Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00130: Permutations —descent tops⟶ Binary words
Images
[.,.] => [1] =>
[.,[.,.]] => [2,1] => 1
[[.,.],.] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => 11
[.,[[.,.],.]] => [2,3,1] => 01
[[.,.],[.,.]] => [3,1,2] => 01
[[.,[.,.]],.] => [2,1,3] => 10
[[[.,.],.],.] => [1,2,3] => 00
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 111
[.,[.,[[.,.],.]]] => [3,4,2,1] => 101
[.,[[.,.],[.,.]]] => [4,2,3,1] => 011
[.,[[.,[.,.]],.]] => [3,2,4,1] => 011
[.,[[[.,.],.],.]] => [2,3,4,1] => 001
[[.,.],[.,[.,.]]] => [4,3,1,2] => 011
[[.,.],[[.,.],.]] => [3,4,1,2] => 001
[[.,[.,.]],[.,.]] => [4,2,1,3] => 101
[[[.,.],.],[.,.]] => [4,1,2,3] => 001
[[.,[.,[.,.]]],.] => [3,2,1,4] => 110
[[.,[[.,.],.]],.] => [2,3,1,4] => 010
[[[.,.],[.,.]],.] => [3,1,2,4] => 010
[[[.,[.,.]],.],.] => [2,1,3,4] => 100
[[[[.,.],.],.],.] => [1,2,3,4] => 000
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 1111
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 1101
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => 1011
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1011
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 1001
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => 0111
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => 0101
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => 0111
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => 0011
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 0111
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 0011
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => 0011
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 0101
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 0001
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 0111
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 0101
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0011
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 0011
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 0001
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 1011
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 1001
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 0011
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 0001
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 1101
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 0101
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 0101
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 1001
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 0001
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1110
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 1010
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => 0110
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 0110
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 0010
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => 0110
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 0010
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 1010
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 0010
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 1100
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 0100
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => 0100
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1000
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0000
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 11101
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => 11011
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 11011
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 11001
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => 10111
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => 10101
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => 10111
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => 10011
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 10111
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 10011
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => 10011
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 10101
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 10001
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => 01111
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => 01101
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 01011
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => 01011
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 01001
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 01111
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 01101
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 00111
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 00101
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 01111
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 00111
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 00111
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 01011
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 00011
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 01111
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 01011
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => 00111
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 00111
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 00011
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => 00111
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => 00011
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => 01011
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => 00011
>>> Load all 1943 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 01101
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 00101
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => 00101
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 01001
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 00001
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 01111
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 01101
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 01011
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 01011
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 01001
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 00111
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 00101
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 00111
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 00011
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 00111
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 00011
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 00011
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 00101
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 00001
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 10111
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 10101
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 10011
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 10011
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 10001
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 00111
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 00101
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 00011
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 00011
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 00001
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 11011
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 11001
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 01011
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 01001
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 01011
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 01001
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 10011
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 10001
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 00011
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 00001
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 11101
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 10101
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 01101
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 01101
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 00101
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 01101
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 00101
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 10101
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 00101
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 11001
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 01001
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 01001
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 10001
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 00001
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 11110
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 11010
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => 10110
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 10110
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 10010
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => 01110
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => 01010
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => 01110
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => 00110
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 01110
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 00110
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => 00110
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 01010
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 00010
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 01110
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 01010
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 00110
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 00110
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 00010
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 10110
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 10010
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 00110
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 00010
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 11010
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 01010
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 01010
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 10010
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 00010
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 11100
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 10100
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => 01100
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 01100
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 00100
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => 01100
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 00100
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 10100
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 00100
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 11000
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 01000
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => 01000
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 10000
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => 111101
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => 111011
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => 111011
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => 111001
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => 110111
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => 110101
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => 110111
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => 110011
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => 110111
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => 110011
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => 110011
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => 110101
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => 110001
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => 101111
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => 101101
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => 101011
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => 101011
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => 101001
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => 101111
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => 101101
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => 100111
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => 100101
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => 101111
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => 100111
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => 100111
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => 101011
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => 100011
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => 101111
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => 101011
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => 100111
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => 100111
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => 100011
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => 100111
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => 100011
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => 101011
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => 100011
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => 101101
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => 100101
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => 100101
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => 101001
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => 100001
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => 011111
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => 011101
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => 011011
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => 011011
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => 011001
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => 010111
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => 010101
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => 010111
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => 010011
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => 010111
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => 010011
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => 010011
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => 010101
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => 010001
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => 011111
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => 011101
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => 011011
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => 011011
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => 011001
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => 001111
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => 001101
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => 001011
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => 001011
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => 001001
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => 011111
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => 011101
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => 001111
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => 001101
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => 001111
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => 001101
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => 010111
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => 010101
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => 000111
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => 000101
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => 011111
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => 010111
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => 001111
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => 001111
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => 000111
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => 001111
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => 000111
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => 010111
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => 000111
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => 011011
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => 001011
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => 001011
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => 010011
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => 000011
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => 011111
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => 011011
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => 010111
