Identifier
Mp00016:
Binary trees
—left-right symmetry⟶
Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
[.,.] => [.,.] => [1] =>
[.,[.,.]] => [[.,.],.] => [1,2] => 0
[[.,.],.] => [.,[.,.]] => [2,1] => 1
[.,[.,[.,.]]] => [[[.,.],.],.] => [1,2,3] => 00
[.,[[.,.],.]] => [[.,[.,.]],.] => [2,1,3] => 10
[[.,.],[.,.]] => [[.,.],[.,.]] => [3,1,2] => 01
[[.,[.,.]],.] => [.,[[.,.],.]] => [2,3,1] => 01
[[[.,.],.],.] => [.,[.,[.,.]]] => [3,2,1] => 11
[.,[.,[.,[.,.]]]] => [[[[.,.],.],.],.] => [1,2,3,4] => 000
[.,[.,[[.,.],.]]] => [[[.,[.,.]],.],.] => [2,1,3,4] => 100
[.,[[.,.],[.,.]]] => [[[.,.],[.,.]],.] => [3,1,2,4] => 010
[.,[[.,[.,.]],.]] => [[.,[[.,.],.]],.] => [2,3,1,4] => 010
[.,[[[.,.],.],.]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 110
[[.,.],[.,[.,.]]] => [[[.,.],.],[.,.]] => [4,1,2,3] => 001
[[.,.],[[.,.],.]] => [[.,[.,.]],[.,.]] => [4,2,1,3] => 101
[[.,[.,.]],[.,.]] => [[.,.],[[.,.],.]] => [3,4,1,2] => 001
[[[.,.],.],[.,.]] => [[.,.],[.,[.,.]]] => [4,3,1,2] => 011
[[.,[.,[.,.]]],.] => [.,[[[.,.],.],.]] => [2,3,4,1] => 001
[[.,[[.,.],.]],.] => [.,[[.,[.,.]],.]] => [3,2,4,1] => 011
[[[.,.],[.,.]],.] => [.,[[.,.],[.,.]]] => [4,2,3,1] => 011
[[[.,[.,.]],.],.] => [.,[.,[[.,.],.]]] => [3,4,2,1] => 101
[[[[.,.],.],.],.] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 111
[.,[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0000
[.,[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1000
[.,[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => 0100
[.,[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 0100
[.,[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 1100
[.,[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 0010
[.,[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 1010
[.,[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 0010
[.,[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => 0110
[.,[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 0010
[.,[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 0110
[.,[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => 0110
[.,[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 1010
[.,[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1110
[[.,.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 0001
[[.,.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 1001
[[.,.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 0101
[[.,.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 0101
[[.,.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 1101
[[.,[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 0001
[[.,[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 1001
[[[.,.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 0011
[[[.,.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 1011
[[.,[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 0001
[[.,[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 0011
[[[.,.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0011
[[[.,[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 0101
[[[[.,.],.],.],[.,.]] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 0111
[[.,[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 0001
[[.,[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 0101
[[.,[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => 0011
[[.,[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 0011
[[.,[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 0111
[[[.,.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => 0011
[[[.,.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => 0111
[[[.,[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => 0101
[[[[.,.],.],[.,.]],.] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => 0111
[[[.,[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 1001
[[[.,[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1011
[[[[.,.],[.,.]],.],.] => [.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => 1011
[[[[.,[.,.]],.],.],.] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 1101
[[[[[.,.],.],.],.],.] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 1111
[.,[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 00000
[.,[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 10000
[.,[.,[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => 01000
[.,[.,[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 01000
[.,[.,[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 11000
[.,[.,[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 00100
[.,[.,[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 10100
[.,[.,[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 00100
[.,[.,[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => 01100
[.,[.,[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 00100
[.,[.,[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 01100
[.,[.,[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => 01100
[.,[.,[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 10100
[.,[.,[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 11100
[.,[[.,.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 00010
[.,[[.,.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 10010
[.,[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 01010
[.,[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 01010
[.,[[.,.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 11010
[.,[[.,[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 00010
[.,[[.,[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 10010
[.,[[[.,.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 00110
[.,[[[.,.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 10110
[.,[[.,[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 00010
[.,[[.,[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 00110
[.,[[[.,.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 00110
[.,[[[.,[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 01010
[.,[[[[.,.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 01110
[.,[[.,[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 00010
[.,[[.,[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 01010
[.,[[.,[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => 00110
[.,[[.,[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 00110
[.,[[.,[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 01110
[.,[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => 00110
[.,[[[.,.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => 01110
[.,[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => 01010
[.,[[[[.,.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => 01110
>>> Load all 1924 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 10010
[.,[[[.,[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 10110
[.,[[[[.,.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => 10110
[.,[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 11010
[.,[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 11110
[[.,.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 00001
[[.,.],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 10001
[[.,.],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 01001
[[.,.],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 01001
[[.,.],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 11001
[[.,.],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 00101
[[.,.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 10101
[[.,.],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 00101
[[.,.],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 01101
[[.,.],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 00101
[[.,.],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 01101
[[.,.],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 01101
[[.,.],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 10101
[[.,.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 11101
[[.,[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 00001
[[.,[.,.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 10001
[[.,[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 01001
[[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 01001
[[.,[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 11001
[[[.,.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 00011
[[[.,.],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 10011
[[[.,.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 01011
[[[.,.],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 01011
[[[.,.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 11011
[[.,[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 00001
[[.,[.,[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 10001
[[.,[[.,.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 00011
[[.,[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 10011
[[[.,.],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 00011
[[[.,.],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 10011
[[[.,[.,.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 00101
[[[.,[.,.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 10101
[[[[.,.],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 00111
[[[[.,.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 10111
[[.,[.,[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 00001
[[.,[.,[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 00101
[[.,[[.,.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 00011
[[.,[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 00011
[[.,[[[.,.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 00111
[[[.,.],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 00011
[[[.,.],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 00111
[[[.,[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 00101
[[[[.,.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 00111
[[[.,[.,[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 01001
[[[.,[[.,.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 01011
[[[[.,.],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 01011
[[[[.,[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 01101
[[[[[.,.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 01111
[[.,[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 00001
[[.,[.,[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 01001
[[.,[.,[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => 00101
[[.,[.,[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 00101
[[.,[.,[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 01101
[[.,[[.,.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => 00011
[[.,[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => 01011
[[.,[[.,[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => 00011
[[.,[[[.,.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => 00111
[[.,[[.,[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 00011
[[.,[[.,[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 00111
[[.,[[[.,.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => 00111
[[.,[[[.,[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 01011
[[.,[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 01111
[[[.,.],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 00011
[[[.,.],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 01011
[[[.,.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 00111
[[[.,.],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 00111
[[[.,.],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 01111
[[[.,[.,.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 00101
[[[.,[.,.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 01101
[[[[.,.],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 00111
[[[[.,.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 01111
[[[.,[.,[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 01001
[[[.,[[.,.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => 01011
[[[[.,.],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 01011
[[[[.,[.,.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => 01101
[[[[[.,.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => 01111
[[[.,[.,[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 10001
[[[.,[.,[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 10101
[[[.,[[.,.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => 10011
[[[.,[[.,[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 10011
[[[.,[[[.,.],.],.]],.],.] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 10111
[[[[.,.],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => 10011
[[[[.,.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => 10111
[[[[.,[.,.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => 10101
[[[[[.,.],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => 10111
[[[[.,[.,[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 11001
[[[[.,[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 11011
[[[[[.,.],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => 11011
[[[[[.,[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 11101
[[[[[[.,.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 000000
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 100000
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => 010000
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 010000
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 110000
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => 001000
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => 101000
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => 001000
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => 011000
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 001000
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => 011000
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => 011000
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => 101000
[.,[.,[.,[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 111000
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => 000100
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => 100100
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => 010100
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => 010100
[.,[.,[[.,.],[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => 110100
