
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [7,8,3,4,2,5,6,1] => 1110000
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [7,8,4,2,3,5,6,1] => 1101000
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => 1110000
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [8,7,2,3,4,5,6,1] => 1100001
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [7,8,2,3,4,5,6,1] => 1100000
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [8,6,5,4,3,2,7,1] => 1111110
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [8,5,6,4,3,2,7,1] => 1111100
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [8,6,4,5,3,2,7,1] => 1111010
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [8,5,4,6,3,2,7,1] => 1111100
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [8,6,5,3,4,2,7,1] => 1110110
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [8,5,6,3,4,2,7,1] => 1110100
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [8,6,4,3,5,2,7,1] => 1111010
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [8,6,3,4,5,2,7,1] => 1110010
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [8,5,4,3,6,2,7,1] => 1111100
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [8,4,5,3,6,2,7,1] => 1111000
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [8,4,3,5,6,2,7,1] => 1111000
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [8,3,4,5,6,2,7,1] => 1110000
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,2,3,7,1] => 1101110
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [8,5,6,4,2,3,7,1] => 1101100
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [8,6,4,5,2,3,7,1] => 1101010
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [8,6,5,3,2,4,7,1] => 1110110
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [8,6,4,3,2,5,7,1] => 1111010
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [8,6,4,2,3,5,7,1] => 1101010
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [8,5,4,3,2,6,7,1] => 1111100
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [8,4,5,3,2,6,7,1] => 1111000
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [8,5,3,4,2,6,7,1] => 1110100
[.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [8,3,4,5,2,6,7,1] => 1110000
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [8,5,4,2,3,6,7,1] => 1101100
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [8,4,5,2,3,6,7,1] => 1101000
[.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [8,5,2,3,4,6,7,1] => 1100100
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [8,4,3,2,5,6,7,1] => 1111000
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [8,3,4,2,5,6,7,1] => 1110000
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [8,4,2,3,5,6,7,1] => 1101000
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [8,3,2,4,5,6,7,1] => 1110000
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [8,2,3,4,5,6,7,1] => 1100000
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 1111110
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => 1111100
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [7,5,6,4,3,2,8,1] => 1111100
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 1111100
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => 1111000
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [7,6,4,5,3,2,8,1] => 1111010
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [6,7,4,5,3,2,8,1] => 1111000
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [7,4,5,6,3,2,8,1] => 1111000
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1] => 1111100
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [6,4,5,7,3,2,8,1] => 1111000
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => 1110000
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [7,6,5,3,4,2,8,1] => 1110110
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [7,5,6,3,4,2,8,1] => 1110100
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [6,5,7,3,4,2,8,1] => 1110100
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [5,6,7,3,4,2,8,1] => 1110000
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [7,6,4,3,5,2,8,1] => 1111010
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [7,6,3,4,5,2,8,1] => 1110010
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [7,5,4,3,6,2,8,1] => 1111100
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [7,4,5,3,6,2,8,1] => 1111000
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [7,5,3,4,6,2,8,1] => 1110100
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [7,3,4,5,6,2,8,1] => 1110000
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 1111100
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [6,4,5,3,7,2,8,1] => 1111000
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 1111000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => 1110000
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [6,5,3,4,7,2,8,1] => 1110100
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [5,6,3,4,7,2,8,1] => 1110000
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [6,4,3,5,7,2,8,1] => 1111000
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [6,3,4,5,7,2,8,1] => 1110000
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => 1111000
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => 1110000
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [4,3,5,6,7,2,8,1] => 1110000
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => 1100000
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => 1101110
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [6,7,5,4,2,3,8,1] => 1101100
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [7,5,6,4,2,3,8,1] => 1101100
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,2,3,8,1] => 1101100
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [5,6,7,4,2,3,8,1] => 1101000
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,2,3,8,1] => 1101010
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => 1101000
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,2,3,8,1] => 1101100
[.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [7,4,5,6,2,3,8,1] => 1101000
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [6,5,4,7,2,3,8,1] => 1101100
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [5,6,4,7,2,3,8,1] => 1101000
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [6,4,5,7,2,3,8,1] => 1101000
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [5,4,6,7,2,3,8,1] => 1101000
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => 1100000
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => 1110110
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [6,7,5,3,2,4,8,1] => 1110100
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [6,5,7,3,2,4,8,1] => 1110100
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => 1100110
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [7,5,6,2,3,4,8,1] => 1100100
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [5,6,7,2,3,4,8,1] => 1100000
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [6,7,4,3,2,5,8,1] => 1111000
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [7,6,4,2,3,5,8,1] => 1101010
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [7,6,3,2,4,5,8,1] => 1110010
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [6,7,3,2,4,5,8,1] => 1110000
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [7,6,2,3,4,5,8,1] => 1100010
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => 1100000
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [7,5,4,3,2,6,8,1] => 1111100
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [7,4,3,5,2,6,8,1] => 1111000
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [7,5,4,2,3,6,8,1] => 1101100
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [7,4,5,2,3,6,8,1] => 1101000
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [7,5,3,2,4,6,8,1] => 1110100
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [7,5,2,3,4,6,8,1] => 1100100
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [7,4,2,3,5,6,8,1] => 1101000
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [7,3,2,4,5,6,8,1] => 1110000
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [7,2,3,4,5,6,8,1] => 1100000
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => 1111100
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => 1111000
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => 1110000
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [6,5,3,4,2,7,8,1] => 1110100
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [6,3,4,5,2,7,8,1] => 1110000
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => 1111000
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => 1110000
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => 1100000
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [6,5,4,2,3,7,8,1] => 1101100
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [5,6,4,2,3,7,8,1] => 1101000
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [6,4,5,2,3,7,8,1] => 1101000
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [5,4,6,2,3,7,8,1] => 1101000
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [4,5,6,2,3,7,8,1] => 1100000
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [6,5,3,2,4,7,8,1] => 1110100
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [6,5,2,3,4,7,8,1] => 1100100
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [6,2,3,4,5,7,8,1] => 1100000
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => 1111000
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [4,5,3,2,6,7,8,1] => 1110000
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [5,3,4,2,6,7,8,1] => 1110000
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => 1110000
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 1100000
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [5,4,2,3,6,7,8,1] => 1101000
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [4,5,2,3,6,7,8,1] => 1100000
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [5,3,2,4,6,7,8,1] => 1110000
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => 1100000
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 1110000
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 1100000
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => 1100000
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 1100000
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 1000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => 1011111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => 1011110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => 1011110
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,3,1,2] => 1011110
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => 1011100