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => 010111
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => 010011
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => 001111
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => 001011
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => 001111
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => 000111
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => 001111
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => 000111
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => 000111
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => 001011
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 000011
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => 001111
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => 001011
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => 000111
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => 000111
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => 000011
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => 010111
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => 010011
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => 000111
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => 000011
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => 011011
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => 001011
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => 001011
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => 010011
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => 000011
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => 011101
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => 010101
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => 001101
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 001101
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 000101
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => 001101
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => 000101
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => 010101
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => 000101
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 011001
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 001001
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => 001001
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 010001
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 000001
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => 011111
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => 011101
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => 011011
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => 011011
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => 011001
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => 010111
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => 010101
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => 010111
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => 010011
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => 010111
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => 010011
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => 010011
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => 010101
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => 010001
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => 001111
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => 001101
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => 001011
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => 001011
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => 001001
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => 001111
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => 001101
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => 000111
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => 000101
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => 001111
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => 000111
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => 000111
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => 001011
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => 000011
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => 001111
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => 001011
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => 000111
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => 000111
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => 000011
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => 000111
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => 000011
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => 001011
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => 000011
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => 001101
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => 000101
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => 000101
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => 001001
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => 000001
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => 101111
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => 101101
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => 101011
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => 101011
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => 101001
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => 100111
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => 100101
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => 100111
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => 100011
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => 100111
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => 100011
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => 100011
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => 100101
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => 100001
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => 001111
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => 001101
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => 001011
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => 001011
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => 001001
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => 000111
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => 000101
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => 000111
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => 000011
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => 000111
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => 000011
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => 000011
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => 000101
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => 000001
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => 110111
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => 110101
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => 110011
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => 110011
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => 110001
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => 010111
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => 010101
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => 010011
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => 010011
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => 010001
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => 010111
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => 010101
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => 010011
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => 010011
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => 010001
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => 100111
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => 100101
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => 100011
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => 100011
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => 100001
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => 000111
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => 000101
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => 000011
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => 000011
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => 000001
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => 111011
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => 111001
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => 101011
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => 101001
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => 011011
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => 011001
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => 011011
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => 011001
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => 001011
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => 001001
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => 011011
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => 011001
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => 001011
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => 001001
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => 101011
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => 101001
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => 001011
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => 001001
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => 110011
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => 110001
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => 010011
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => 010001
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => 010011
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => 010001
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => 100011
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => 100001
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => 000011
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => 000001
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => 111101
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => 110101
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => 101101
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => 101101
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => 100101
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => 011101
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => 010101
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => 011101
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => 001101
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => 011101
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => 001101
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => 001101
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => 010101
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => 000101
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => 011101
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => 010101
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => 001101
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => 001101
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => 000101
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => 101101
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => 100101
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => 001101
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => 000101
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => 110101
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => 010101
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => 010101
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => 100101
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => 000101
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => 111001
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => 101001
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => 011001
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => 011001
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => 001001
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => 011001
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => 001001
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => 101001
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => 001001
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => 110001
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => 010001
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => 010001
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => 100001
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => 000001
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 111110
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 111010
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => 110110
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 110110
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 110010
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => 101110
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => 101010
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => 101110
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => 100110
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 101110
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 100110
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => 100110
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => 101010
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => 100010
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => 011110
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => 011010
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => 010110
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => 010110
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => 010010
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => 011110
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => 011010
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => 001110
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => 001010
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => 011110
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => 001110
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => 001110
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => 010110
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => 000110
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 011110
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => 010110
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => 001110
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => 001110
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => 000110
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => 001110
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => 000110
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => 010110
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => 000110
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => 011010
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => 001010
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => 001010
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => 010010
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 000010
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => 011110
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => 011010
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => 010110
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => 010110
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => 010010
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => 001110
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => 001010
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => 001110
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => 000110
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => 001110
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => 000110
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => 000110
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => 001010
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => 000010
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => 101110
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => 101010
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => 100110
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => 100110
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => 100010
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => 001110
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => 001010
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => 000110
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => 000110
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => 000010
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => 110110