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => 000100
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => 100100
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => 001100
[.,[.,[[[.,.],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => 101100
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => 000100
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => 001100
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => 001100
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => 010100
[.,[.,[[[[.,.],.],.],[.,.]]]] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => 011100
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 000100
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => 010100
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => 001100
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => 001100
[.,[.,[[.,[[[.,.],.],.]],.]]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => 011100
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => 001100
[.,[.,[[[.,.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => 011100
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => 010100
[.,[.,[[[[.,.],.],[.,.]],.]]] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => 011100
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => 100100
[.,[.,[[[.,[[.,.],.]],.],.]]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => 101100
[.,[.,[[[[.,.],[.,.]],.],.]]] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => 101100
[.,[.,[[[[.,[.,.]],.],.],.]]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => 110100
[.,[.,[[[[[.,.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 111100
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => 000010
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => 100010
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => 010010
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => 010010
[.,[[.,.],[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => 110010
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => 001010
[.,[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => 101010
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => 001010
[.,[[.,.],[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => 011010
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => 001010
[.,[[.,.],[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => 011010
[.,[[.,.],[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => 011010
[.,[[.,.],[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => 101010
[.,[[.,.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => 111010
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => 000010
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => 100010
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => 010010
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => 010010
[.,[[.,[.,.]],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => 110010
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => 000110
[.,[[[.,.],.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => 100110
[.,[[[.,.],.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => 010110
[.,[[[.,.],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => 010110
[.,[[[.,.],.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => 110110
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => 000010
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => 100010
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => 000110
[.,[[.,[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => 100110
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => 000110
[.,[[[.,.],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => 100110
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => 001010
[.,[[[.,[.,.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => 101010
[.,[[[[.,.],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => 001110
[.,[[[[.,.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => 101110
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => 000010
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => 001010
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => 000110
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => 000110
[.,[[.,[[[.,.],.],.]],[.,.]]] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => 001110
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => 000110
[.,[[[.,.],[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => 001110
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => 001010
[.,[[[[.,.],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => 001110
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => 010010
[.,[[[.,[[.,.],.]],.],[.,.]]] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => 010110
[.,[[[[.,.],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => 010110
[.,[[[[.,[.,.]],.],.],[.,.]]] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => 011010
[.,[[[[[.,.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => 011110
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 000010
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => 010010
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => 001010
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => 001010
[.,[[.,[.,[[[.,.],.],.]]],.]] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => 011010
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => 000110
[.,[[.,[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => 010110
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => 000110
[.,[[.,[[[.,.],.],[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => 001110
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => 000110
[.,[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => 001110
[.,[[.,[[[.,.],[.,.]],.]],.]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => 001110
[.,[[.,[[[.,[.,.]],.],.]],.]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => 010110
[.,[[.,[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 011110
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => 000110
[.,[[[.,.],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => 010110
[.,[[[.,.],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => 001110
[.,[[[.,.],[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => 001110
[.,[[[.,.],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => 011110
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => 001010
[.,[[[.,[.,.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => 011010
[.,[[[[.,.],.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => 001110
[.,[[[[.,.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => 011110
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => 010010
[.,[[[.,[[.,.],.]],[.,.]],.]] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => 010110
[.,[[[[.,.],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => 010110
[.,[[[[.,[.,.]],.],[.,.]],.]] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => 011010
[.,[[[[[.,.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => 011110
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => 100010
[.,[[[.,[.,[[.,.],.]]],.],.]] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => 101010
[.,[[[.,[[.,.],[.,.]]],.],.]] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => 100110
[.,[[[.,[[.,[.,.]],.]],.],.]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 100110
[.,[[[.,[[[.,.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 101110
[.,[[[[.,.],[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => 100110
[.,[[[[.,.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => 101110
[.,[[[[.,[.,.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => 101010
[.,[[[[[.,.],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => 101110
[.,[[[[.,[.,[.,.]]],.],.],.]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 110010
[.,[[[[.,[[.,.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 110110
[.,[[[[[.,.],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => 110110
[.,[[[[[.,[.,.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 111010
[.,[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 111110
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => 000001
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => 100001
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => 010001
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => 010001
[[.,.],[.,[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => 110001
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => 001001
[[.,.],[.,[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => 101001
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => 001001
[[.,.],[.,[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => 011001
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => 001001
[[.,.],[.,[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => 011001
[[.,.],[.,[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => 011001
[[.,.],[.,[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => 101001
[[.,.],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => 111001
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => 000101
[[.,.],[[.,.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => 100101
[[.,.],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => 010101
[[.,.],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => 010101
[[.,.],[[.,.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => 110101
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => 000101
[[.,.],[[.,[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => 100101
[[.,.],[[[.,.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => 001101
[[.,.],[[[.,.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => 101101
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => 000101
[[.,.],[[.,[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => 001101
[[.,.],[[[.,.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => 001101
[[.,.],[[[.,[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => 010101
[[.,.],[[[[.,.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => 011101
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => 000101
[[.,.],[[.,[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => 010101
[[.,.],[[.,[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => 001101
[[.,.],[[.,[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => 001101
[[.,.],[[.,[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => 011101
[[.,.],[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => 001101
[[.,.],[[[.,.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => 011101
[[.,.],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => 010101
[[.,.],[[[[.,.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => 011101
[[.,.],[[[.,[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => 100101
[[.,.],[[[.,[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => 101101
[[.,.],[[[[.,.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => 101101
[[.,.],[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => 110101
[[.,.],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => 111101
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => 000001
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => 100001
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => 010001
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => 010001
[[.,[.,.]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => 110001
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => 001001
[[.,[.,.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => 101001
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => 001001
[[.,[.,.]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => 011001
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => 001001
[[.,[.,.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => 011001
[[.,[.,.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => 011001
[[.,[.,.]],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => 101001
[[.,[.,.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => 111001
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => 000011
[[[.,.],.],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => 100011
[[[.,.],.],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => 010011
[[[.,.],.],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => 010011
[[[.,.],.],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => 110011
[[[.,.],.],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => 001011
[[[.,.],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => 101011
[[[.,.],.],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => 001011
[[[.,.],.],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => 011011
[[[.,.],.],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => 001011
[[[.,.],.],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => 011011
[[[.,.],.],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => 011011
[[[.,.],.],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => 101011
[[[.,.],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => 111011
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => 000001
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => 100001
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => 010001
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => 010001
[[.,[.,[.,.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => 110001
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => 000011
[[.,[[.,.],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => 100011
[[.,[[.,.],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => 010011
[[.,[[.,.],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => 010011
[[.,[[.,.],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => 110011
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => 000011
[[[.,.],[.,.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => 100011
[[[.,.],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => 010011
[[[.,.],[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => 010011
[[[.,.],[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => 110011
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => 000101
[[[.,[.,.]],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => 100101