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => 1011101
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,3,1,2] => 1011100
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,3,1,2] => 1011110
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,3,1,2] => 1011110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,3,1,2] => 1011100
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => 1011100
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => 1011100
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => 1011000
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => 1011011
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => 1011010
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => 1011010
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => 1011000
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,3,1,2] => 1011101
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => 1011000
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,3,1,2] => 1011100
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => 1011010
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [8,5,4,6,7,3,1,2] => 1011100
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,3,1,2] => 1011110
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,3,1,2] => 1011100
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,3,1,2] => 1011100
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => 1011010
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,3,1,2] => 1011000
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,3,1,2] => 1011100
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [5,6,4,7,8,3,1,2] => 1011000
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [5,4,6,7,8,3,1,2] => 1011000
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => 1010000
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => 1010111
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => 1010110
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,4,1,2] => 1010110
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => 1010100
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => 1010101
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => 1010100
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,4,1,2] => 1010110
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,4,1,2] => 1010100
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => 1010110
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => 1010100
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => 1010100
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => 1010100
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => 1010000
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [6,7,8,4,3,5,1,2] => 1011000
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => 1010011
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => 1010010
[[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => 1010010
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [6,7,8,3,4,5,1,2] => 1010000
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => 1011100
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [8,7,4,5,3,6,1,2] => 1011001
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => 1011000
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => 1010100
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [8,7,4,3,5,6,1,2] => 1011001
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => 1011000
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [8,7,3,4,5,6,1,2] => 1010001
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => 1010000
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,3,7,1,2] => 1011110
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [8,5,4,6,3,7,1,2] => 1011100
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [8,5,4,3,6,7,1,2] => 1011100
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [8,5,3,4,6,7,1,2] => 1010100
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => 1011000
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => 1010000
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => 1011110
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [7,5,6,4,3,8,1,2] => 1011100
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2] => 1011100
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [5,6,7,4,3,8,1,2] => 1011000
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => 1011000
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,3,8,1,2] => 1011100
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [6,5,4,7,3,8,1,2] => 1011100
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => 1011000
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [5,4,6,7,3,8,1,2] => 1011000
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => 1010000
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [7,6,5,3,4,8,1,2] => 1010110
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => 1010100
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [5,6,7,3,4,8,1,2] => 1010000
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [7,6,4,3,5,8,1,2] => 1011010
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => 1010010
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [7,5,4,3,6,8,1,2] => 1011100
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [7,4,5,3,6,8,1,2] => 1011000
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [7,5,3,4,6,8,1,2] => 1010100
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [7,3,4,5,6,8,1,2] => 1010000
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [6,5,4,3,7,8,1,2] => 1011100
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [5,6,4,3,7,8,1,2] => 1011000
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => 1011000
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [4,5,6,3,7,8,1,2] => 1010000
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [6,5,3,4,7,8,1,2] => 1010100
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => 1010000
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => 1011000
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => 1010000
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => 1011000
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => 1010000
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [5,3,4,6,7,8,1,2] => 1010000
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => 1010000
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => 1000000
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => 1101111
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,2,1,3] => 1101110
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [8,6,7,5,4,2,1,3] => 1101110
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => 1101110
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,2,1,3] => 1101100
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [8,7,5,6,4,2,1,3] => 1101101
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,2,1,3] => 1101100
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,2,1,3] => 1101110
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,2,1,3] => 1101110
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,2,1,3] => 1101100
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,2,1,3] => 1101100
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,2,1,3] => 1101100
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => 1101000
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,2,1,3] => 1101011
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,2,1,3] => 1101010
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [7,6,8,4,5,2,1,3] => 1101010
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,2,1,3] => 1101001
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,2,1,3] => 1101110
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,2,1,3] => 1101010
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,2,1,3] => 1101000
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,2,1,3] => 1101110
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,2,1,3] => 1101100
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [7,5,6,4,8,2,1,3] => 1101100
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,2,1,3] => 1101100
[[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,2,1,3] => 1101000
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,2,1,3] => 1101010
[[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,2,1,3] => 1101000
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,2,1,3] => 1101000
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => 1100000
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => 1001111
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => 1001110
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,1,2,3] => 1001110
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => 1001100
[[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,1,2,3] => 1001100
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,1,2,3] => 1001110
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => 1001100
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,1,2,3] => 1001110
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,1,2,3] => 1001100
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,1,2,3] => 1001100
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => 1001100
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => 1001000
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => 1001011
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => 1001010
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [6,7,8,4,5,1,2,3] => 1001000
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [8,7,5,4,6,1,2,3] => 1001101
[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [7,8,5,4,6,1,2,3] => 1001100
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => 1001001
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => 1001000
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,1,2,3] => 1001110
[[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [8,5,6,4,7,1,2,3] => 1001100
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => 1001010
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [8,5,4,6,7,1,2,3] => 1001100
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => 1001000
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,1,2,3] => 1001110
[[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,1,2,3] => 1001100
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [7,5,6,4,8,1,2,3] => 1001100
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,1,2,3] => 1001100
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,1,2,3] => 1001000