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => 110010
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => 010110
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => 010010
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => 010110
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => 010010
[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => 100110
[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => 100010
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => 000110
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => 000010
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => 111010
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => 101010
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => 011010
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => 011010
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => 001010
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => 011010
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => 001010
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => 101010
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => 001010
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => 110010
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => 010010
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => 010010
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => 100010
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => 000010
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 111100
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => 110100
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => 101100
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => 101100
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => 100100
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => 011100
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => 010100
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => 011100
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => 001100
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => 011100
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => 001100
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => 001100
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => 010100
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 000100
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => 011100
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => 010100
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => 001100
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => 001100
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => 000100
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => 101100
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => 100100
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => 001100
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => 000100
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => 110100
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => 010100
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => 010100
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => 100100
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => 000100
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 111000
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => 101000
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => 011000
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => 011000
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 001000
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => 011000
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => 001000
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => 101000
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => 001000
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 110000
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 010000
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => 010000
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 100000
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => 1111101
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [8,6,7,5,4,3,2,1] => 1111011
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 1111011
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => 1111001
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [8,7,5,6,4,3,2,1] => 1110111
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => 1110101
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [8,6,5,7,4,3,2,1] => 1110111
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [8,5,6,7,4,3,2,1] => 1110011
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => 1110111
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => 1110011
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => 1110011
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => 1110101
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => 1110001
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => 1101111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => 1101101
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => 1101011
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [7,6,8,4,5,3,2,1] => 1101011
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [6,7,8,4,5,3,2,1] => 1101001
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [8,7,5,4,6,3,2,1] => 1101111
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [8,7,4,5,6,3,2,1] => 1100111
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [8,6,5,4,7,3,2,1] => 1101111
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [8,5,6,4,7,3,2,1] => 1100111
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [8,6,4,5,7,3,2,1] => 1100111
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [8,5,4,6,7,3,2,1] => 1101011
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [8,4,5,6,7,3,2,1] => 1100011
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 1101111
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => 1101011
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [7,5,6,4,8,3,2,1] => 1100111
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 1100111
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => 1100011
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => 1100111
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [6,7,4,5,8,3,2,1] => 1100011
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => 1101011
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => 1100011
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => 1101101
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => 1100101
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [6,4,5,7,8,3,2,1] => 1100101
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => 1101001
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => 1100001
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => 1011111
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => 1011101
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => 1011011
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [7,6,8,5,3,4,2,1] => 1011011
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => 1010111
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [7,8,5,6,3,4,2,1] => 1010101
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [8,5,6,7,3,4,2,1] => 1010011
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [7,6,5,8,3,4,2,1] => 1010111
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [6,7,5,8,3,4,2,1] => 1010011
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [6,5,7,8,3,4,2,1] => 1010101
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => 1010001
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [8,7,6,4,3,5,2,1] => 1011111
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [7,8,6,4,3,5,2,1] => 1011101
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [8,6,7,4,3,5,2,1] => 1011011
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [7,6,8,4,3,5,2,1] => 1011011
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [6,7,8,4,3,5,2,1] => 1011001
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1] => 1001111
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [7,8,6,3,4,5,2,1] => 1001101
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [8,6,7,3,4,5,2,1] => 1001011
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [7,6,8,3,4,5,2,1] => 1001011
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => 1001001
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => 1011111
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [7,8,5,4,3,6,2,1] => 1011101
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [8,7,4,5,3,6,2,1] => 1001111
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [8,7,5,3,4,6,2,1] => 1001111
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [7,8,5,3,4,6,2,1] => 1001101
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [8,7,4,3,5,6,2,1] => 1010111
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [8,7,3,4,5,6,2,1] => 1000111
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [7,8,3,4,5,6,2,1] => 1000101
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [8,6,5,4,3,7,2,1] => 1011111
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [8,6,4,5,3,7,2,1] => 1001111
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [8,6,4,3,5,7,2,1] => 1010111
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [8,5,4,3,6,7,2,1] => 1011011
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [8,5,3,4,6,7,2,1] => 1001011
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [8,4,3,5,6,7,2,1] => 1010011
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [8,3,4,5,6,7,2,1] => 1000011
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => 1011111
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => 1011011
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [7,5,6,4,3,8,2,1] => 1010111
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [6,5,7,4,3,8,2,1] => 1010111
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => 1010011
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [6,7,4,5,3,8,2,1] => 1001011
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [7,5,4,6,3,8,2,1] => 1001111
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [7,4,5,6,3,8,2,1] => 1000111
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => 1001111
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [6,4,5,7,3,8,2,1] => 1000111
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => 1001011
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => 1000011
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => 1001111
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => 1010111
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => 1000111
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [7,5,4,3,6,8,2,1] => 1011011
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [7,5,3,4,6,8,2,1] => 1001011
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [7,3,4,5,6,8,2,1] => 1000011
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => 1011101
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => 1000101
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [6,5,3,4,7,8,2,1] => 1001101
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [6,3,4,5,7,8,2,1] => 1000101
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => 1011001
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [5,3,4,6,7,8,2,1] => 1001001
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => 1010001
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => 1000001
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => 0111111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => 0111101
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => 0111011
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,2,3,1] => 0111011
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => 0110111
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,2,3,1] => 0110111
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,2,3,1] => 0110011
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,2,3,1] => 0110111
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,2,3,1] => 0110011
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,2,3,1] => 0110011
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => 0110001
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => 0101111
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => 0101011
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [7,6,8,4,5,2,3,1] => 0101011
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,2,3,1] => 0101001
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,2,3,1] => 0101111
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,2,3,1] => 0100111
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => 0100101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [8,6,5,4,7,2,3,1] => 0101111
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,2,3,1] => 0100111
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,2,3,1] => 0100111
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [8,4,5,6,7,2,3,1] => 0100011
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,2,3,1] => 0101111
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,2,3,1] => 0100111
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,2,3,1] => 0100111
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,2,3,1] => 0100011
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => 0100001
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,2,4,1] => 0111111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,2,4,1] => 0111101
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [8,6,7,5,3,2,4,1] => 0111011
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,2,4,1] => 0111011
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,2,4,1] => 0111001
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,2,4,1] => 0110111
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => 0110111
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,2,4,1] => 0110011
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,2,4,1] => 0110111
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,2,4,1] => 0110011
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => 0110001
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => 0011111
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,2,3,4,1] => 0011011
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,2,3,4,1] => 0011011
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => 0011001
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,2,3,4,1] => 0010111
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [7,8,5,6,2,3,4,1] => 0010101
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [8,6,5,7,2,3,4,1] => 0010111
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => 0010011
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,2,3,4,1] => 0010111
[.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [6,7,5,8,2,3,4,1] => 0010011
[.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [6,5,7,8,2,3,4,1] => 0010101
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => 0010001
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [8,7,6,4,3,2,5,1] => 0111111
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [7,8,6,4,3,2,5,1] => 0111101
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [8,6,7,4,3,2,5,1] => 0111011
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [7,6,8,4,3,2,5,1] => 0111011
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [6,7,8,4,3,2,5,1] => 0111001
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [8,7,6,3,4,2,5,1] => 0011111
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [7,8,6,3,4,2,5,1] => 0011101
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [8,6,7,3,4,2,5,1] => 0011011
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [7,6,8,3,4,2,5,1] => 0011011
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [6,7,8,3,4,2,5,1] => 0011001
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,2,3,5,1] => 0011111
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [8,6,7,4,2,3,5,1] => 0011011
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [7,6,8,4,2,3,5,1] => 0011011
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [6,7,8,4,2,3,5,1] => 0011001
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [8,7,6,3,2,4,5,1] => 0101111
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [7,8,6,3,2,4,5,1] => 0101101
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [8,6,7,3,2,4,5,1] => 0101011
[.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [6,7,8,3,2,4,5,1] => 0101001
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => 0001111
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [7,8,6,2,3,4,5,1] => 0001101
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [8,6,7,2,3,4,5,1] => 0001011
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [7,6,8,2,3,4,5,1] => 0001011
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [6,7,8,2,3,4,5,1] => 0001001
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [8,7,5,4,3,2,6,1] => 0111111