[[[.,[.,.]],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => 010101
[[[.,[.,.]],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => 010101
[[[.,[.,.]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => 110101
[[[[.,.],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => 000111
[[[[.,.],.],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => 100111
[[[[.,.],.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => 010111
[[[[.,.],.],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => 010111
[[[[.,.],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => 110111
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => 000001
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => 100001
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => 000101
[[.,[.,[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => 100101
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => 000011
[[.,[[.,.],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => 100011
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => 000011
[[.,[[.,[.,.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => 100011
[[.,[[[.,.],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => 000111
[[.,[[[.,.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => 100111
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => 000011
[[[.,.],[.,[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => 100011
[[[.,.],[[.,.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => 000111
[[[.,.],[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => 100111
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => 000101
[[[.,[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => 100101
[[[[.,.],.],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => 000111
[[[[.,.],.],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => 100111
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => 001001
[[[.,[.,[.,.]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => 101001
[[[.,[[.,.],.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => 001011
[[[.,[[.,.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => 101011
[[[[.,.],[.,.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => 001011
[[[[.,.],[.,.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => 101011
[[[[.,[.,.]],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => 001101
[[[[.,[.,.]],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => 101101
[[[[[.,.],.],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => 001111
[[[[[.,.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => 101111
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => 000001
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => 001001
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => 000101
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => 000101
[[.,[.,[[[.,.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => 001101
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => 000011
[[.,[[.,.],[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => 001011
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => 000011
[[.,[[[.,.],.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => 000111
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => 000011
[[.,[[.,[[.,.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => 000111
[[.,[[[.,.],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => 000111
[[.,[[[.,[.,.]],.],.]],[.,.]] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => 001011
[[.,[[[[.,.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => 001111
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => 000011
[[[.,.],[.,[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => 001011
[[[.,.],[[.,.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => 000111
[[[.,.],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => 000111
[[[.,.],[[[.,.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => 001111
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => 000101
[[[.,[.,.]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => 001101
[[[[.,.],.],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => 000111
[[[[.,.],.],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => 001111
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => 001001
[[[.,[[.,.],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => 001011
[[[[.,.],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => 001011
[[[[.,[.,.]],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => 001101
[[[[[.,.],.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => 001111
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => 010001
[[[.,[.,[[.,.],.]]],.],[.,.]] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => 010101
[[[.,[[.,.],[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => 010011
[[[.,[[.,[.,.]],.]],.],[.,.]] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => 010011
[[[.,[[[.,.],.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => 010111
[[[[.,.],[.,[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => 010011
[[[[.,.],[[.,.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => 010111
[[[[.,[.,.]],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => 010101
[[[[[.,.],.],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => 010111
[[[[.,[.,[.,.]]],.],.],[.,.]] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => 011001
[[[[.,[[.,.],.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => 011011
[[[[[.,.],[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => 011011
[[[[[.,[.,.]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => 011101
[[[[[[.,.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => 011111
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 000001
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 010001
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => 001001
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 001001
[[.,[.,[.,[[[.,.],.],.]]]],.] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 011001
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => 000101
[[.,[.,[[.,.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => 010101
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => 000101
[[.,[.,[[[.,.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => 001101
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 000101
[[.,[.,[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 001101
[[.,[.,[[[.,.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => 001101
[[.,[.,[[[.,[.,.]],.],.]]],.] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => 010101
[[.,[.,[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => 011101
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => 000011
[[.,[[.,.],[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => 010011
[[.,[[.,.],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => 001011
[[.,[[.,.],[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => 001011
[[.,[[.,.],[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => 011011
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => 000011
[[.,[[.,[.,.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => 010011
[[.,[[[.,.],.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => 000111
[[.,[[[.,.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => 010111
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => 000011
[[.,[[.,[[.,.],.]],[.,.]]],.] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => 000111
[[.,[[[.,.],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => 000111
[[.,[[[.,[.,.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => 001011
[[.,[[[[.,.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => 001111
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 000011
[[.,[[.,[.,[[.,.],.]]],.]],.] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => 001011
[[.,[[.,[[.,.],[.,.]]],.]],.] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => 000111
[[.,[[.,[[.,[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => 000111
[[.,[[.,[[[.,.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => 001111
[[.,[[[.,.],[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => 000111
[[.,[[[.,.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => 001111
[[.,[[[.,[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => 001011
[[.,[[[[.,.],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => 001111
[[.,[[[.,[.,[.,.]]],.],.]],.] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => 010011
[[.,[[[.,[[.,.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => 010111
[[.,[[[[.,.],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => 010111
[[.,[[[[.,[.,.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => 011011
[[.,[[[[[.,.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => 011111
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => 000011
[[[.,.],[.,[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => 010011
[[[.,.],[.,[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => 001011
[[[.,.],[.,[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => 001011
[[[.,.],[.,[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => 011011
[[[.,.],[[.,.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => 000111
[[[.,.],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => 010111
[[[.,.],[[.,[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => 000111
[[[.,.],[[[.,.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => 001111
[[[.,.],[[.,[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => 000111
[[[.,.],[[.,[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => 001111
[[[.,.],[[[.,.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => 001111
[[[.,.],[[[.,[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => 010111
[[[.,.],[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => 011111
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => 000101
[[[.,[.,.]],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => 010101
[[[.,[.,.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => 001101
[[[.,[.,.]],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => 001101
[[[.,[.,.]],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => 011101
[[[[.,.],.],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => 000111
[[[[.,.],.],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => 010111
[[[[.,.],.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => 001111
[[[[.,.],.],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => 001111
[[[[.,.],.],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => 011111
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => 001001
[[[.,[.,[.,.]]],[[.,.],.]],.] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => 011001
[[[.,[[.,.],.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => 001011
[[[.,[[.,.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => 011011
[[[[.,.],[.,.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => 001011
[[[[.,.],[.,.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => 011011
[[[[.,[.,.]],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => 001101
[[[[.,[.,.]],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => 011101
[[[[[.,.],.],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => 001111
[[[[[.,.],.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => 011111
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => 010001
[[[.,[.,[[.,.],.]]],[.,.]],.] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => 010101
[[[.,[[.,.],[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => 010011
[[[.,[[.,[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => 010011
[[[.,[[[.,.],.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => 010111
[[[[.,.],[.,[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => 010011
[[[[.,.],[[.,.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => 010111
[[[[.,[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => 010101
[[[[[.,.],.],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => 010111
[[[[.,[.,[.,.]]],.],[.,.]],.] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => 011001
[[[[.,[[.,.],.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => 011011
[[[[[.,.],[.,.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => 011011
[[[[[.,[.,.]],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => 011101
[[[[[[.,.],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => 011111
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => 100001
[[[.,[.,[.,[[.,.],.]]]],.],.] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => 101001
[[[.,[.,[[.,.],[.,.]]]],.],.] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => 100101
[[[.,[.,[[.,[.,.]],.]]],.],.] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => 100101
[[[.,[.,[[[.,.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => 101101
[[[.,[[.,.],[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => 100011
[[[.,[[.,.],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => 101011
[[[.,[[.,[.,.]],[.,.]]],.],.] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => 100011
[[[.,[[[.,.],.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => 100111
[[[.,[[.,[.,[.,.]]],.]],.],.] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => 100011
[[[.,[[.,[[.,.],.]],.]],.],.] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => 100111
[[[.,[[[.,.],[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => 100111
[[[.,[[[.,[.,.]],.],.]],.],.] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => 101011
[[[.,[[[[.,.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => 101111
[[[[.,.],[.,[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => 100011
[[[[.,.],[.,[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => 101011
[[[[.,.],[[.,.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => 100111
[[[[.,.],[[.,[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => 100111
[[[[.,.],[[[.,.],.],.]],.],.] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => 101111
[[[[.,[.,.]],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => 100101
[[[[.,[.,.]],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => 101101
[[[[[.,.],.],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => 100111
[[[[[.,.],.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => 101111