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,1,2,3] => 1001010
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => 1001000
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,1,2,3] => 1001100
[[[.,.],.],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,1,2,3] => 1001000
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => 1001100
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [5,6,4,7,8,1,2,3] => 1001000
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [6,4,5,7,8,1,2,3] => 1001000
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,1,2,3] => 1001000
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => 1000000
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => 1110111
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,2,1,4] => 1110110
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,2,1,4] => 1110110
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,2,1,4] => 1110110
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,2,1,4] => 1110100
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,2,1,4] => 1110101
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => 1110100
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,2,1,4] => 1110110
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,2,1,4] => 1110100
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => 1110110
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,2,1,4] => 1110100
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,2,1,4] => 1110100
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,2,1,4] => 1110100
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => 1110000
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,3,1,4] => 1100111
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,3,1,4] => 1100110
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,3,1,4] => 1100110
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,3,1,4] => 1100110
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [6,7,8,5,2,3,1,4] => 1100100
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,3,1,4] => 1100101
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [7,8,5,6,2,3,1,4] => 1100100
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,3,1,4] => 1100110
[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [8,5,6,7,2,3,1,4] => 1100100
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,3,1,4] => 1100110
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [6,7,5,8,2,3,1,4] => 1100100
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => 1100100
[[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [6,5,7,8,2,3,1,4] => 1100100
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [5,6,7,8,2,3,1,4] => 1100000
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => 1010111
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,1,2,4] => 1010110
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,1,2,4] => 1010110
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,1,2,4] => 1010110
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,1,2,4] => 1010101
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => 1010100
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,1,2,4] => 1010110
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,1,2,4] => 1010110
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => 1010100
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => 1010100
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,1,2,4] => 1010100
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => 1010000
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => 1100111
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => 1100110
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,1,3,4] => 1100110
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => 1100100
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,1,3,4] => 1100101
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => 1100100
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,1,3,4] => 1100110
[[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [8,5,6,7,2,1,3,4] => 1100100
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,1,3,4] => 1100110
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [6,7,5,8,2,1,3,4] => 1100100
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [7,5,6,8,2,1,3,4] => 1100100
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => 1100100
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => 1100000
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => 1000111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => 1000110
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => 1000110
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => 1000110
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => 1000100
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => 1000101
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => 1000100
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => 1000110
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => 1000100
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => 1000110
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => 1000100
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => 1000100
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => 1000100
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => 1000000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => 1111011
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [7,8,6,4,3,2,1,5] => 1111010
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [8,6,7,4,3,2,1,5] => 1111010
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [7,6,8,4,3,2,1,5] => 1111010
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [6,7,8,4,3,2,1,5] => 1111000
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => 1110011
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [7,8,6,3,4,2,1,5] => 1110010
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [6,7,8,3,4,2,1,5] => 1110000
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,2,3,1,5] => 1101011
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [8,6,7,4,2,3,1,5] => 1101010
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [7,6,8,4,2,3,1,5] => 1101010
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [6,7,8,4,2,3,1,5] => 1101000
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => 1110011
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [8,6,7,3,2,4,1,5] => 1110010
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [6,7,8,3,2,4,1,5] => 1110000
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [8,7,6,2,3,4,1,5] => 1100011
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [8,6,7,2,3,4,1,5] => 1100010
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [7,6,8,2,3,4,1,5] => 1100010
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [6,7,8,2,3,4,1,5] => 1100000
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => 1011011
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => 1011000
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => 1010011
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [7,8,6,3,4,1,2,5] => 1010010
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [8,6,7,3,4,1,2,5] => 1010010
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => 1010000
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => 1101011
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,2,1,3,5] => 1101010
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,2,1,3,5] => 1101010
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => 1101000
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => 1001011
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => 1001010
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [7,6,8,4,1,2,3,5] => 1001010
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => 1001000
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => 1110011
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [7,8,6,3,2,1,4,5] => 1110010
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [8,6,7,3,2,1,4,5] => 1110010
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [7,6,8,3,2,1,4,5] => 1110010
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [6,7,8,3,2,1,4,5] => 1110000
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [8,7,6,2,3,1,4,5] => 1100011
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [7,8,6,2,3,1,4,5] => 1100010
[[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [8,6,7,2,3,1,4,5] => 1100010
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [7,6,8,2,3,1,4,5] => 1100010
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [6,7,8,2,3,1,4,5] => 1100000
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [8,7,6,3,1,2,4,5] => 1010011
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [7,8,6,3,1,2,4,5] => 1010010
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [8,6,7,3,1,2,4,5] => 1010010
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [7,6,8,3,1,2,4,5] => 1010010
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [6,7,8,3,1,2,4,5] => 1010000
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => 1100011
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [7,8,6,2,1,3,4,5] => 1100010
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [8,6,7,2,1,3,4,5] => 1100010
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => 1100000
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => 1000011
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => 1000010
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => 1000010
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => 1000010
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => 1000000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [8,7,5,4,3,2,1,6] => 1111101
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => 1111100
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [8,7,4,5,3,2,1,6] => 1111001
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [7,8,4,5,3,2,1,6] => 1111000
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [8,7,5,3,4,2,1,6] => 1110101
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [8,7,4,3,5,2,1,6] => 1111001
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [8,7,3,4,5,2,1,6] => 1110001
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [7,8,3,4,5,2,1,6] => 1110000
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [8,7,4,5,2,3,1,6] => 1101001
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [7,8,4,5,2,3,1,6] => 1101000
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [8,7,5,3,2,4,1,6] => 1110101
[[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [7,8,5,2,3,4,1,6] => 1100100