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [7,8,5,4,3,2,6,1] => 0111101
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [8,7,5,3,4,2,6,1] => 0011111
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [7,8,5,3,4,2,6,1] => 0011101
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [8,7,4,3,5,2,6,1] => 0011111
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [7,8,4,3,5,2,6,1] => 0011101
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,2,3,6,1] => 0011111
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [8,7,5,3,2,4,6,1] => 0101111
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [8,7,4,3,2,5,6,1] => 0110111
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [7,8,4,3,2,5,6,1] => 0110101
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [7,8,3,4,2,5,6,1] => 0010101
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [7,8,4,2,3,5,6,1] => 0010101
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => 0100101
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [8,7,2,3,4,5,6,1] => 0000111
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [7,8,2,3,4,5,6,1] => 0000101
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [8,6,5,4,3,2,7,1] => 0111111
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [8,5,6,4,3,2,7,1] => 0110111
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [8,6,4,5,3,2,7,1] => 0101111
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [8,5,4,6,3,2,7,1] => 0101111
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [8,6,5,3,4,2,7,1] => 0011111
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [8,5,6,3,4,2,7,1] => 0010111
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [8,6,4,3,5,2,7,1] => 0011111
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [8,6,3,4,5,2,7,1] => 0001111
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [8,5,4,3,6,2,7,1] => 0011111
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [8,4,5,3,6,2,7,1] => 0001111
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [8,4,3,5,6,2,7,1] => 0010111
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [8,3,4,5,6,2,7,1] => 0000111
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,2,3,7,1] => 0011111
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [8,5,6,4,2,3,7,1] => 0010111
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [8,6,4,5,2,3,7,1] => 0001111
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [8,6,5,3,2,4,7,1] => 0101111
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [8,6,4,3,2,5,7,1] => 0110111
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [8,6,4,2,3,5,7,1] => 0010111
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [8,5,4,3,2,6,7,1] => 0111011
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [8,4,5,3,2,6,7,1] => 0101011
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [8,5,3,4,2,6,7,1] => 0011011
[.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [8,3,4,5,2,6,7,1] => 0001011
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [8,5,4,2,3,6,7,1] => 0011011
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [8,4,5,2,3,6,7,1] => 0001011
[.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [8,5,2,3,4,6,7,1] => 0001011
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [8,4,3,2,5,6,7,1] => 0110011
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [8,3,4,2,5,6,7,1] => 0010011
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [8,4,2,3,5,6,7,1] => 0010011
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [8,3,2,4,5,6,7,1] => 0100011
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [8,2,3,4,5,6,7,1] => 0000011
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 0111111
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => 0111011
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [7,5,6,4,3,2,8,1] => 0110111
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 0110111
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => 0110011
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [7,6,4,5,3,2,8,1] => 0101111
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [6,7,4,5,3,2,8,1] => 0101011
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [7,4,5,6,3,2,8,1] => 0100111
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1] => 0101111
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [6,4,5,7,3,2,8,1] => 0100111
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => 0100011
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [7,6,5,3,4,2,8,1] => 0011111
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [7,5,6,3,4,2,8,1] => 0010111
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [6,5,7,3,4,2,8,1] => 0010111
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [5,6,7,3,4,2,8,1] => 0010011
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [7,6,4,3,5,2,8,1] => 0011111
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [7,6,3,4,5,2,8,1] => 0001111
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [7,5,4,3,6,2,8,1] => 0011111
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [7,4,5,3,6,2,8,1] => 0001111
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [7,5,3,4,6,2,8,1] => 0001111
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [7,3,4,5,6,2,8,1] => 0000111
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 0011111
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [6,4,5,3,7,2,8,1] => 0001111
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 0001111
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => 0000111
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [6,5,3,4,7,2,8,1] => 0001111
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [5,6,3,4,7,2,8,1] => 0000111
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [6,4,3,5,7,2,8,1] => 0010111
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [6,3,4,5,7,2,8,1] => 0000111
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => 0011011
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => 0001011
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [4,3,5,6,7,2,8,1] => 0010011
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => 0000011
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => 0011111
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [6,7,5,4,2,3,8,1] => 0011011
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [7,5,6,4,2,3,8,1] => 0010111
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,2,3,8,1] => 0010111
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [5,6,7,4,2,3,8,1] => 0010011
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,2,3,8,1] => 0001111
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => 0001011
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,2,3,8,1] => 0001111
[.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [7,4,5,6,2,3,8,1] => 0000111
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [6,5,4,7,2,3,8,1] => 0001111
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [5,6,4,7,2,3,8,1] => 0000111
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [6,4,5,7,2,3,8,1] => 0000111
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [5,4,6,7,2,3,8,1] => 0001011
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => 0000011
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => 0101111
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [6,7,5,3,2,4,8,1] => 0101011
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [6,5,7,3,2,4,8,1] => 0100111
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => 0001111
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [7,5,6,2,3,4,8,1] => 0000111
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [5,6,7,2,3,4,8,1] => 0000011
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [6,7,4,3,2,5,8,1] => 0110011
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [7,6,4,2,3,5,8,1] => 0010111
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [7,6,3,2,4,5,8,1] => 0100111
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [6,7,3,2,4,5,8,1] => 0100011
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [7,6,2,3,4,5,8,1] => 0000111
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => 0000011
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [7,5,4,3,2,6,8,1] => 0111011
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [7,4,3,5,2,6,8,1] => 0011011
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [7,5,4,2,3,6,8,1] => 0011011
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [7,4,5,2,3,6,8,1] => 0001011
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [7,5,3,2,4,6,8,1] => 0101011
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [7,5,2,3,4,6,8,1] => 0001011
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [7,4,3,2,5,6,8,1] => 0110011
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [7,4,2,3,5,6,8,1] => 0010011
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [7,3,2,4,5,6,8,1] => 0100011
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [7,2,3,4,5,6,8,1] => 0000011
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => 0111101
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => 0101101
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => 0100101
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [6,5,3,4,2,7,8,1] => 0011101
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [6,3,4,5,2,7,8,1] => 0001101
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => 0011101
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => 0010101
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => 0000101
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [6,5,4,2,3,7,8,1] => 0011101
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [5,6,4,2,3,7,8,1] => 0010101
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [6,4,5,2,3,7,8,1] => 0001101
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [5,4,6,2,3,7,8,1] => 0001101
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [4,5,6,2,3,7,8,1] => 0000101
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [6,5,3,2,4,7,8,1] => 0101101
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [6,5,2,3,4,7,8,1] => 0001101
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [6,2,3,4,5,7,8,1] => 0000101
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => 0111001
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [4,5,3,2,6,7,8,1] => 0101001
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [5,3,4,2,6,7,8,1] => 0011001
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => 0011001
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 0001001
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [5,4,2,3,6,7,8,1] => 0011001
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [4,5,2,3,6,7,8,1] => 0001001
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [5,3,2,4,6,7,8,1] => 0101001
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => 0001001
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 0110001
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 0010001
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => 0010001
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 0100001
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 0000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => 0111111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => 0111101
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => 0111011
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,3,1,2] => 0111011
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => 0111001
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => 0110111
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,3,1,2] => 0110101
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,3,1,2] => 0110111
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,3,1,2] => 0110111
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,3,1,2] => 0110011
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => 0110011
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => 0110101
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => 0110001
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => 0101111
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => 0101101
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => 0101011
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => 0101001
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,3,1,2] => 0101111
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => 0100101
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,3,1,2] => 0100111
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => 0100111
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [8,5,4,6,7,3,1,2] => 0101011
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,3,1,2] => 0101111
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,3,1,2] => 0100111
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,3,1,2] => 0100111
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => 0100111
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,3,1,2] => 0100011
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,3,1,2] => 0101101
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [5,6,4,7,8,3,1,2] => 0100101
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [5,4,6,7,8,3,1,2] => 0101001
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => 0100001
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => 0011111
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => 0011101
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,4,1,2] => 0011011
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => 0011001
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => 0010111
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => 0010101
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,4,1,2] => 0010111
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,4,1,2] => 0010011
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => 0010111
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => 0010011
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => 0010011
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => 0010101
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => 0010001
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [6,7,8,4,3,5,1,2] => 0011001
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => 0001111
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => 0001101
[[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => 0001011
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [6,7,8,3,4,5,1,2] => 0001001
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => 0011101
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [8,7,4,5,3,6,1,2] => 0001111
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => 0001101
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => 0001101
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [8,7,4,3,5,6,1,2] => 0010111
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => 0010101
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [8,7,3,4,5,6,1,2] => 0000111
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => 0000101
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,3,7,1,2] => 0011111
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [8,5,4,6,3,7,1,2] => 0001111
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [8,5,4,3,6,7,1,2] => 0011011
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [8,5,3,4,6,7,1,2] => 0001011
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => 0010011
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => 0000011
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => 0011111
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [7,5,6,4,3,8,1,2] => 0010111
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2] => 0010111
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [5,6,7,4,3,8,1,2] => 0010011
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => 0001011
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,3,8,1,2] => 0001111
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [6,5,4,7,3,8,1,2] => 0001111
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => 0000111
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [5,4,6,7,3,8,1,2] => 0001011
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => 0000011
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [7,6,5,3,4,8,1,2] => 0001111
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => 0000111
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [5,6,7,3,4,8,1,2] => 0000011
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [7,6,4,3,5,8,1,2] => 0010111
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => 0000111
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [7,5,4,3,6,8,1,2] => 0011011
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [7,4,5,3,6,8,1,2] => 0001011
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [7,5,3,4,6,8,1,2] => 0001011
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [7,3,4,5,6,8,1,2] => 0000011
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [6,5,4,3,7,8,1,2] => 0011101
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [5,6,4,3,7,8,1,2] => 0010101
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => 0001101