[[[[.,[.,[.,.]]],[.,.]],.],.] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => 101001
[[[[.,[[.,.],.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => 101011
[[[[[.,.],[.,.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => 101011
[[[[[.,[.,.]],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => 101101
[[[[[[.,.],.],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => 101111
[[[[.,[.,[.,[.,.]]]],.],.],.] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => 110001
[[[[.,[.,[[.,.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => 110101
[[[[.,[[.,.],[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => 110011
[[[[.,[[.,[.,.]],.]],.],.],.] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => 110011
[[[[.,[[[.,.],.],.]],.],.],.] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => 110111
[[[[[.,.],[.,[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => 110011
[[[[[.,.],[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => 110111
[[[[[.,[.,.]],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => 110101
[[[[[[.,.],.],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => 110111
[[[[[.,[.,[.,.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => 111001
[[[[[.,[[.,.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => 111011
[[[[[[.,.],[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => 111011
[[[[[[.,[.,.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => 111101
[[[[[[[.,.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 0000000
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 1000000
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => 0100000
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => 0100000
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 1100000
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => 0010000
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [4,2,1,3,5,6,7,8] => 1010000
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => 0010000
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [4,3,1,2,5,6,7,8] => 0110000
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => 0010000
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => 0110000
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [[[[[.,[[.,.],[.,.]]],.],.],.],.] => [4,2,3,1,5,6,7,8] => 0110000
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => 1010000
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 1110000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => 0001000
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [5,2,1,3,4,6,7,8] => 1001000
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => 0101000
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => [5,2,3,1,4,6,7,8] => 0101000
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [5,3,2,1,4,6,7,8] => 1101000
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [[[[[[.,.],.],[[.,.],.]],.],.],.] => [4,5,1,2,3,6,7,8] => 0001000
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [4,5,2,1,3,6,7,8] => 1001000
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [5,4,1,2,3,6,7,8] => 0011000
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [5,4,2,1,3,6,7,8] => 1011000
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [[[[[.,.],[[[.,.],.],.]],.],.],.] => [3,4,5,1,2,6,7,8] => 0001000
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => [4,3,5,1,2,6,7,8] => 0011000
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [[[[[.,.],[[.,.],[.,.]]],.],.],.] => [5,3,4,1,2,6,7,8] => 0011000
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [5,4,3,1,2,6,7,8] => 0111000
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 0001000
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => 0101000
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [[[[.,[[[.,.],[.,.]],.]],.],.],.] => [4,2,3,5,1,6,7,8] => 0011000
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => 0011000
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => 0111000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [[[[.,[[[.,.],.],[.,.]]],.],.],.] => [5,2,3,4,1,6,7,8] => 0011000
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [5,3,2,4,1,6,7,8] => 0111000
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [[[[.,[[.,.],[[.,.],.]]],.],.],.] => [4,5,2,3,1,6,7,8] => 0101000
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [5,4,2,3,1,6,7,8] => 0111000
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => 1001000
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => 1011000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [5,3,4,2,1,6,7,8] => 1011000
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => 1101000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 1111000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => 0000100
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [6,2,1,3,4,5,7,8] => 1000100
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [6,3,1,2,4,5,7,8] => 0100100
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],.],[.,.]],.],.] => [6,2,3,1,4,5,7,8] => 0100100
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [6,3,2,1,4,5,7,8] => 1100100
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => 0010100
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [6,4,2,1,3,5,7,8] => 1010100
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [6,4,3,1,2,5,7,8] => 0110100
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [6,3,4,2,1,5,7,8] => 1010100
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8] => 1110100
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [5,6,2,1,3,4,7,8] => 1000100
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => 1100100
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [6,5,3,2,1,4,7,8] => 1101100
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => 0000100
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [4,5,6,2,1,3,7,8] => 1000100
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [5,4,6,2,1,3,7,8] => 1001100
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [6,4,5,2,1,3,7,8] => 1001100
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => 1010100
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8] => 0011100
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [6,5,4,2,1,3,7,8] => 1011100
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [3,4,5,6,1,2,7,8] => 0000100
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [[[[.,.],[[[.,[.,.]],.],.]],.],.] => [4,3,5,6,1,2,7,8] => 0010100
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => 0011100
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [6,4,3,5,1,2,7,8] => 0011100
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => 0010100
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => 0101100
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [6,4,5,3,1,2,7,8] => 0101100
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => 0110100
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [6,5,4,3,1,2,7,8] => 0111100
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 0000100
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => 0100100
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [[[.,[[[[.,.],[.,.]],.],.]],.],.] => [4,2,3,5,6,1,7,8] => 0010100
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => 0010100
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => 0110100
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],[.,.]],.]],.],.] => [5,2,3,4,6,1,7,8] => 0001100
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [5,3,2,4,6,1,7,8] => 0101100
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => 0001100
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => 0011100
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => 0101100
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => 0111100
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],.],[.,.]]],.],.] => [6,2,3,4,5,1,7,8] => 0001100
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [6,4,3,2,5,1,7,8] => 0111100
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [[[.,[[[.,.],.],[[.,.],.]]],.],.] => [5,6,2,3,4,1,7,8] => 0010100
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [5,6,3,2,4,1,7,8] => 0110100
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [6,5,2,3,4,1,7,8] => 0011100
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [5,4,6,2,3,1,7,8] => 0101100
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => 1000100
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => 1011100
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [5,6,3,4,2,1,7,8] => 1010100
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [6,5,3,4,2,1,7,8] => 1011100
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => 1100100
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => 1101100
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => 1110100
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 1111100
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => 0000010
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => 1000010
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => 0100010
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],.],.],[.,.]],.] => [7,2,3,1,4,5,6,8] => 0100010
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [7,3,2,1,4,5,6,8] => 1100010
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [7,4,1,2,3,5,6,8] => 0010010
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [7,3,4,1,2,5,6,8] => 0010010
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [7,4,3,1,2,5,6,8] => 0110010
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [[[[.,[[[.,.],.],.]],.],[.,.]],.] => [7,2,3,4,1,5,6,8] => 0010010
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8] => 1110010
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => 0001010
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8] => 0101010
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [7,5,2,3,1,4,6,8] => 0101010
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [7,5,3,2,1,4,6,8] => 1101010
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [7,4,5,1,2,3,6,8] => 0001010
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [7,4,5,2,1,3,6,8] => 1001010
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [7,5,3,4,1,2,6,8] => 0011010
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [7,5,4,3,1,2,6,8] => 0111010
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],.],.]],[.,.]],.] => [7,2,3,4,5,1,6,8] => 0001010
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [7,4,2,3,5,1,6,8] => 0011010
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [7,5,2,3,4,1,6,8] => 0011010
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [7,5,3,2,4,1,6,8] => 0111010
[.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [7,5,4,2,3,1,6,8] => 0111010
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [7,3,4,5,2,1,6,8] => 1001010
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [7,4,3,5,2,1,6,8] => 1011010
[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [7,4,5,3,2,1,6,8] => 1101010
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [7,5,4,3,2,1,6,8] => 1111010
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => 0000010
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [6,7,3,1,2,4,5,8] => 0100010
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [6,7,2,3,1,4,5,8] => 0100010
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [6,7,3,2,1,4,5,8] => 1100010
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [6,7,3,4,1,2,5,8] => 0010010
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],[[.,.],.]],.] => [6,7,2,3,4,1,5,8] => 0010010
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [6,7,3,2,4,1,5,8] => 0110010
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [6,7,3,4,2,1,5,8] => 1010010
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [6,7,4,3,2,1,5,8] => 1110010
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => 0000110
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [7,6,2,3,1,4,5,8] => 0100110
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [7,6,3,2,1,4,5,8] => 1100110
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [7,6,4,2,1,3,5,8] => 1010110
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => 0110110
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [7,6,2,3,4,1,5,8] => 0010110
[.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [7,6,3,2,4,1,5,8] => 0110110
[.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [7,6,4,2,3,1,5,8] => 0110110
[.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [7,6,3,4,2,1,5,8] => 1010110
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => 1110110
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => 0000010
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => 1000010
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => 0100010
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[[.,.],.],.]],.] => [5,6,7,2,3,1,4,8] => 0100010
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => 0000110
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [6,5,7,2,3,1,4,8] => 0100110
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => 0000110
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [7,5,6,2,1,3,4,8] => 1000110
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [7,5,6,3,1,2,4,8] => 0100110
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [7,5,6,2,3,1,4,8] => 0100110
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => 0001010
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [6,7,5,2,1,3,4,8] => 1001010
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [6,7,5,2,3,1,4,8] => 0101010
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => 0001110
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [7,6,5,2,1,3,4,8] => 1001110
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [7,6,5,2,3,1,4,8] => 0101110
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [7,6,5,3,2,1,4,8] => 1101110
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => 0000010
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [4,5,6,7,2,1,3,8] => 1000010
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => 0001010
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [5,4,6,7,2,1,3,8] => 1001010
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => 0000110
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => 0000110