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [8,7,4,3,2,5,1,6] => 1111001
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [7,8,4,3,2,5,1,6] => 1111000
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [8,7,3,4,2,5,1,6] => 1110001
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [7,8,3,4,2,5,1,6] => 1110000
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [8,7,2,3,4,5,1,6] => 1100001
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [7,8,2,3,4,5,1,6] => 1100000
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => 1011101
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [7,8,5,4,3,1,2,6] => 1011100
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [8,7,5,3,4,1,2,6] => 1010101
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [7,8,5,3,4,1,2,6] => 1010100
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [8,7,3,4,5,1,2,6] => 1010001
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [7,8,3,4,5,1,2,6] => 1010000
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => 1101100
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => 1001101
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => 1001100
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => 1001001
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => 1001000
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [8,7,5,3,2,1,4,6] => 1110101
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [7,8,5,3,2,1,4,6] => 1110100
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]] => [8,7,5,2,3,1,4,6] => 1100101
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [8,7,5,3,1,2,4,6] => 1010101
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [7,8,5,3,1,2,4,6] => 1010100
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => 1100101
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => 1100100
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => 1000101
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => 1000100
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [8,7,4,3,2,1,5,6] => 1111001
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => 1111000
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [8,7,3,4,2,1,5,6] => 1110001
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [7,8,3,4,2,1,5,6] => 1110000
[[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [7,8,4,2,3,1,5,6] => 1101000
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [8,7,3,2,4,1,5,6] => 1110001
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [7,8,3,2,4,1,5,6] => 1110000
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [8,7,2,3,4,1,5,6] => 1100001
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [7,8,2,3,4,1,5,6] => 1100000
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [7,8,4,3,1,2,5,6] => 1011000
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [8,7,3,4,1,2,5,6] => 1010001
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => 1010000
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [8,7,4,2,1,3,5,6] => 1101001
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => 1101000
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => 1001001
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [7,8,4,1,2,3,5,6] => 1001000
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => 1110001
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => 1110000
[[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [8,7,2,3,1,4,5,6] => 1100001
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [7,8,2,3,1,4,5,6] => 1100000
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [7,8,3,1,2,4,5,6] => 1010000
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [8,7,2,1,3,4,5,6] => 1100001
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => 1100000
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => 1000001
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => 1000000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => 1111110
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [8,5,6,4,3,2,1,7] => 1111100
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [8,6,4,5,3,2,1,7] => 1111010
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [8,5,4,6,3,2,1,7] => 1111100
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => 1111000
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [8,6,5,3,4,2,1,7] => 1110110
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [8,5,6,3,4,2,1,7] => 1110100
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [8,6,4,3,5,2,1,7] => 1111010
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [8,4,5,3,6,2,1,7] => 1111000
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [8,4,3,5,6,2,1,7] => 1111000
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [8,3,4,5,6,2,1,7] => 1110000
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,2,3,1,7] => 1101110
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [8,5,6,4,2,3,1,7] => 1101100
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,2,3,1,7] => 1101010
[[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [8,4,5,6,2,3,1,7] => 1101000
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [8,6,5,3,2,4,1,7] => 1110110
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [8,6,5,2,3,4,1,7] => 1100110
[[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [8,5,6,2,3,4,1,7] => 1100100
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [8,6,4,3,2,5,1,7] => 1111010
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [8,6,4,2,3,5,1,7] => 1101010
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [8,6,3,2,4,5,1,7] => 1110010
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [8,5,4,3,2,6,1,7] => 1111100
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [8,4,3,5,2,6,1,7] => 1111000
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [8,5,4,2,3,6,1,7] => 1101100
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [8,4,5,2,3,6,1,7] => 1101000
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [8,5,3,2,4,6,1,7] => 1110100
[[.,[[[[.,.],.],[.,.]],.]],[.,.]] => [8,5,2,3,4,6,1,7] => 1100100
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [8,3,4,2,5,6,1,7] => 1110000
[[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [8,3,2,4,5,6,1,7] => 1110000
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [8,2,3,4,5,6,1,7] => 1100000
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => 1011110
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,3,1,2,7] => 1011010
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [8,6,5,3,4,1,2,7] => 1010110
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => 1010100
[[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [8,6,3,4,5,1,2,7] => 1010010
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [8,5,4,3,6,1,2,7] => 1011100
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [8,4,5,3,6,1,2,7] => 1011000
[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [8,5,3,4,6,1,2,7] => 1010100
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [8,4,3,5,6,1,2,7] => 1011000
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => 1010000
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => 1101110
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,2,1,3,7] => 1101100
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,2,1,3,7] => 1101010
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [8,4,5,6,2,1,3,7] => 1101000
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => 1001110
[[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,1,2,3,7] => 1001100
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => 1001010
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [8,4,5,6,1,2,3,7] => 1001000
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [8,6,5,3,2,1,4,7] => 1110110
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [8,5,6,3,2,1,4,7] => 1110100
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => 1100110
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [8,5,6,2,3,1,4,7] => 1100100
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [8,5,6,3,1,2,4,7] => 1010100
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [8,6,5,2,1,3,4,7] => 1100110
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => 1100100
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => 1000110
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => 1000100
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => 1111010
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [8,6,3,4,2,1,5,7] => 1110010
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [8,6,4,2,3,1,5,7] => 1101010
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [8,6,3,2,4,1,5,7] => 1110010
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [8,6,2,3,4,1,5,7] => 1100010
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [8,6,4,3,1,2,5,7] => 1011010
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [8,6,3,4,1,2,5,7] => 1010010
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => 1101010
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [8,6,3,2,1,4,5,7] => 1110010
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => 1000010
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [8,5,4,3,2,1,6,7] => 1111100
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [8,4,5,3,2,1,6,7] => 1111000
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [8,4,3,5,2,1,6,7] => 1111000
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [8,3,4,5,2,1,6,7] => 1110000
[[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [8,4,5,2,3,1,6,7] => 1101000
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [8,4,2,3,5,1,6,7] => 1101000
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [8,2,3,4,5,1,6,7] => 1100000
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [8,5,3,4,1,2,6,7] => 1010100
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [8,3,4,5,1,2,6,7] => 1010000
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [8,5,4,2,1,3,6,7] => 1101100
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [8,5,4,1,2,3,6,7] => 1001100
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [8,4,5,1,2,3,6,7] => 1001000
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [8,5,3,2,1,4,6,7] => 1110100
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [8,5,3,1,2,4,6,7] => 1010100
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [8,5,2,1,3,4,6,7] => 1100100
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => 1000100
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => 1111000
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [8,3,4,2,1,5,6,7] => 1110000
[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [8,4,2,3,1,5,6,7] => 1101000