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [4,5,6,3,7,8,1,2] => 0000101
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [6,5,3,4,7,8,1,2] => 0001101
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => 0000101
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => 0010101
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => 0000101
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => 0011001
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => 0001001
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [5,3,4,6,7,8,1,2] => 0001001
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => 0010001
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => 0000001
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => 1011111
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,2,1,3] => 1011101
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [8,6,7,5,4,2,1,3] => 1011011
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => 1011011
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,2,1,3] => 1011001
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [8,7,5,6,4,2,1,3] => 1010111
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,2,1,3] => 1010101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,2,1,3] => 1010111
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,2,1,3] => 1010111
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,2,1,3] => 1010011
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,2,1,3] => 1010011
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,2,1,3] => 1010101
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => 1010001
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,2,1,3] => 1001111
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,2,1,3] => 1001011
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [7,6,8,4,5,2,1,3] => 1001011
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,2,1,3] => 1000111
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,2,1,3] => 1001111
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,2,1,3] => 1000111
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,2,1,3] => 1000011
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,2,1,3] => 1001111
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,2,1,3] => 1001011
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [7,5,6,4,8,2,1,3] => 1000111
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,2,1,3] => 1000111
[[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,2,1,3] => 1000011
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,2,1,3] => 1000111
[[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,2,1,3] => 1000011
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,2,1,3] => 1001001
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => 1000001
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => 0011111
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => 0011101
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,1,2,3] => 0011011
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => 0011001
[[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,1,2,3] => 0010101
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,1,2,3] => 0010111
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => 0010011
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,1,2,3] => 0010111
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,1,2,3] => 0010011
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,1,2,3] => 0010011
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => 0010101
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => 0010001
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => 0001111
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => 0001011
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [6,7,8,4,5,1,2,3] => 0001001
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [8,7,5,4,6,1,2,3] => 0001111
[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [7,8,5,4,6,1,2,3] => 0001101
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => 0000111
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => 0000101
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,1,2,3] => 0001111
[[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [8,5,6,4,7,1,2,3] => 0000111
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => 0000111
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [8,5,4,6,7,1,2,3] => 0001011
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => 0000011
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,1,2,3] => 0001111
[[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,1,2,3] => 0001011
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [7,5,6,4,8,1,2,3] => 0000111
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,1,2,3] => 0000111
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,1,2,3] => 0000011
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,1,2,3] => 0000111
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => 0000011
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,1,2,3] => 0001011
[[[.,.],.],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,1,2,3] => 0000011
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => 0001101
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [5,6,4,7,8,1,2,3] => 0000101
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [6,4,5,7,8,1,2,3] => 0000101
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,1,2,3] => 0001001
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => 0000001
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => 1101111
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,2,1,4] => 1101101
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,2,1,4] => 1101011
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,2,1,4] => 1101011
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,2,1,4] => 1101001
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,2,1,4] => 1100111
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => 1100101
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,2,1,4] => 1100111
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,2,1,4] => 1100011
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => 1100111
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,2,1,4] => 1100011
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,2,1,4] => 1100011
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,2,1,4] => 1100101
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => 1100001
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,3,1,4] => 0101111
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,3,1,4] => 0101101
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,3,1,4] => 0101011
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,3,1,4] => 0101011
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [6,7,8,5,2,3,1,4] => 0101001
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,3,1,4] => 0100111
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [7,8,5,6,2,3,1,4] => 0100101
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,3,1,4] => 0100111
[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [8,5,6,7,2,3,1,4] => 0100011
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,3,1,4] => 0100111
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [6,7,5,8,2,3,1,4] => 0100011
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => 0100011
[[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [6,5,7,8,2,3,1,4] => 0100101
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [5,6,7,8,2,3,1,4] => 0100001
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => 0101111
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,1,2,4] => 0101101
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,1,2,4] => 0101011
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,1,2,4] => 0101011
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,1,2,4] => 0100111
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => 0100101
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,1,2,4] => 0100111
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,1,2,4] => 0100111
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => 0100011
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => 0100011
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,1,2,4] => 0100101
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => 0100001
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => 1001111
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => 1001101
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,1,3,4] => 1001011
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => 1001001
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,1,3,4] => 1000111
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => 1000101
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,1,3,4] => 1000111
[[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [8,5,6,7,2,1,3,4] => 1000011
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,1,3,4] => 1000111
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [6,7,5,8,2,1,3,4] => 1000011
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [7,5,6,8,2,1,3,4] => 1000011
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => 1000101
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => 1000001
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => 0001111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => 0001101
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => 0001011
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => 0001011
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => 0001001
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => 0000111
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => 0000101
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => 0000111
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => 0000011
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => 0000111
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => 0000011
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => 0000011
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => 0000101
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => 0000001
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => 1110111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [7,8,6,4,3,2,1,5] => 1110101
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [8,6,7,4,3,2,1,5] => 1110011
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [7,6,8,4,3,2,1,5] => 1110011
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [6,7,8,4,3,2,1,5] => 1110001
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => 1010111
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [7,8,6,3,4,2,1,5] => 1010101
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [6,7,8,3,4,2,1,5] => 1010001
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,2,3,1,5] => 0110111
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [8,6,7,4,2,3,1,5] => 0110011
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [7,6,8,4,2,3,1,5] => 0110011
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [6,7,8,4,2,3,1,5] => 0110001
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => 0110111
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [8,6,7,3,2,4,1,5] => 0110011
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [6,7,8,3,2,4,1,5] => 0110001
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [8,7,6,2,3,4,1,5] => 0010111
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [8,6,7,2,3,4,1,5] => 0010011
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [7,6,8,2,3,4,1,5] => 0010011
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [6,7,8,2,3,4,1,5] => 0010001
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => 0110111
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => 0110001
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => 0010111
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [7,8,6,3,4,1,2,5] => 0010101
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [8,6,7,3,4,1,2,5] => 0010011
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => 0010001
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => 1010111
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,2,1,3,5] => 1010101
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,2,1,3,5] => 1010011
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => 1010001
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => 0010111
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => 0010101
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [7,6,8,4,1,2,3,5] => 0010011
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => 0010001
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => 1100111
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [7,8,6,3,2,1,4,5] => 1100101
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [8,6,7,3,2,1,4,5] => 1100011
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [7,6,8,3,2,1,4,5] => 1100011
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [6,7,8,3,2,1,4,5] => 1100001
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [8,7,6,2,3,1,4,5] => 0100111
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [7,8,6,2,3,1,4,5] => 0100101
[[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [8,6,7,2,3,1,4,5] => 0100011
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [7,6,8,2,3,1,4,5] => 0100011
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [6,7,8,2,3,1,4,5] => 0100001
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [8,7,6,3,1,2,4,5] => 0100111
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [7,8,6,3,1,2,4,5] => 0100101
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [8,6,7,3,1,2,4,5] => 0100011
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [7,6,8,3,1,2,4,5] => 0100011
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [6,7,8,3,1,2,4,5] => 0100001
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => 1000111
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [7,8,6,2,1,3,4,5] => 1000101
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [8,6,7,2,1,3,4,5] => 1000011
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => 1000001
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => 0000111
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => 0000101
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => 0000011
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => 0000011
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => 0000001
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [8,7,5,4,3,2,1,6] => 1111011
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => 1111001
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [8,7,4,5,3,2,1,6] => 1101011
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [7,8,4,5,3,2,1,6] => 1101001
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [8,7,5,3,4,2,1,6] => 1011011
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [8,7,4,3,5,2,1,6] => 1011011
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [8,7,3,4,5,2,1,6] => 1001011
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [7,8,3,4,5,2,1,6] => 1001001
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [8,7,4,5,2,3,1,6] => 0101011
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [7,8,4,5,2,3,1,6] => 0101001
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [8,7,5,3,2,4,1,6] => 0111011
[[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [7,8,5,2,3,4,1,6] => 0011001
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [8,7,4,3,2,5,1,6] => 0111011
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [7,8,4,3,2,5,1,6] => 0111001
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [8,7,3,4,2,5,1,6] => 0011011
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [7,8,3,4,2,5,1,6] => 0011001
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [8,7,2,3,4,5,1,6] => 0001011
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [7,8,2,3,4,5,1,6] => 0001001
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => 0111011
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [7,8,5,4,3,1,2,6] => 0111001
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [8,7,5,3,4,1,2,6] => 0011011
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [7,8,5,3,4,1,2,6] => 0011001
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [8,7,3,4,5,1,2,6] => 0001011
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [7,8,3,4,5,1,2,6] => 0001001
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => 1011001
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => 0011011
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => 0011001
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => 0001011
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => 0001001
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [8,7,5,3,2,1,4,6] => 1101011
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [7,8,5,3,2,1,4,6] => 1101001
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]] => [8,7,5,2,3,1,4,6] => 0101011