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [7,4,5,6,2,1,3,8] => 1000110
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,1,2,3,8] => 0001110
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => 1001110
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,1,2,3,8] => 0001110
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,2,1,3,8] => 1001110
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => 0010010
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => 1010110
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,1,2,3,8] => 0010110
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => 0011110
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => 1011110
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [3,4,5,6,7,1,2,8] => 0000010
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => [4,3,5,6,7,1,2,8] => 0010010
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [6,3,4,5,7,1,2,8] => 0000110
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [6,4,3,5,7,1,2,8] => 0010110
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [5,6,3,4,7,1,2,8] => 0000110
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [6,4,5,3,7,1,2,8] => 0001110
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [6,5,4,3,7,1,2,8] => 0011110
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [7,5,3,4,6,1,2,8] => 0001110
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [6,7,3,4,5,1,2,8] => 0001010
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [6,5,7,3,4,1,2,8] => 0010110
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [7,5,6,3,4,1,2,8] => 0010110
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [7,6,5,3,4,1,2,8] => 0011110
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => [4,5,6,7,3,1,2,8] => 0100010
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [5,4,6,7,3,1,2,8] => 0101010
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [7,4,5,6,3,1,2,8] => 0100110
[.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,3,1,2,8] => 0101110
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => 0110110
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,3,1,2,8] => 0111010
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => 0111110
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 0000010
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => 0100010
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [[.,[[[[[.,.],[.,.]],.],.],.]],.] => [4,2,3,5,6,7,1,8] => 0010010
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => 0010010
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => 0110010
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],[.,.]],.],.]],.] => [5,2,3,4,6,7,1,8] => 0001010
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [[.,[[[[.,.],[[.,.],.]],.],.]],.] => [4,5,2,3,6,7,1,8] => 0001010
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [5,4,2,3,6,7,1,8] => 0011010
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => 0001010
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => 0111010
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],[.,.]],.]],.] => [6,2,3,4,5,7,1,8] => 0000110
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [6,3,2,4,5,7,1,8] => 0100110
[.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [6,5,3,2,4,7,1,8] => 0101110
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [5,4,6,2,3,7,1,8] => 0001110
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => 0000110
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => 0010110
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [5,3,4,6,2,7,1,8] => 0001110
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => 0001110
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => 0011110
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [6,3,4,5,2,7,1,8] => 0001110
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [5,6,3,4,2,7,1,8] => 0010110
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => 0101110
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => 0110110
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => 0111110
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],[.,.]]],.] => [7,2,3,4,5,6,1,8] => 0000110
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [7,5,3,2,4,6,1,8] => 0101110
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [7,4,5,2,3,6,1,8] => 0001110
[.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [7,5,4,2,3,6,1,8] => 0011110
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [7,4,3,5,2,6,1,8] => 0011110
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [7,5,3,4,2,6,1,8] => 0011110
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [7,4,5,3,2,6,1,8] => 0101110
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [7,5,4,3,2,6,1,8] => 0111110
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],[[.,.],.]]],.] => [6,7,2,3,4,5,1,8] => 0001010
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [6,7,3,2,4,5,1,8] => 0101010
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [6,7,4,2,3,5,1,8] => 0011010
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [6,7,3,4,2,5,1,8] => 0011010
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [6,7,4,3,2,5,1,8] => 0111010
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [7,6,2,3,4,5,1,8] => 0001110
[.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [7,6,3,2,4,5,1,8] => 0101110
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [7,6,4,2,3,5,1,8] => 0011110
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [7,6,4,3,2,5,1,8] => 0111110
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => 0010010
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => 0110010
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => 0010110
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => 0110110
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [7,5,6,2,3,4,1,8] => 0010110
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [6,7,5,2,3,4,1,8] => 0011010
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => 0011110
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [7,6,5,3,2,4,1,8] => 0111110
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [[.,[[.,.],[[[[.,.],.],.],.]]],.] => [4,5,6,7,2,3,1,8] => 0100010
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [5,4,6,7,2,3,1,8] => 0101010
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [5,6,4,7,2,3,1,8] => 0100110
[.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [6,5,4,7,2,3,1,8] => 0101110
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [7,4,5,6,2,3,1,8] => 0100110
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [7,5,4,6,2,3,1,8] => 0101110
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [6,7,4,5,2,3,1,8] => 0101010
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => 0101110
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [5,6,7,4,2,3,1,8] => 0110010
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,2,3,1,8] => 0110110
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => 0111010
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,2,3,1,8] => 0111110
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => 1000010
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => 1011010
[.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => 1001110
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => 1010110
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => 1011110
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [7,3,4,5,6,2,1,8] => 1000110
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [7,4,5,3,6,2,1,8] => 1001110
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => 1011110
[.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [6,7,4,3,5,2,1,8] => 1011010
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => 1001110
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => 1011110
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [5,6,7,3,4,2,1,8] => 1010010
[.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,[.,.]],.]]]],.] => [6,5,7,3,4,2,1,8] => 1010110
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => 1010110
[.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [6,7,5,3,4,2,1,8] => 1011010
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [7,6,5,3,4,2,1,8] => 1011110
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => 1100010
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => 1101010
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => 1100110
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 1101110
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => 1100110
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [7,5,4,6,3,2,1,8] => 1101110
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [6,7,4,5,3,2,1,8] => 1101010
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => 1101110
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 1110010
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 1110110
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [7,5,6,4,3,2,1,8] => 1110110
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 1111010
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 1111110
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => 0000001
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => 1000001
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => 0100001
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => 0100001
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => 1100001
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => 0010001
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [8,4,2,1,3,5,6,7] => 1010001
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [8,3,4,1,2,5,6,7] => 0010001
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => 0010001
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [8,4,2,3,1,5,6,7] => 0110001
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [8,3,4,2,1,5,6,7] => 1010001
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => 1110001
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => 0001001
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [8,5,2,1,3,4,6,7] => 1001001
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [8,5,3,1,2,4,6,7] => 0101001
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [8,5,3,2,1,4,6,7] => 1101001
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [8,4,5,1,2,3,6,7] => 0001001
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [8,5,4,1,2,3,6,7] => 0011001
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [8,5,4,2,1,3,6,7] => 1011001
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [8,3,4,5,1,2,6,7] => 0001001
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [8,5,3,4,1,2,6,7] => 0011001
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],.],.]],.],[.,.]] => [8,2,3,4,5,1,6,7] => 0001001
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [8,4,2,3,5,1,6,7] => 0011001
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [8,5,2,3,4,1,6,7] => 0011001
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [8,4,5,2,3,1,6,7] => 0101001
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [8,3,4,5,2,1,6,7] => 1001001
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [8,4,3,5,2,1,6,7] => 1011001
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [8,4,5,3,2,1,6,7] => 1101001
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [8,5,4,3,2,1,6,7] => 1111001
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => 0000101
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [8,6,3,2,1,4,5,7] => 1100101
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => 1010101
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [8,6,3,4,1,2,5,7] => 0010101
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [8,6,4,3,1,2,5,7] => 0110101
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [8,6,2,3,4,1,5,7] => 0010101
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [8,6,3,2,4,1,5,7] => 0110101
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [8,6,4,2,3,1,5,7] => 0110101
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [8,6,3,4,2,1,5,7] => 1010101
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => 1110101
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => 0000101
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => 1000101
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [8,5,6,3,1,2,4,7] => 0100101
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [8,5,6,2,3,1,4,7] => 0100101
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [8,5,6,3,2,1,4,7] => 1100101
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => 0001101
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [8,6,5,2,1,3,4,7] => 1001101
[[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => 0101101
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [8,6,5,3,2,1,4,7] => 1101101
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [8,4,5,6,1,2,3,7] => 0000101
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [8,4,5,6,2,1,3,7] => 1000101
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => 0001101
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,2,1,3,7] => 1001101
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,1,2,3,7] => 0010101
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,2,1,3,7] => 1010101
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => 0011101
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => 1011101
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => 0000101
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [8,4,3,5,6,1,2,7] => 0010101
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [8,5,3,4,6,1,2,7] => 0001101
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [8,4,5,3,6,1,2,7] => 0001101
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [8,5,4,3,6,1,2,7] => 0011101
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [8,6,3,4,5,1,2,7] => 0001101
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => 0010101
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [8,6,5,3,4,1,2,7] => 0011101
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,3,1,2,7] => 0101101
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => 0111101
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [8,2,3,4,5,6,1,7] => 0000101
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [8,3,2,4,5,6,1,7] => 0100101