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => 1100000
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [8,3,4,1,2,5,6,7] => 1010000
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [8,4,2,1,3,5,6,7] => 1101000
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => 1001000
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => 1110000
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => 1100000
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => 1010000
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => 1100000
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => 1000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 1111110
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 1111100
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [7,5,6,4,3,2,1,8] => 1111100
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 1111100
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 1111000
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => 1111010
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [6,7,4,5,3,2,1,8] => 1111000
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [7,5,4,6,3,2,1,8] => 1111100
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => 1111000
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 1111100
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => 1111000
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => 1111000
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => 1110000
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [7,6,5,3,4,2,1,8] => 1110110
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [6,7,5,3,4,2,1,8] => 1110100
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => 1110100
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.] => [6,5,7,3,4,2,1,8] => 1110100
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [5,6,7,3,4,2,1,8] => 1110000
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => 1111010
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [6,7,4,3,5,2,1,8] => 1111000
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => 1110010
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => 1111100
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [7,4,5,3,6,2,1,8] => 1111000
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [7,3,4,5,6,2,1,8] => 1110000
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => 1111100
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => 1111000
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => 1111000
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => 1111000
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => 1100000
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,2,3,1,8] => 1101110
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => 1101100
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,2,3,1,8] => 1101100
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [5,6,7,4,2,3,1,8] => 1101000
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => 1101010
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [6,7,4,5,2,3,1,8] => 1101000
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [7,5,4,6,2,3,1,8] => 1101100
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [7,4,5,6,2,3,1,8] => 1101000
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [6,5,4,7,2,3,1,8] => 1101100
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [5,6,4,7,2,3,1,8] => 1101000
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [5,4,6,7,2,3,1,8] => 1101000
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [4,5,6,7,2,3,1,8] => 1100000
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [7,6,5,3,2,4,1,8] => 1110110
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => 1110100
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => 1110000
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => 1100110
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [6,7,5,2,3,4,1,8] => 1100100
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [7,5,6,2,3,4,1,8] => 1100100
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => 1100100
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => 1100000
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [7,6,4,3,2,5,1,8] => 1111010
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [6,7,4,3,2,5,1,8] => 1111000
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [6,7,3,4,2,5,1,8] => 1110000
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [7,6,4,2,3,5,1,8] => 1101010
[[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [6,7,4,2,3,5,1,8] => 1101000
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [7,6,3,2,4,5,1,8] => 1110010
[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [6,7,3,2,4,5,1,8] => 1110000
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [7,6,2,3,4,5,1,8] => 1100010
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [6,7,2,3,4,5,1,8] => 1100000
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [7,5,4,3,2,6,1,8] => 1111100
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [7,4,5,3,2,6,1,8] => 1111000
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [7,5,3,4,2,6,1,8] => 1110100
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [7,4,3,5,2,6,1,8] => 1111000
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [7,5,4,2,3,6,1,8] => 1101100
[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [7,4,5,2,3,6,1,8] => 1101000
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [7,5,3,2,4,6,1,8] => 1110100
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [7,2,3,4,5,6,1,8] => 1100000
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => 1111100
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => 1111000
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => 1111000
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [5,6,3,4,2,7,1,8] => 1110000
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [6,3,4,5,2,7,1,8] => 1110000
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => 1111000
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => 1110000
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [5,3,4,6,2,7,1,8] => 1110000
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => 1110000
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => 1100000
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [5,4,6,2,3,7,1,8] => 1101000
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [6,5,3,2,4,7,1,8] => 1110100
[[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [6,3,2,4,5,7,1,8] => 1110000
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [6,2,3,4,5,7,1,8] => 1100000
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => 1111000
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => 1100000
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [5,4,2,3,6,7,1,8] => 1101000
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [4,5,2,3,6,7,1,8] => 1100000
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [5,2,3,4,6,7,1,8] => 1100000
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => 1110000
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => 1100000
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [4,2,3,5,6,7,1,8] => 1100000
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => 1100000
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 1000000
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => 1011110
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,3,1,2,8] => 1011100
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => 1011100
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,3,1,2,8] => 1011010
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [7,4,5,6,3,1,2,8] => 1011000
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [5,4,6,7,3,1,2,8] => 1011000
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [4,5,6,7,3,1,2,8] => 1010000
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [7,6,5,3,4,1,2,8] => 1010110
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [7,5,6,3,4,1,2,8] => 1010100
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [6,5,7,3,4,1,2,8] => 1010100
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [6,7,3,4,5,1,2,8] => 1010000
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [7,5,3,4,6,1,2,8] => 1010100
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [6,5,4,3,7,1,2,8] => 1011100
[[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [6,4,5,3,7,1,2,8] => 1011000
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [5,6,3,4,7,1,2,8] => 1010000
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [6,4,3,5,7,1,2,8] => 1011000
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [6,3,4,5,7,1,2,8] => 1010000
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [4,3,5,6,7,1,2,8] => 1010000
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [3,4,5,6,7,1,2,8] => 1000000
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => 1101110
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => 1101100
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,2,1,3,8] => 1101010
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => 1101100
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [7,4,5,6,2,1,3,8] => 1101000
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [5,4,6,7,2,1,3,8] => 1101000
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [4,5,6,7,2,1,3,8] => 1100000
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => 1001110
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,1,2,3,8] => 1001100
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => 1001000
[[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,1,2,3,8] => 1001010
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,1,2,3,8] => 1001100
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => 1001000
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => 1001000
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => 1001000
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => 1000000
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [7,6,5,3,2,1,4,8] => 1110110
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [7,6,5,2,3,1,4,8] => 1100110
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [6,7,5,2,3,1,4,8] => 1100100
[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [7,5,6,2,3,1,4,8] => 1100100
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [6,5,7,2,3,1,4,8] => 1100100
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [5,6,7,2,3,1,4,8] => 1100000
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [7,5,6,3,1,2,4,8] => 1010100
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => 1010000