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [8,7,5,3,1,2,4,6] => 0101011
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [7,8,5,3,1,2,4,6] => 0101001
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => 1001011
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => 1001001
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => 0001011
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => 0001001
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [8,7,4,3,2,1,5,6] => 1110011
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => 1110001
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [8,7,3,4,2,1,5,6] => 1010011
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [7,8,3,4,2,1,5,6] => 1010001
[[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [7,8,4,2,3,1,5,6] => 0110001
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [8,7,3,2,4,1,5,6] => 0110011
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [7,8,3,2,4,1,5,6] => 0110001
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [8,7,2,3,4,1,5,6] => 0010011
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [7,8,2,3,4,1,5,6] => 0010001
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [7,8,4,3,1,2,5,6] => 0110001
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [8,7,3,4,1,2,5,6] => 0010011
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => 0010001
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [8,7,4,2,1,3,5,6] => 1010011
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => 1010001
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => 0010011
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [7,8,4,1,2,3,5,6] => 0010001
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => 1100011
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => 1100001
[[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [8,7,2,3,1,4,5,6] => 0100011
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [7,8,2,3,1,4,5,6] => 0100001
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [7,8,3,1,2,4,5,6] => 0100001
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [8,7,2,1,3,4,5,6] => 1000011
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => 1000001
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => 0000011
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => 0000001
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => 1111101
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [8,5,6,4,3,2,1,7] => 1110101
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [8,6,4,5,3,2,1,7] => 1101101
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [8,5,4,6,3,2,1,7] => 1101101
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => 1100101
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [8,6,5,3,4,2,1,7] => 1011101
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [8,5,6,3,4,2,1,7] => 1010101
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [8,6,4,3,5,2,1,7] => 1011101
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [8,4,5,3,6,2,1,7] => 1001101
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [8,4,3,5,6,2,1,7] => 1010101
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [8,3,4,5,6,2,1,7] => 1000101
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,2,3,1,7] => 0111101
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [8,5,6,4,2,3,1,7] => 0110101
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,2,3,1,7] => 0101101
[[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [8,4,5,6,2,3,1,7] => 0100101
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [8,6,5,3,2,4,1,7] => 0111101
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [8,6,5,2,3,4,1,7] => 0011101
[[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [8,5,6,2,3,4,1,7] => 0010101
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [8,6,4,3,2,5,1,7] => 0111101
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [8,6,4,2,3,5,1,7] => 0011101
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [8,6,3,2,4,5,1,7] => 0101101
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [8,5,4,3,2,6,1,7] => 0111101
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [8,4,3,5,2,6,1,7] => 0011101
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [8,5,4,2,3,6,1,7] => 0011101
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [8,4,5,2,3,6,1,7] => 0001101
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [8,5,3,2,4,6,1,7] => 0101101
[[.,[[[[.,.],.],[.,.]],.]],[.,.]] => [8,5,2,3,4,6,1,7] => 0001101
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [8,3,4,2,5,6,1,7] => 0010101
[[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [8,3,2,4,5,6,1,7] => 0100101
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [8,2,3,4,5,6,1,7] => 0000101
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => 0111101
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,3,1,2,7] => 0101101
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [8,6,5,3,4,1,2,7] => 0011101
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => 0010101
[[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [8,6,3,4,5,1,2,7] => 0001101
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [8,5,4,3,6,1,2,7] => 0011101
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [8,4,5,3,6,1,2,7] => 0001101
[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [8,5,3,4,6,1,2,7] => 0001101
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [8,4,3,5,6,1,2,7] => 0010101
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => 0000101
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => 1011101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,2,1,3,7] => 1010101
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,2,1,3,7] => 1001101
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [8,4,5,6,2,1,3,7] => 1000101
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => 0011101
[[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,1,2,3,7] => 0010101
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => 0001101
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [8,4,5,6,1,2,3,7] => 0000101
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [8,6,5,3,2,1,4,7] => 1101101
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [8,5,6,3,2,1,4,7] => 1100101
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => 0101101
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [8,5,6,2,3,1,4,7] => 0100101
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [8,5,6,3,1,2,4,7] => 0100101
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [8,6,5,2,1,3,4,7] => 1001101
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => 1000101
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => 0001101
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => 0000101
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => 1110101
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [8,6,3,4,2,1,5,7] => 1010101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [8,6,4,2,3,1,5,7] => 0110101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [8,6,3,2,4,1,5,7] => 0110101
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [8,6,2,3,4,1,5,7] => 0010101
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [8,6,4,3,1,2,5,7] => 0110101
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [8,6,3,4,1,2,5,7] => 0010101
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => 1010101
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [8,6,3,2,1,4,5,7] => 1100101
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => 0000101
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [8,5,4,3,2,1,6,7] => 1111001
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [8,4,5,3,2,1,6,7] => 1101001
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [8,4,3,5,2,1,6,7] => 1011001
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [8,3,4,5,2,1,6,7] => 1001001
[[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [8,4,5,2,3,1,6,7] => 0101001
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [8,5,2,3,4,1,6,7] => 0011001
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [8,4,2,3,5,1,6,7] => 0011001
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [8,2,3,4,5,1,6,7] => 0001001
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [8,5,3,4,1,2,6,7] => 0011001
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [8,3,4,5,1,2,6,7] => 0001001
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [8,5,4,2,1,3,6,7] => 1011001
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [8,5,4,1,2,3,6,7] => 0011001
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [8,4,5,1,2,3,6,7] => 0001001
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [8,5,3,2,1,4,6,7] => 1101001
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [8,5,3,1,2,4,6,7] => 0101001
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [8,5,2,1,3,4,6,7] => 1001001
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => 0001001
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => 1110001
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [8,3,4,2,1,5,6,7] => 1010001
[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [8,4,2,3,1,5,6,7] => 0110001
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => 0010001
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [8,3,4,1,2,5,6,7] => 0010001
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [8,4,2,1,3,5,6,7] => 1010001
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => 0010001
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => 1100001
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => 0100001
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => 0100001
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => 1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => 0000001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 1111110
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 1111010
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [7,5,6,4,3,2,1,8] => 1110110
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 1110110
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 1110010
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => 1101110
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [6,7,4,5,3,2,1,8] => 1101010
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [7,5,4,6,3,2,1,8] => 1101110
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => 1100110
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 1101110
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => 1100110
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => 1101010
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => 1100010
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [7,6,5,3,4,2,1,8] => 1011110
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [6,7,5,3,4,2,1,8] => 1011010
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => 1010110
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.] => [6,5,7,3,4,2,1,8] => 1010110
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [5,6,7,3,4,2,1,8] => 1010010
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => 1011110
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [6,7,4,3,5,2,1,8] => 1011010
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => 1001110
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => 1011110
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [7,4,5,3,6,2,1,8] => 1001110
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [7,3,4,5,6,2,1,8] => 1000110
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => 1011110
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => 1010110
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => 1001110
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => 1011010
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => 1000010
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,2,3,1,8] => 0111110
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => 0111010
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,2,3,1,8] => 0110110
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [5,6,7,4,2,3,1,8] => 0110010
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => 0101110
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [6,7,4,5,2,3,1,8] => 0101010
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [7,5,4,6,2,3,1,8] => 0101110
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [7,4,5,6,2,3,1,8] => 0100110
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [6,5,4,7,2,3,1,8] => 0101110
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [5,6,4,7,2,3,1,8] => 0100110
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [5,4,6,7,2,3,1,8] => 0101010
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [4,5,6,7,2,3,1,8] => 0100010
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [7,6,5,3,2,4,1,8] => 0111110
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => 0110110
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => 0110010
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => 0011110
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [6,7,5,2,3,4,1,8] => 0011010
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [7,5,6,2,3,4,1,8] => 0010110
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => 0010110
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => 0010010
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [7,6,4,3,2,5,1,8] => 0111110
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [6,7,4,3,2,5,1,8] => 0111010
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [6,7,3,4,2,5,1,8] => 0011010
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [7,6,4,2,3,5,1,8] => 0011110
[[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [6,7,4,2,3,5,1,8] => 0011010
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [7,6,3,2,4,5,1,8] => 0101110
[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [6,7,3,2,4,5,1,8] => 0101010
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [7,6,2,3,4,5,1,8] => 0001110
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [6,7,2,3,4,5,1,8] => 0001010
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [7,5,4,3,2,6,1,8] => 0111110
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [7,4,5,3,2,6,1,8] => 0101110
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [7,5,3,4,2,6,1,8] => 0011110
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [7,4,3,5,2,6,1,8] => 0011110
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [7,5,4,2,3,6,1,8] => 0011110
[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [7,4,5,2,3,6,1,8] => 0001110
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [7,5,3,2,4,6,1,8] => 0101110
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [7,2,3,4,5,6,1,8] => 0000110
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => 0111110
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => 0110110
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => 0101110
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [5,6,3,4,2,7,1,8] => 0010110
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [6,3,4,5,2,7,1,8] => 0001110
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => 0011110
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => 0001110
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [5,3,4,6,2,7,1,8] => 0001110
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => 0010110
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => 0000110
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [5,4,6,2,3,7,1,8] => 0001110
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [6,5,3,2,4,7,1,8] => 0101110
[[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [6,3,2,4,5,7,1,8] => 0100110
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [6,2,3,4,5,7,1,8] => 0000110
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => 0111010
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => 0001010
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [5,4,2,3,6,7,1,8] => 0011010
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [4,5,2,3,6,7,1,8] => 0001010
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [5,2,3,4,6,7,1,8] => 0001010
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => 0110010
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => 0010010
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [4,2,3,5,6,7,1,8] => 0010010
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => 0100010
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 0000010
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => 0111110
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,3,1,2,8] => 0111010
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => 0110110
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,3,1,2,8] => 0101110
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [7,4,5,6,3,1,2,8] => 0100110
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [5,4,6,7,3,1,2,8] => 0101010
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [4,5,6,7,3,1,2,8] => 0100010
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [7,6,5,3,4,1,2,8] => 0011110
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [7,5,6,3,4,1,2,8] => 0010110