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [8,3,4,2,5,6,1,7] => 0010101
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[.,.]],.]],[.,.]] => [8,5,2,3,4,6,1,7] => 0001101
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [8,5,3,2,4,6,1,7] => 0101101
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [8,4,5,2,3,6,1,7] => 0001101
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [8,5,4,2,3,6,1,7] => 0011101
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [8,4,3,5,2,6,1,7] => 0011101
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [8,5,4,3,2,6,1,7] => 0111101
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [8,6,3,2,4,5,1,7] => 0101101
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [8,6,4,2,3,5,1,7] => 0011101
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [8,6,4,3,2,5,1,7] => 0111101
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [8,5,6,2,3,4,1,7] => 0010101
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [8,6,5,2,3,4,1,7] => 0011101
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [8,6,5,3,2,4,1,7] => 0111101
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [8,4,5,6,2,3,1,7] => 0100101
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,2,3,1,7] => 0101101
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [8,5,6,4,2,3,1,7] => 0110101
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,2,3,1,7] => 0111101
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [8,3,4,5,6,2,1,7] => 1000101
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [8,4,3,5,6,2,1,7] => 1010101
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [8,4,5,3,6,2,1,7] => 1001101
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [8,6,4,3,5,2,1,7] => 1011101
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [8,5,6,3,4,2,1,7] => 1010101
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [8,6,5,3,4,2,1,7] => 1011101
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => 1100101
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [8,5,4,6,3,2,1,7] => 1101101
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [8,6,4,5,3,2,1,7] => 1101101
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [8,5,6,4,3,2,1,7] => 1110101
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => 1111101
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => 0000001
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => 1000001
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [7,8,3,1,2,4,5,6] => 0100001
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [7,8,2,3,1,4,5,6] => 0100001
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => 1100001
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [7,8,4,1,2,3,5,6] => 0010001
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => 1010001
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => 0010001
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [7,8,4,3,1,2,5,6] => 0110001
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],.],[[.,.],.]] => [7,8,2,3,4,1,5,6] => 0010001
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [7,8,3,2,4,1,5,6] => 0110001
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [7,8,4,2,3,1,5,6] => 0110001
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [7,8,3,4,2,1,5,6] => 1010001
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => 1110001
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => 0001001
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => 1001001
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [7,8,5,3,1,2,4,6] => 0101001
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [7,8,5,3,2,1,4,6] => 1101001
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => 0001001
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => 0011001
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => 1011001
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [7,8,3,4,5,1,2,6] => 0001001
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [7,8,5,3,4,1,2,6] => 0011001
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [7,8,5,4,3,1,2,6] => 0111001
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],.]],[[.,.],.]] => [7,8,2,3,4,5,1,6] => 0001001
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [7,8,3,4,2,5,1,6] => 0011001
[[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [7,8,4,3,2,5,1,6] => 0111001
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [7,8,5,2,3,4,1,6] => 0011001
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [7,8,4,5,2,3,1,6] => 0101001
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [7,8,3,4,5,2,1,6] => 1001001
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [7,8,4,5,3,2,1,6] => 1101001
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => 1111001
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => 0000011
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [8,7,2,1,3,4,5,6] => 1000011
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [8,7,2,3,1,4,5,6] => 0100011
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => 1100011
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => 0010011
[[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [8,7,4,2,1,3,5,6] => 1010011
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [8,7,3,4,1,2,5,6] => 0010011
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [8,7,2,3,4,1,5,6] => 0010011
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [8,7,3,2,4,1,5,6] => 0110011
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [8,7,3,4,2,1,5,6] => 1010011
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [8,7,4,3,2,1,5,6] => 1110011
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => 0001011
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => 1001011
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [8,7,5,3,1,2,4,6] => 0101011
[[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,.]],[.,[.,.]]] => [8,7,5,2,3,1,4,6] => 0101011
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [8,7,5,3,2,1,4,6] => 1101011
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => 0001011
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => 0011011
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [8,7,3,4,5,1,2,6] => 0001011
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [8,7,5,3,4,1,2,6] => 0011011
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => 0111011
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [8,7,2,3,4,5,1,6] => 0001011
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [8,7,3,4,2,5,1,6] => 0011011
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [8,7,4,3,2,5,1,6] => 0111011
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [8,7,5,3,2,4,1,6] => 0111011
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [8,7,4,5,2,3,1,6] => 0101011
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [8,7,3,4,5,2,1,6] => 1001011
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [8,7,4,3,5,2,1,6] => 1011011
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [8,7,5,3,4,2,1,6] => 1011011
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [8,7,4,5,3,2,1,6] => 1101011
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [8,7,5,4,3,2,1,6] => 1111011
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => 0000001
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => 1000001
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [6,7,8,3,1,2,4,5] => 0100001
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [6,7,8,2,3,1,4,5] => 0100001
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [6,7,8,3,2,1,4,5] => 1100001
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => 0010001
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => 1010001
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => 0010001
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => 0110001
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [6,7,8,2,3,4,1,5] => 0010001
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [6,7,8,3,2,4,1,5] => 0110001
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [6,7,8,4,2,3,1,5] => 0110001
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [6,7,8,3,4,2,1,5] => 1010001
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [6,7,8,4,3,2,1,5] => 1110001
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => 0000011
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [7,6,8,3,1,2,4,5] => 0100011
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [7,6,8,2,3,1,4,5] => 0100011
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [7,6,8,3,2,1,4,5] => 1100011
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [7,6,8,4,1,2,3,5] => 0010011
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [7,6,8,2,3,4,1,5] => 0010011
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [7,6,8,4,2,3,1,5] => 0110011
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [7,6,8,4,3,2,1,5] => 1110011
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => 0000011
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [8,6,7,2,1,3,4,5] => 1000011
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [8,6,7,3,1,2,4,5] => 0100011
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [8,6,7,2,3,1,4,5] => 0100011
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [8,6,7,3,2,1,4,5] => 1100011
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,2,1,3,5] => 1010011
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [8,6,7,3,4,1,2,5] => 0010011
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [8,6,7,2,3,4,1,5] => 0010011
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [8,6,7,3,2,4,1,5] => 0110011
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [8,6,7,4,2,3,1,5] => 0110011
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [8,6,7,4,3,2,1,5] => 1110011
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => 0000101
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [7,8,6,2,1,3,4,5] => 1000101
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [7,8,6,3,1,2,4,5] => 0100101
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [7,8,6,2,3,1,4,5] => 0100101
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [7,8,6,3,2,1,4,5] => 1100101
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => 0010101
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,2,1,3,5] => 1010101
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [7,8,6,3,4,1,2,5] => 0010101
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [7,8,6,3,4,2,1,5] => 1010101
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [7,8,6,4,3,2,1,5] => 1110101
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => 0000111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => 1000111
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [8,7,6,3,1,2,4,5] => 0100111
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [8,7,6,2,3,1,4,5] => 0100111
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => 1100111
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => 0010111
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => 1010111
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => 0010111
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => 0110111
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [8,7,6,2,3,4,1,5] => 0010111
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => 0110111
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,2,3,1,5] => 0110111
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => 1010111
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => 1110111
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => 0000001
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => 1000001
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => 0100001
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => [5,6,7,8,2,3,1,4] => 0100001
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => 1100001
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => 0000101
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => 1000101
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,1,2,4] => 0100101
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [6,5,7,8,2,3,1,4] => 0100101
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,2,1,4] => 1100101
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => 0000011
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [7,5,6,8,2,1,3,4] => 1000011
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => 0100011
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => 0100011
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,2,1,4] => 1100011
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => 0000011
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [6,7,5,8,2,1,3,4] => 1000011
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => 0100011
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [6,7,5,8,2,3,1,4] => 0100011
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,2,1,4] => 1100011
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => 0000111
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,1,3,4] => 1000111
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,1,2,4] => 0100111
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,3,1,4] => 0100111
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => 1100111
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => 0000011
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [8,5,6,7,2,1,3,4] => 1000011
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [8,5,6,7,2,3,1,4] => 0100011
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,2,1,4] => 1100011
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => 0000111
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,1,3,4] => 1000111
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,1,2,4] => 0100111
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,3,1,4] => 0100111
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,2,1,4] => 1100111
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => 0000101
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => 1000101
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => 0100101
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [7,8,5,6,2,3,1,4] => 0100101
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => 1100101
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => 0000111