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [7,6,5,2,1,3,4,8] => 1100110
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [6,7,5,2,1,3,4,8] => 1100100
[[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [7,5,6,2,1,3,4,8] => 1100100
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => 1100000
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => 1000110
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => 1000100
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => 1000100
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => 1000100
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => 1000000
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => 1111010
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [6,7,4,3,2,1,5,8] => 1111000
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [7,6,3,4,2,1,5,8] => 1110010
[[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [6,7,3,4,2,1,5,8] => 1110000
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [7,6,4,2,3,1,5,8] => 1101010
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [7,6,3,2,4,1,5,8] => 1110010
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [6,7,3,2,4,1,5,8] => 1110000
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [7,6,2,3,4,1,5,8] => 1100010
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [6,7,2,3,4,1,5,8] => 1100000
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => 1011010
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [6,7,3,4,1,2,5,8] => 1010000
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [7,6,4,2,1,3,5,8] => 1101010
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [7,6,3,2,1,4,5,8] => 1110010
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [6,7,3,2,1,4,5,8] => 1110000
[[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [7,6,2,3,1,4,5,8] => 1100010
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [6,7,2,3,1,4,5,8] => 1100000
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [6,7,3,1,2,4,5,8] => 1010000
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => 1000010
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => 1000000
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [7,5,4,3,2,1,6,8] => 1111100
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [7,4,5,3,2,1,6,8] => 1111000
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [7,4,3,5,2,1,6,8] => 1111000
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [7,3,4,5,2,1,6,8] => 1110000
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [7,5,4,2,3,1,6,8] => 1101100
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [7,5,3,2,4,1,6,8] => 1110100
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [7,5,2,3,4,1,6,8] => 1100100
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [7,4,2,3,5,1,6,8] => 1101000
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [7,2,3,4,5,1,6,8] => 1100000
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [7,5,4,3,1,2,6,8] => 1011100
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [7,5,3,4,1,2,6,8] => 1010100
[[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [7,4,5,2,1,3,6,8] => 1101000
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [7,4,5,1,2,3,6,8] => 1001000
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [7,5,3,2,1,4,6,8] => 1110100
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [7,5,2,3,1,4,6,8] => 1100100
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8] => 1010100
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => 1000100
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8] => 1111000
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [7,2,3,4,1,5,6,8] => 1100000
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [7,4,3,1,2,5,6,8] => 1011000
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [7,3,4,1,2,5,6,8] => 1010000
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [7,4,1,2,3,5,6,8] => 1001000
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [7,3,2,1,4,5,6,8] => 1110000
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [7,2,3,1,4,5,6,8] => 1100000
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => 1010000
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => 1100000
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => 1000000
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 1111100
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => 1111000
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => 1111000
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => 1110000
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [6,5,3,4,2,1,7,8] => 1110100
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [5,6,3,4,2,1,7,8] => 1110000
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => 1111000
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => 1100000
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [5,4,6,2,3,1,7,8] => 1101000
[[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [5,6,3,2,4,1,7,8] => 1110000
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [6,5,2,3,4,1,7,8] => 1100100
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [5,6,2,3,4,1,7,8] => 1100000
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [6,4,3,2,5,1,7,8] => 1111000
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [6,2,3,4,5,1,7,8] => 1100000
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => 1111000
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => 1110000
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => 1110000
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => 1100000
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [5,3,2,4,6,1,7,8] => 1110000
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [5,2,3,4,6,1,7,8] => 1100000
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => 1110000
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => 1100000
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [4,2,3,5,6,1,7,8] => 1100000
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => 1100000
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 1000000
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [6,5,4,3,1,2,7,8] => 1011100
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => 1011000
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [6,4,5,3,1,2,7,8] => 1011000
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => 1011000
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => 1010000
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [6,4,3,5,1,2,7,8] => 1011000
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => 1011000
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [4,3,5,6,1,2,7,8] => 1010000
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [3,4,5,6,1,2,7,8] => 1000000
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [6,5,4,2,1,3,7,8] => 1101100
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => 1101000
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [6,4,5,2,1,3,7,8] => 1101000
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [5,4,6,2,1,3,7,8] => 1101000
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [4,5,6,2,1,3,7,8] => 1100000
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8] => 1001100
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => 1000000
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [6,5,3,2,1,4,7,8] => 1110100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => 1110000
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [5,6,2,1,3,4,7,8] => 1100000
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8] => 1111000
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [6,3,4,2,1,5,7,8] => 1110000
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [6,4,3,1,2,5,7,8] => 1011000
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [6,4,2,1,3,5,7,8] => 1101000
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => 1001000
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [6,3,2,1,4,5,7,8] => 1110000
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [6,2,3,1,4,5,7,8] => 1100000
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [6,3,1,2,4,5,7,8] => 1010000
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [6,2,1,3,4,5,7,8] => 1100000
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => 1000000
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 1111000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => 1110000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [5,3,4,2,1,6,7,8] => 1110000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => 1110000
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => 1100000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [5,4,2,3,1,6,7,8] => 1101000
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [4,5,2,3,1,6,7,8] => 1100000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [5,3,2,4,1,6,7,8] => 1110000
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [5,2,3,4,1,6,7,8] => 1100000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => 1110000
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => 1100000
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [4,2,3,5,1,6,7,8] => 1100000
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => 1100000
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 1000000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [5,4,3,1,2,6,7,8] => 1011000
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [5,3,4,1,2,6,7,8] => 1010000
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [4,3,5,1,2,6,7,8] => 1010000
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [3,4,5,1,2,6,7,8] => 1000000
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [5,4,2,1,3,6,7,8] => 1101000
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [4,5,2,1,3,6,7,8] => 1100000
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [5,4,1,2,3,6,7,8] => 1001000
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [4,5,1,2,3,6,7,8] => 1000000
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [5,3,2,1,4,6,7,8] => 1110000
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [5,2,3,1,4,6,7,8] => 1100000
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => 1010000
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [5,2,1,3,4,6,7,8] => 1100000
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => 1000000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 1110000
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => 1100000
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [4,2,3,1,5,6,7,8] => 1100000
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => 1100000
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => 1000000