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [6,5,7,3,4,1,2,8] => 0010110
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [6,7,3,4,5,1,2,8] => 0001010
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [7,5,3,4,6,1,2,8] => 0001110
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [6,5,4,3,7,1,2,8] => 0011110
[[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [6,4,5,3,7,1,2,8] => 0001110
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [5,6,3,4,7,1,2,8] => 0000110
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [6,4,3,5,7,1,2,8] => 0010110
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [6,3,4,5,7,1,2,8] => 0000110
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [4,3,5,6,7,1,2,8] => 0010010
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [3,4,5,6,7,1,2,8] => 0000010
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => 1011110
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => 1010110
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,2,1,3,8] => 1001110
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => 1001110
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [7,4,5,6,2,1,3,8] => 1000110
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [5,4,6,7,2,1,3,8] => 1001010
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [4,5,6,7,2,1,3,8] => 1000010
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => 0011110
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,1,2,3,8] => 0010110
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => 0010010
[[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,1,2,3,8] => 0001110
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,1,2,3,8] => 0001110
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => 0000110
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => 0000110
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => 0001010
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => 0000010
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [7,6,5,3,2,1,4,8] => 1101110
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [7,6,5,2,3,1,4,8] => 0101110
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [6,7,5,2,3,1,4,8] => 0101010
[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [7,5,6,2,3,1,4,8] => 0100110
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [6,5,7,2,3,1,4,8] => 0100110
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [5,6,7,2,3,1,4,8] => 0100010
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [7,5,6,3,1,2,4,8] => 0100110
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => 0100010
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [7,6,5,2,1,3,4,8] => 1001110
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [6,7,5,2,1,3,4,8] => 1001010
[[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [7,5,6,2,1,3,4,8] => 1000110
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => 1000010
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => 0001110
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => 0001010
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => 0000110
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => 0000110
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => 0000010
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => 1110110
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [6,7,4,3,2,1,5,8] => 1110010
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [7,6,3,4,2,1,5,8] => 1010110
[[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [6,7,3,4,2,1,5,8] => 1010010
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [7,6,4,2,3,1,5,8] => 0110110
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [7,6,3,2,4,1,5,8] => 0110110
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [6,7,3,2,4,1,5,8] => 0110010
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [7,6,2,3,4,1,5,8] => 0010110
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [6,7,2,3,4,1,5,8] => 0010010
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => 0110110
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [6,7,3,4,1,2,5,8] => 0010010
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [7,6,4,2,1,3,5,8] => 1010110
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [7,6,3,2,1,4,5,8] => 1100110
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [6,7,3,2,1,4,5,8] => 1100010
[[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [7,6,2,3,1,4,5,8] => 0100110
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [6,7,2,3,1,4,5,8] => 0100010
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [6,7,3,1,2,4,5,8] => 0100010
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => 0000110
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => 0000010
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [7,5,4,3,2,1,6,8] => 1111010
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [7,4,5,3,2,1,6,8] => 1101010
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [7,4,3,5,2,1,6,8] => 1011010
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [7,3,4,5,2,1,6,8] => 1001010
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [7,5,4,2,3,1,6,8] => 0111010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [7,5,3,2,4,1,6,8] => 0111010
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [7,5,2,3,4,1,6,8] => 0011010
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [7,4,2,3,5,1,6,8] => 0011010
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [7,2,3,4,5,1,6,8] => 0001010
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [7,5,4,3,1,2,6,8] => 0111010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [7,5,3,4,1,2,6,8] => 0011010
[[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [7,4,5,2,1,3,6,8] => 1001010
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [7,4,5,1,2,3,6,8] => 0001010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [7,5,3,2,1,4,6,8] => 1101010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [7,5,2,3,1,4,6,8] => 0101010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8] => 0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => 0001010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8] => 1110010
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [7,2,3,4,1,5,6,8] => 0010010
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [7,4,3,1,2,5,6,8] => 0110010
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [7,3,4,1,2,5,6,8] => 0010010
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [7,4,1,2,3,5,6,8] => 0010010
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [7,3,2,1,4,5,6,8] => 1100010
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [7,2,3,1,4,5,6,8] => 0100010
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => 0100010
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => 1000010
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => 0000010
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 1111100
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => 1110100
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => 1101100
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => 1100100
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [6,5,3,4,2,1,7,8] => 1011100
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [5,6,3,4,2,1,7,8] => 1010100
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => 1011100
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => 1000100
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [5,4,6,2,3,1,7,8] => 0101100
[[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [5,6,3,2,4,1,7,8] => 0110100
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [6,5,2,3,4,1,7,8] => 0011100
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [5,6,2,3,4,1,7,8] => 0010100
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [6,4,3,2,5,1,7,8] => 0111100
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [6,2,3,4,5,1,7,8] => 0001100
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => 0111100
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => 0101100
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => 0011100
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => 0001100
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [5,3,2,4,6,1,7,8] => 0101100
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [5,2,3,4,6,1,7,8] => 0001100
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => 0110100
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => 0010100
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [4,2,3,5,6,1,7,8] => 0010100
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => 0100100
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 0000100
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [6,5,4,3,1,2,7,8] => 0111100
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => 0110100
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [6,4,5,3,1,2,7,8] => 0101100
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => 0101100
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => 0010100
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [6,4,3,5,1,2,7,8] => 0011100
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => 0011100
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [4,3,5,6,1,2,7,8] => 0010100
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [3,4,5,6,1,2,7,8] => 0000100
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [6,5,4,2,1,3,7,8] => 1011100
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => 1010100
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [6,4,5,2,1,3,7,8] => 1001100
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [5,4,6,2,1,3,7,8] => 1001100
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [4,5,6,2,1,3,7,8] => 1000100
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8] => 0011100
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => 0000100
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [6,5,3,2,1,4,7,8] => 1101100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => 1100100
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [5,6,2,1,3,4,7,8] => 1000100
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8] => 1110100
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [6,3,4,2,1,5,7,8] => 1010100
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [6,4,3,1,2,5,7,8] => 0110100
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [6,4,2,1,3,5,7,8] => 1010100
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => 0010100
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [6,3,2,1,4,5,7,8] => 1100100
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [6,2,3,1,4,5,7,8] => 0100100
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [6,3,1,2,4,5,7,8] => 0100100
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [6,2,1,3,4,5,7,8] => 1000100
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => 0000100
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 1111000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => 1101000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [5,3,4,2,1,6,7,8] => 1011000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => 1011000
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => 1001000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [5,4,2,3,1,6,7,8] => 0111000
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [4,5,2,3,1,6,7,8] => 0101000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [5,3,2,4,1,6,7,8] => 0111000
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [5,2,3,4,1,6,7,8] => 0011000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => 0111000
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => 0011000
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [4,2,3,5,1,6,7,8] => 0011000
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => 0101000
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 0001000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [5,4,3,1,2,6,7,8] => 0111000
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [5,3,4,1,2,6,7,8] => 0011000
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [4,3,5,1,2,6,7,8] => 0011000
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [3,4,5,1,2,6,7,8] => 0001000
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [5,4,2,1,3,6,7,8] => 1011000
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [4,5,2,1,3,6,7,8] => 1001000
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [5,4,1,2,3,6,7,8] => 0011000
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [4,5,1,2,3,6,7,8] => 0001000
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [5,3,2,1,4,6,7,8] => 1101000
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [5,2,3,1,4,6,7,8] => 0101000
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => 0101000
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [5,2,1,3,4,6,7,8] => 1001000
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => 0001000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 1110000
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => 1010000
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [4,2,3,1,5,6,7,8] => 0110000
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => 0110000
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => 0010000
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [4,3,1,2,5,6,7,8] => 0110000
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => 0010000
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [4,2,1,3,5,6,7,8] => 1010000
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => 0010000
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 1100000
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => 0100000
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => 0100000
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 1000000
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => 11111101
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => 11111001
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => 11110001
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => 11100001
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => 11000001
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => 10000001
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => 111111101
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [9,7,8,6,5,4,3,2,1] => 11111011
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => 111111001
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [8,9,6,7,5,4,3,2,1] => 11110101
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => 111110001
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [7,8,9,5,6,4,3,2,1] => 11101001
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => 111100001
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [6,7,8,9,4,5,3,2,1] => 11010001
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => 111000001
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [5,6,7,8,9,3,4,2,1] => 10100001
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => 110000001
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,2,3,1] => 01000001
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => 100000001
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => 00000001
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 000000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => 11111011
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => 11110111
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => 11101111
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => 11011111
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => 10111111
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => 01111111
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 11111110
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => 111111011
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [8,6,7,9,5,4,3,2,1] => 11110011
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => 111110111
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [8,7,5,6,9,4,3,2,1] => 11100111
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => 111101111
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [8,7,6,4,5,9,3,2,1] => 11001111
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => 111011111
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [8,7,6,5,3,4,9,2,1] => 10011111
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => 110111111
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,2,3,9,1] => 00111111
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => 101111111
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9] => 01111110
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => 011111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 111111110
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => 001010101
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => [9,10,6,7,4,5,2,3,1,8] => 010101001
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => 000011110
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => 00101010101
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [10,8,6,4,2,1,3,5,7,9] => 101010101