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,1,3,4] => 1000111
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,1,2,4] => 0100111
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,3,1,4] => 0100111
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,2,1,4] => 1100111
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => 0001001
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => 1001001
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [6,7,8,5,2,3,1,4] => 0101001
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,2,1,4] => 1101001
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => 0001011
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,1,3,4] => 1001011
[[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,1,2,4] => 0101011
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,3,1,4] => 0101011
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,2,1,4] => 1101011
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => 0001011
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,1,2,4] => 0101011
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,3,1,4] => 0101011
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,2,1,4] => 1101011
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => 0001101
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => 1001101
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,1,2,4] => 0101101
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,3,1,4] => 0101101
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,2,1,4] => 1101101
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => 0001111
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => 1001111
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => 0101111
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,3,1,4] => 0101111
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => 1101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => 0000001
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => 1000001
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,1,2,3] => 0001001
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,2,1,3] => 1001001
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [6,4,5,7,8,1,2,3] => 0000101
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [5,6,4,7,8,1,2,3] => 0000101
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => 0001101
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,1,2,3] => 0000011
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,2,1,3] => 1000011
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,1,2,3] => 0001011
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => 0000011
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,1,2,3] => 0000111
[[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,2,1,3] => 1000111
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,1,2,3] => 0000011
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,2,1,3] => 1000011
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,1,2,3] => 0000111
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,2,1,3] => 1000111
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [7,5,6,4,8,1,2,3] => 0000111
[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [7,5,6,4,8,2,1,3] => 1000111
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,1,2,3] => 0001011
[[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,2,1,3] => 1001011
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,1,2,3] => 0001111
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,2,1,3] => 1001111
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => 0000011
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,2,1,3] => 1000011
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [8,5,4,6,7,1,2,3] => 0001011
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => 0000111
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,2,1,3] => 1000111
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [8,5,6,4,7,1,2,3] => 0000111
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,1,2,3] => 0001111
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,2,1,3] => 1001111
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => 0000101
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [7,8,5,4,6,1,2,3] => 0001101
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => 0000111
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,2,1,3] => 1000111
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [8,7,5,4,6,1,2,3] => 0001111
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [6,7,8,4,5,1,2,3] => 0001001
[[[.,[[.,.],.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [7,6,8,4,5,2,1,3] => 1001011
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => 0001011
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,2,1,3] => 1001011
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => 0001111
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,2,1,3] => 1001111
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => 0010001
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => 1010001
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => 0010101
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,2,1,3] => 1010101
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,1,2,3] => 0010011
[[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,2,1,3] => 1010011
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,1,2,3] => 0010011
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,2,1,3] => 1010011
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,1,2,3] => 0010111
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,2,1,3] => 1010111
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => 0010011
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,1,2,3] => 0010111
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,2,1,3] => 1010111
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,1,2,3] => 0010101
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,2,1,3] => 1010101
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [8,7,5,6,4,2,1,3] => 1010111
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => 0011001
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,2,1,3] => 1011001
[[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,1,2,3] => 0011011
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => 1011011
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [8,6,7,5,4,2,1,3] => 1011011
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => 0011101
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,2,1,3] => 1011101
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => 0011111
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => 1011111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => 0000001
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => 0010001
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [5,3,4,6,7,8,1,2] => 0001001
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => 0001001
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => 0011001
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => 0000101
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => 0010101
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => 0000101
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [6,5,3,4,7,8,1,2] => 0001101
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => [4,5,6,3,7,8,1,2] => 0000101
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => 0001101
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [5,6,4,3,7,8,1,2] => 0010101
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [6,5,4,3,7,8,1,2] => 0011101
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [7,3,4,5,6,8,1,2] => 0000011
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [7,5,3,4,6,8,1,2] => 0001011
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [7,4,5,3,6,8,1,2] => 0001011
[[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [7,5,4,3,6,8,1,2] => 0011011
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => 0000111
[[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [7,6,4,3,5,8,1,2] => 0010111
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [5,6,7,3,4,8,1,2] => 0000011
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => 0000111
[[.,[[[[.,.],.],.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [7,6,5,3,4,8,1,2] => 0001111
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => 0000011
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [5,4,6,7,3,8,1,2] => 0001011
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => 0000111
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [6,5,4,7,3,8,1,2] => 0001111
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,3,8,1,2] => 0001111
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => 0001011
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [5,6,7,4,3,8,1,2] => 0010011
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2] => 0010111
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [7,5,6,4,3,8,1,2] => 0010111
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => 0011111
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => 0000011
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => 0010011
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [8,5,3,4,6,7,1,2] => 0001011
[[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [8,5,4,3,6,7,1,2] => 0011011
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [8,5,4,6,3,7,1,2] => 0001111
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,3,7,1,2] => 0011111
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => 0000101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => 0010101
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => 0001101
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => 0001101
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => 0011101
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [8,7,3,4,5,6,1,2] => 0000111
[[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [8,7,4,3,5,6,1,2] => 0010111
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [8,7,4,5,3,6,1,2] => 0001111
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [6,7,8,3,4,5,1,2] => 0001001
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [6,7,8,4,3,5,1,2] => 0011001
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => 0001011
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => 0001101
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => 0001111
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => 0010001
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => 0010101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => 0010011
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => 0010011
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => 0010111
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,4,1,2] => 0010011
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,4,1,2] => 0010111
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => 0010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => 0010111
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => 0011001
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,4,1,2] => 0011011
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => 0011101
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => 0011111
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => 0100001
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [5,4,6,7,8,3,1,2] => 0101001
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [5,6,4,7,8,3,1,2] => 0100101
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,3,1,2] => 0101101
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,3,1,2] => 0100011
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => 0100111
[[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,3,1,2] => 0100111
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,3,1,2] => 0100111
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,3,1,2] => 0101111
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [8,5,4,6,7,3,1,2] => 0101011
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => 0100111
[[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,3,1,2] => 0100111
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => 0100101
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,3,1,2] => 0101111
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => 0101001
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => 0101011
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => 0101101
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => 0101111
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => 0110001
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => 0110101
[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => 0110011
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,3,1,2] => 0110011
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,3,1,2] => 0110111
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,3,1,2] => 0110111
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,3,1,2] => 0110101
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => 0110111
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => 0111001
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,3,1,2] => 0111011
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => 0111011
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => 0111101
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => 0111111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 0000001
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 0100001
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => 0010001
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 0010001
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 0110001
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => 0001001
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [5,3,2,4,6,7,8,1] => 0101001
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => [4,5,2,3,6,7,8,1] => 0001001
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [5,4,2,3,6,7,8,1] => 0011001
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 0001001
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => 0011001
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [5,3,4,2,6,7,8,1] => 0011001