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [4,3,1,2,5,6,7,8] => 1010000
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => 1000000
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [4,2,1,3,5,6,7,8] => 1100000
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => 1000000
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 1100000
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => 1000000
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => 1000000
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 1000000
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => 11111110
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => 11111100
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => 11111000
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => 11110000
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => 11100000
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => 11000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 10000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => 111111110
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [9,7,8,6,5,4,3,2,1] => 11111110
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => 111111100
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [8,9,6,7,5,4,3,2,1] => 11111100
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => 111111000
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [7,8,9,5,6,4,3,2,1] => 11111000
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => 111110000
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [6,7,8,9,4,5,3,2,1] => 11110000
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => 111100000
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [5,6,7,8,9,3,4,2,1] => 11100000
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => 111000000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,2,3,1] => 11000000
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => 110000000
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => 10000000
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 100000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => 11111110
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => 11111110
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => 11111110
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => 11111110
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => 11111110
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => 11111110
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 11111110
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => 111111110
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [8,6,7,9,5,4,3,2,1] => 11111100
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => 111111110
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [8,7,5,6,9,4,3,2,1] => 11111010
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => 111111110
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [8,7,6,4,5,9,3,2,1] => 11110110
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => 111111110
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [8,7,6,5,3,4,9,2,1] => 11101110
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => 111111110
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,2,3,9,1] => 11011110
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => 111111110
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9] => 10111110
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => 111111110
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 111111110
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => 101010100
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => [9,10,6,7,4,5,2,3,1,8] => 110101000
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => 111100000
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => 10101010100
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [10,8,6,4,2,1,3,5,7,9] => 110101010
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [12,10,8,6,4,2,1,3,5,7,9,11] => 11010101010
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => 10000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => 100000000
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => 11000000
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 11000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => 1000000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => 110000000
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => 10100000
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [9,2,3,1,4,5,6,7,8] => 11000000
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => 11000000
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 11000000
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 110000000
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 1000000000
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => 10000000
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => 10000000
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => 10000000
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [5,6,7,8,9,1,2,3,4] => 10000000
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,1,2,3] => 10000000
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => 10000001
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => 100000000
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [8,7,9,1,2,3,4,5,6] => 10000010
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => 100000000
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [7,6,8,9,1,2,3,4,5] => 10000100
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => 100000000
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [6,5,7,8,9,1,2,3,4] => 10001000
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => 100000000
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [5,4,6,7,8,9,1,2,3] => 10010000
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [5,6,7,8,9,10,1,2,3,4] => 100000000
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [4,3,5,6,7,8,9,1,2] => 10100000
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [4,5,6,7,8,9,10,1,2,3] => 100000000
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => 100000000
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => 10111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 11111100
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2] => 10111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => 101111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 111111100
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 11111100
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => [8,6,7,5,4,3,2,1,9] => 11111100
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,3,1,2] => 10111110
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => 10111110
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [9,10,8,7,6,5,4,3,1,2] => 101111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2] => 1011111111
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => 111110000
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [7,6,8,5,9,4,10,3,11,2,12,1] => 11111100000
[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [9,8,10,6,7,4,5,2,3,1] => 110101010
[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.] => [6,4,5,7,3,8,2,9,1,10] => 111100000
[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]] => [8,9,6,7,4,5,2,3,10,1] => 110101000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,2,1,3] => 11011111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,2,1,4] => 11101111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,3,2,1,5] => 11110111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [9,8,7,5,4,3,2,1,6] => 11111011
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [9,8,6,5,4,3,2,1,7] => 11111101
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [9,7,6,5,4,3,2,1,8] => 11111110
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => 10011111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,2,1,3] => 110111111
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,2,3,1,4] => 11001111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,3,2,1,4] => 111011111
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,3,4,2,1,5] => 11100111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,4,3,2,1,5] => 111101111
[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => [9,8,7,4,5,3,2,1,6] => 11110011
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [10,9,8,7,5,4,3,2,1,6] => 111110111
[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => [9,8,5,6,4,3,2,1,7] => 11111001
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [10,9,8,6,5,4,3,2,1,7] => 111111011
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [9,6,7,5,4,3,2,1,8] => 11111100
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [10,9,7,6,5,4,3,2,1,8] => 111111101
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [10,8,7,6,5,4,3,2,1,9] => 111111110
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 11111100
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 11111000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 11110000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 11100000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 11000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 10000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 111111100
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 111111000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 111110000
[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => [6,5,4,3,1,2,7,8,9] => 10111000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 111100000
[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] => [5,4,3,1,2,6,7,8,9] => 10110000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 111000000
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [4,3,1,2,5,6,7,8,9] => 10100000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 110000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9] => 10000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 100000000
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [9,8,7,5,6,4,3,2,1] => 11111011
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,4,5,3,2,1] => 11110111
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,3,4,2,1] => 11101111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => 11011111
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [10,8,9,7,6,5,4,3,2,1] => 111111110
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [10,9,8,6,7,5,4,3,2,1] => 111111011
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,5,6,4,3,2,1] => 111110111