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [12,10,8,6,4,2,1,3,5,7,9,11] => 10101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => 00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => 000000001
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => 10000001
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 01000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => 0000000001
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => 100000001
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => 01000001
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [9,2,3,1,4,5,6,7,8] => 01000001
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => 00100001
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 00100001
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 010000001
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000001
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => 00000001
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => 00000001
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => 00000001
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [5,6,7,8,9,1,2,3,4] => 00000001
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,1,2,3] => 00000001
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => 00000011
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => 000000001
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [8,7,9,1,2,3,4,5,6] => 00000011
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => 000000001
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [7,6,8,9,1,2,3,4,5] => 00000101
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => 000000001
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [6,5,7,8,9,1,2,3,4] => 00001001
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => 000000001
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [5,4,6,7,8,9,1,2,3] => 00010001
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [5,6,7,8,9,10,1,2,3,4] => 000000001
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [4,3,5,6,7,8,9,1,2] => 00100001
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [4,5,6,7,8,9,10,1,2,3] => 000000001
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => 000000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => 01111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 11111010
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2] => 01111101
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => 011111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 111111010
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 11110110
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => [8,6,7,5,4,3,2,1,9] => 11110110
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,3,1,2] => 01111011
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => 01111011
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [9,10,8,7,6,5,4,3,1,2] => 011111101
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2] => 0111111111
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => 000011111
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [7,6,8,5,9,4,10,3,11,2,12,1] => 00000111111
[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [9,8,10,6,7,4,5,2,3,1] => 010101011
[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.] => [6,4,5,7,3,8,2,9,1,10] => 000011110
[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]] => [8,9,6,7,4,5,2,3,10,1] => 000101011
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,2,1,3] => 10111111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,2,1,4] => 11011111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,3,2,1,5] => 11101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [9,8,7,5,4,3,2,1,6] => 11110111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [9,8,6,5,4,3,2,1,7] => 11111011
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [9,7,6,5,4,3,2,1,8] => 11111101
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => 00111111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,2,1,3] => 101111111
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,2,3,1,4] => 01011111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,3,2,1,4] => 110111111
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,3,4,2,1,5] => 10101111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,4,3,2,1,5] => 111011111
[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => [9,8,7,4,5,3,2,1,6] => 11010111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [10,9,8,7,5,4,3,2,1,6] => 111101111
[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => [9,8,5,6,4,3,2,1,7] => 11101011
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [10,9,8,6,5,4,3,2,1,7] => 111110111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [9,6,7,5,4,3,2,1,8] => 11110101
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [10,9,7,6,5,4,3,2,1,8] => 111111011
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [10,8,7,6,5,4,3,2,1,9] => 111111101
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 11111100
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 11111000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 11110000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 11100000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 11000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 10000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 111111100
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 111111000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 111110000
[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => [6,5,4,3,1,2,7,8,9] => 01111000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 111100000
[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] => [5,4,3,1,2,6,7,8,9] => 01110000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 111000000
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [4,3,1,2,5,6,7,8,9] => 01100000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 110000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9] => 01000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 100000000
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [9,8,7,5,6,4,3,2,1] => 11101111
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,4,5,3,2,1] => 11011111
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,3,4,2,1] => 10111111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => 01111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [10,8,9,7,6,5,4,3,2,1] => 111111011
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [10,9,8,6,7,5,4,3,2,1] => 111101111
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,5,6,4,3,2,1] => 111011111
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,2,3,1] => 011111111
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [10,8,9,6,7,4,5,2,3,1] => 010101011
[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [10,8,9,6,7,4,5,2,1,3] => 100101011
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [9,2,3,4,5,6,7,8,1] => 00000011
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [8,2,1,3,4,5,6,7,9] => 10000010
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [8,9,2,1,3,4,5,6,7] => 10000001
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => [8,2,3,4,5,6,7,9,1] => 00000011
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [8,9,2,3,4,5,6,7,1] => 00000101
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [10,2,3,4,5,6,7,8,9,1] => 000000011
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [8,6,5,4,3,2,1,7,9] => 11111010
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => 00000011
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 00000010
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => 01000000
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.] => [2,3,4,5,1,6,7,8,9] => 00010000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 00000100
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [4,2,3,1,5,6,7,8,9] => 01100000
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [5,2,3,4,1,6,7,8,9] => 00110000
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [6,2,3,4,5,1,7,8,9] => 00011000
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [7,2,3,4,5,6,1,8,9] => 00001100
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [8,2,3,4,5,6,7,1,9] => 00000110
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 000000010
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9] => 00100000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [5,1,2,3,4,6,7,8,9] => 00010000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [6,1,2,3,4,5,7,8,9] => 00001000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => 00000100
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => 00000010
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9,10] => 010000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9,10] => 001000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [5,1,2,3,4,6,7,8,9,10] => 000100000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [6,1,2,3,4,5,7,8,9,10] => 000010000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [7,1,2,3,4,5,6,8,9,10] => 000001000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [8,1,2,3,4,5,6,7,9,10] => 000000100
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => 000000010
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [9,3,4,5,6,7,8,1,2] => 00000011
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [9,7,6,5,4,3,2,8,1] => 01111111
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => 01111001
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [9,7,6,5,4,3,1,2,8] => 01111101
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [8,9,6,5,4,3,2,1,7] => 11111001
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => 001111111
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,1,2,4] => 01011111
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,2,1,3,9] => 10111110
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [9,8,7,6,5,4,3,1,2,10] => 011111110
[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,2,3,1] => 01111011
[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]] => [7,8,2,3,4,5,6,9,1] => 00000011
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [3,4,5,1,2,6,7,8,9] => 00010000
[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]] => [9,2,3,4,5,1,6,7,8] => 00010001
[.,[.,[[[[.,[[[.,.],.],.]],.],.],.]]] => [4,5,6,3,7,8,9,2,1] => 10001001
[.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]] => [3,4,5,6,2,7,8,9,10,1] => 000010001
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [4,5,2,1,3,6,7,8,9] => 10010000
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [5,3,1,2,4,6,7,8,9] => 01010000
[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]] => [6,2,3,4,5,7,8,9,10,1] => 000010001
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [10,8,7,6,5,4,3,2,9,1] => 011111111
[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,3,1,2] => 01000001
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,2,1,3] => 10000001
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [3,4,5,6,7,8,1,2,9] => 00000010
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] => [8,9,7,6,5,4,2,1,3] => 10111101
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => 000000011
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => 11110010
[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => [6,5,4,3,2,7,8,1,9] => 01111010
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => 111110010
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]] => [10,9,8,7,6,5,4,3,2,11,1] => 0111111111
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => 00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => 00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => 00011111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [9,7,1,2,3,4,5,6,8] => 00000101
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => 000000111
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [9,8,6,1,2,3,4,5,7] => 00001011
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => 000001111
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [9,8,7,5,1,2,3,4,6] => 00010111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => 000011111
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,1,2,3,5] => 00101111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => 000111111
[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.] => [3,2,4,1,5,6,7,8,9] => 01100000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => 1111111011
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [9,8,10,7,6,5,4,3,1,2] => 011111011
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,2,3,1] => 01111101
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => 1111111101
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => 01111011
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]] => [8,9,7,6,5,4,3,2,10,1] => 011111011
[.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]] => [7,6,8,5,4,3,2,9,1] => 01110111
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => 10100000
[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]] => [5,4,6,7,8,9,3,2,1] => 11010001
[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]] => [6,5,7,8,9,4,3,2,1] => 11101001
[.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]] => [6,5,7,8,9,10,4,3,2,1] => 111010001
[.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]] => [5,4,6,7,8,3,9,2,1] => 10010011
[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]] => [5,4,6,7,8,9,10,3,2,1] => 110100001
[.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]] => [6,5,7,8,9,10,11,4,3,2,1] => 1110100001
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => 01111110
[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.] => [6,5,4,3,2,7,1,8,9] => 01111100
[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.] => [5,4,3,2,6,1,7,8,9] => 01111000
[[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.] => [4,3,2,5,1,6,7,8,9] => 01110000
[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]] => [8,9,7,6,4,3,2,1,5] => 11101101
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => 11010000
[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,4,3,2,1,5] => 111000001
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => 01000010
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [8,7,5,4,3,2,1,6,9] => 11110110
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [9,7,6,5,4,3,2,1,8,10] => 111111010
[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [9,6,7,8,5,4,3,2,1] => 11110011
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,3,9,1,2] => 00111111
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,2,3,1,9] => 01111110
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [9,2,3,4,5,6,7,1,8] => 00000101
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => 00100000
[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,9,2,10,1] => 000000011
[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [4,5,6,7,8,3,9,1,2] => 00000011
[[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]] => [9,3,4,5,6,7,2,1,8] => 10000101
[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => [4,5,6,7,8,9,10,2,3,1] => 010000001
[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.] => [3,4,5,6,2,1,7,8,9] => 10001000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [10,11,1,2,3,4,5,6,7,8,9] => 0000000001
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,1,2,3,9] => 00111110
[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => [9,8,2,3,4,5,6,7,1] => 00000111
[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]] => [10,9,2,3,4,5,6,7,8,1] => 000000111
[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.] => [3,4,5,6,7,8,2,1,9] => 10000010
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => [10,3,1,2,4,5,6,7,8,9] => 010000001
[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]] => [9,2,3,4,5,6,1,7,8] => 00001001
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [10,8,7,6,5,4,3,1,2,9] => 011111101
[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.] => [3,4,5,6,7,2,1,8,9] => 10000100
[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]] => [5,6,7,4,8,9,1,2,3] => 00000101
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => 11110100
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [9,10,7,6,5,4,3,2,1,8] => 111111001
[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]] => [9,8,2,3,4,5,6,1,7] => 00001011
[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.] => [3,4,5,2,1,6,7,8,9] => 10010000
[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]] => [9,3,4,5,6,7,8,2,1] => 10000011
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]] => [7,6,8,9,5,4,3,2,1] => 11110101
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => [11,9,10,8,7,6,5,4,3,2,1] => 1111111011
[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]] => [7,6,8,5,9,4,3,2,1] => 11100111
[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]] => [8,7,9,10,6,5,4,3,2,1] => 111110101
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 tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
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