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,2,3,1] => 110111111
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [10,8,9,6,7,4,5,2,3,1] => 110101010
[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [10,8,9,6,7,4,5,2,1,3] => 110101010
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [9,2,3,4,5,6,7,8,1] => 11000000
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [8,2,1,3,4,5,6,7,9] => 11000000
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [8,9,2,1,3,4,5,6,7] => 11000000
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => [8,2,3,4,5,6,7,9,1] => 11000000
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [8,9,2,3,4,5,6,7,1] => 11000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [10,2,3,4,5,6,7,8,9,1] => 110000000
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [8,6,5,4,3,2,1,7,9] => 11111100
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => 11000000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 10000000
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => 10000000
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.] => [2,3,4,5,1,6,7,8,9] => 10000000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 10000000
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [4,2,3,1,5,6,7,8,9] => 11000000
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [5,2,3,4,1,6,7,8,9] => 11000000
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [6,2,3,4,5,1,7,8,9] => 11000000
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [7,2,3,4,5,6,1,8,9] => 11000000
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [8,2,3,4,5,6,7,1,9] => 11000000
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 100000000
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9] => 10000000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [5,1,2,3,4,6,7,8,9] => 10000000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [6,1,2,3,4,5,7,8,9] => 10000000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => 10000000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => 10000000
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9,10] => 100000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9,10] => 100000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [5,1,2,3,4,6,7,8,9,10] => 100000000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [6,1,2,3,4,5,7,8,9,10] => 100000000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [7,1,2,3,4,5,6,8,9,10] => 100000000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [8,1,2,3,4,5,6,7,9,10] => 100000000
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => 100000000
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [9,3,4,5,6,7,8,1,2] => 10100000
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [9,7,6,5,4,3,2,8,1] => 11111110
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => 11111000
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [9,7,6,5,4,3,1,2,8] => 10111110
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [8,9,6,5,4,3,2,1,7] => 11111100
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => 100111111
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,1,2,4] => 10101111
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,2,1,3,9] => 11011110
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [9,8,7,6,5,4,3,1,2,10] => 101111110
[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,2,3,1] => 11011110
[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]] => [7,8,2,3,4,5,6,9,1] => 11000000
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [3,4,5,1,2,6,7,8,9] => 10000000
[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]] => [9,2,3,4,5,1,6,7,8] => 11000000
[.,[.,[[[[.,[[[.,.],.],.]],.],.],.]]] => [4,5,6,3,7,8,9,2,1] => 11100000
[.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]] => [3,4,5,6,2,7,8,9,10,1] => 110000000
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [4,5,2,1,3,6,7,8,9] => 11000000
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [5,3,1,2,4,6,7,8,9] => 10100000
[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]] => [6,2,3,4,5,7,8,9,10,1] => 110000000
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [10,8,7,6,5,4,3,2,9,1] => 111111110
[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,3,1,2] => 10100000
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,2,1,3] => 11000000
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [3,4,5,6,7,8,1,2,9] => 10000000
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] => [8,9,7,6,5,4,2,1,3] => 11011110
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => 100000001
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => 11111000
[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => [6,5,4,3,2,7,8,1,9] => 11111000
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => 111111000
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]] => [10,9,8,7,6,5,4,3,2,11,1] => 1111111110
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => 10000011
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => 10000111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => 10001111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [9,7,1,2,3,4,5,6,8] => 10000010
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => 100000011
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [9,8,6,1,2,3,4,5,7] => 10000101
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => 100000111
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [9,8,7,5,1,2,3,4,6] => 10001011
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => 100001111
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,1,2,3,5] => 10010111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => 100011111
[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.] => [3,2,4,1,5,6,7,8,9] => 11000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => 1111111110
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [9,8,10,7,6,5,4,3,1,2] => 101111110
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,2,3,1] => 11011110
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => 1111111110
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => 11111100
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]] => [8,9,7,6,5,4,3,2,10,1] => 111111100
[.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]] => [7,6,8,5,4,3,2,9,1] => 11111100
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => 11000000
[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]] => [5,4,6,7,8,9,3,2,1] => 11110000
[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]] => [6,5,7,8,9,4,3,2,1] => 11111000
[.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]] => [6,5,7,8,9,10,4,3,2,1] => 111110000
[.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]] => [5,4,6,7,8,3,9,2,1] => 11110000
[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]] => [5,4,6,7,8,9,10,3,2,1] => 111100000
[.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]] => [6,5,7,8,9,10,11,4,3,2,1] => 1111100000
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => 11111100
[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.] => [6,5,4,3,2,7,1,8,9] => 11111000
[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.] => [5,4,3,2,6,1,7,8,9] => 11110000
[[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.] => [4,3,2,5,1,6,7,8,9] => 11100000
[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]] => [8,9,7,6,4,3,2,1,5] => 11110110
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => 11100000
[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,4,3,2,1,5] => 111100000
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => 11000000
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [8,7,5,4,3,2,1,6,9] => 11111010
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [9,7,6,5,4,3,2,1,8,10] => 111111100
[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [9,6,7,8,5,4,3,2,1] => 11111100
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,3,9,1,2] => 10111110
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,2,3,1,9] => 11011110
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [9,2,3,4,5,6,7,1,8] => 11000000
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => 10000000
[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,9,2,10,1] => 110000000
[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [4,5,6,7,8,3,9,1,2] => 10100000
[[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]] => [9,3,4,5,6,7,2,1,8] => 11100000
[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => [4,5,6,7,8,9,10,2,3,1] => 110000000
[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.] => [3,4,5,6,2,1,7,8,9] => 11000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [10,11,1,2,3,4,5,6,7,8,9] => 1000000000
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,1,2,3,9] => 10011110
[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => [9,8,2,3,4,5,6,7,1] => 11000001
[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]] => [10,9,2,3,4,5,6,7,8,1] => 110000001
[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.] => [3,4,5,6,7,8,2,1,9] => 11000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => [10,3,1,2,4,5,6,7,8,9] => 101000000
[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]] => [9,2,3,4,5,6,1,7,8] => 11000000
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [10,8,7,6,5,4,3,1,2,9] => 101111110
[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.] => [3,4,5,6,7,2,1,8,9] => 11000000
[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]] => [5,6,7,4,8,9,1,2,3] => 10010000
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => 11111000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [9,10,7,6,5,4,3,2,1,8] => 111111100
[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]] => [9,8,2,3,4,5,6,1,7] => 11000001
[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.] => [3,4,5,2,1,6,7,8,9] => 11000000
[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]] => [9,3,4,5,6,7,8,2,1] => 11100000
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]] => [7,6,8,9,5,4,3,2,1] => 11111100
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => [11,9,10,8,7,6,5,4,3,2,1] => 1111111110
[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]] => [7,6,8,5,9,4,3,2,1] => 11111100
[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]] => [8,7,9,10,6,5,4,3,2,1] => 111111100
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the 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 maximal element of the Sylvester class.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
searching the database
Sorry, this map was not found in the database.