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [4,5,3,2,6,7,8,1] => 0101001
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => 0111001
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [6,2,3,4,5,7,8,1] => 0000101
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [6,5,2,3,4,7,8,1] => 0001101
[[.,[.,[[[.,.],.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [6,5,3,2,4,7,8,1] => 0101101
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [.,[[[[.,.],[[[.,.],.],.]],.],.]] => [4,5,6,2,3,7,8,1] => 0000101
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [5,4,6,2,3,7,8,1] => 0001101
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [6,4,5,2,3,7,8,1] => 0001101
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [5,6,4,2,3,7,8,1] => 0010101
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [6,5,4,2,3,7,8,1] => 0011101
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => 0000101
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => 0010101
[[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => 0011101
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [6,3,4,5,2,7,8,1] => 0001101
[[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [6,5,3,4,2,7,8,1] => 0011101
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => 0100101
[[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => 0101101
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => 0111101
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [7,2,3,4,5,6,8,1] => 0000011
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [7,3,2,4,5,6,8,1] => 0100011
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [7,4,2,3,5,6,8,1] => 0010011
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [7,4,3,2,5,6,8,1] => 0110011
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [7,5,2,3,4,6,8,1] => 0001011
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [7,5,3,2,4,6,8,1] => 0101011
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [7,4,5,2,3,6,8,1] => 0001011
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [7,5,4,2,3,6,8,1] => 0011011
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [7,4,3,5,2,6,8,1] => 0011011
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [7,5,4,3,2,6,8,1] => 0111011
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => 0000011
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [6,7,3,2,4,5,8,1] => 0100011
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [6,7,4,3,2,5,8,1] => 0110011
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [7,6,2,3,4,5,8,1] => 0000111
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [7,6,3,2,4,5,8,1] => 0100111
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [7,6,4,2,3,5,8,1] => 0010111
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => [5,6,7,2,3,4,8,1] => 0000011
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [6,5,7,3,2,4,8,1] => 0100111
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [7,5,6,2,3,4,8,1] => 0000111
[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [6,7,5,3,2,4,8,1] => 0101011
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => 0001111
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => 0101111
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => 0000011
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [5,4,6,7,2,3,8,1] => 0001011
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [6,4,5,7,2,3,8,1] => 0000111
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [5,6,4,7,2,3,8,1] => 0000111
[[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [6,5,4,7,2,3,8,1] => 0001111
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [7,4,5,6,2,3,8,1] => 0000111
[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,2,3,8,1] => 0001111
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => 0001011
[[.,[[[[.,.],.],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,2,3,8,1] => 0001111
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [5,6,7,4,2,3,8,1] => 0010011
[[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,2,3,8,1] => 0010111
[[.,[[[[.,.],[.,.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [7,5,6,4,2,3,8,1] => 0010111
[[.,[[[[.,[.,.]],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [6,7,5,4,2,3,8,1] => 0011011
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => 0011111
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => 0000011
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [4,3,5,6,7,2,8,1] => 0010011
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => 0001011
[[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => 0011011
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [6,3,4,5,7,2,8,1] => 0000111
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [6,4,3,5,7,2,8,1] => 0010111
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [5,6,3,4,7,2,8,1] => 0000111
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [6,5,3,4,7,2,8,1] => 0001111
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => 0000111
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 0001111
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [6,4,5,3,7,2,8,1] => 0001111
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 0011111
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [7,3,4,5,6,2,8,1] => 0000111
[[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [7,5,3,4,6,2,8,1] => 0001111
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [7,4,5,3,6,2,8,1] => 0001111
[[.,[[[.,.],[[[.,.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [7,5,4,3,6,2,8,1] => 0011111
[[.,[[[[.,.],.],[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [7,6,3,4,5,2,8,1] => 0001111
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [7,6,4,3,5,2,8,1] => 0011111
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [5,6,7,3,4,2,8,1] => 0010011
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [6,5,7,3,4,2,8,1] => 0010111
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [7,5,6,3,4,2,8,1] => 0010111
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [7,6,5,3,4,2,8,1] => 0011111
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => 0100011
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [6,4,5,7,3,2,8,1] => 0100111
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1] => 0101111
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [7,4,5,6,3,2,8,1] => 0100111
[[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [6,7,4,5,3,2,8,1] => 0101011
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [7,6,4,5,3,2,8,1] => 0101111
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => 0110011
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 0110111
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [7,5,6,4,3,2,8,1] => 0110111
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => 0111011
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 0111111
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [8,2,3,4,5,6,7,1] => 0000011
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [8,3,2,4,5,6,7,1] => 0100011
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [8,4,2,3,5,6,7,1] => 0010011
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [8,3,4,2,5,6,7,1] => 0010011
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [8,4,3,2,5,6,7,1] => 0110011
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [8,5,2,3,4,6,7,1] => 0001011
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [8,4,5,2,3,6,7,1] => 0001011
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [8,5,4,2,3,6,7,1] => 0011011
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [8,3,4,5,2,6,7,1] => 0001011
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [8,5,3,4,2,6,7,1] => 0011011
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [8,4,5,3,2,6,7,1] => 0101011
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [8,5,4,3,2,6,7,1] => 0111011
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [8,6,4,2,3,5,7,1] => 0010111
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [8,6,4,3,2,5,7,1] => 0110111
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [8,6,5,3,2,4,7,1] => 0101111
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [8,6,4,5,2,3,7,1] => 0001111
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [8,5,6,4,2,3,7,1] => 0010111
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,2,3,7,1] => 0011111
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [8,3,4,5,6,2,7,1] => 0000111
[[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [8,4,3,5,6,2,7,1] => 0010111
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [8,4,5,3,6,2,7,1] => 0001111
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [8,5,4,3,6,2,7,1] => 0011111
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [8,6,3,4,5,2,7,1] => 0001111
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [8,6,4,3,5,2,7,1] => 0011111
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [8,5,6,3,4,2,7,1] => 0010111
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [8,6,5,3,4,2,7,1] => 0011111
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [8,5,4,6,3,2,7,1] => 0101111
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [8,6,4,5,3,2,7,1] => 0101111
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [8,5,6,4,3,2,7,1] => 0110111
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [8,6,5,4,3,2,7,1] => 0111111
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [7,8,2,3,4,5,6,1] => 0000101
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => 0100101
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [7,8,4,2,3,5,6,1] => 0010101
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [7,8,3,4,2,5,6,1] => 0010101
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [7,8,4,3,2,5,6,1] => 0110101
[[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [7,8,4,3,5,2,6,1] => 0011101
[[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [7,8,5,3,4,2,6,1] => 0011101
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [7,8,5,4,3,2,6,1] => 0111101
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [8,7,2,3,4,5,6,1] => 0000111
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [8,7,4,3,2,5,6,1] => 0110111
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [8,7,5,3,2,4,6,1] => 0101111
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,2,3,6,1] => 0011111
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [8,7,4,3,5,2,6,1] => 0011111
[[[[.,.],.],[[[.,.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [8,7,5,3,4,2,6,1] => 0011111
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [8,7,5,4,3,2,6,1] => 0111111
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [6,7,8,2,3,4,5,1] => 0001001
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [6,7,8,3,2,4,5,1] => 0101001
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [6,7,8,4,2,3,5,1] => 0011001
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [6,7,8,3,4,2,5,1] => 0011001
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [6,7,8,4,3,2,5,1] => 0111001
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [7,6,8,2,3,4,5,1] => 0001011
[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [7,6,8,4,2,3,5,1] => 0011011
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [7,6,8,3,4,2,5,1] => 0011011
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [7,6,8,4,3,2,5,1] => 0111011
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [8,6,7,2,3,4,5,1] => 0001011
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [8,6,7,3,2,4,5,1] => 0101011
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [8,6,7,4,2,3,5,1] => 0011011
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [8,6,7,3,4,2,5,1] => 0011011
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [8,6,7,4,3,2,5,1] => 0111011
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [7,8,6,2,3,4,5,1] => 0001101
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [7,8,6,3,2,4,5,1] => 0101101
[[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [7,8,6,3,4,2,5,1] => 0011101
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [7,8,6,4,3,2,5,1] => 0111101
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => 0001111
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [8,7,6,3,2,4,5,1] => 0101111
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,2,3,5,1] => 0011111
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [8,7,6,3,4,2,5,1] => 0011111
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [8,7,6,4,3,2,5,1] => 0111111
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => 0010001
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => 0110001
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [6,5,7,8,2,3,4,1] => 0010101
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [6,7,5,8,2,3,4,1] => 0010011
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,2,4,1] => 0110011
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,2,3,4,1] => 0010111
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,2,4,1] => 0110111
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => 0010011
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,2,4,1] => 0110011
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [8,6,5,7,2,3,4,1] => 0010111
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => 0110111
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [7,8,5,6,2,3,4,1] => 0010101
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,2,3,4,1] => 0010111
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,2,4,1] => 0110111
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => 0011001
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,2,4,1] => 0111001
[[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,2,3,4,1] => 0011011
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,2,4,1] => 0111011
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,2,3,4,1] => 0011011
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [8,6,7,5,3,2,4,1] => 0111011
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,2,4,1] => 0111101
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => 0011111
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,2,4,1] => 0111111
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => 0100001
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,2,3,1] => 0100011
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,2,3,1] => 0100111
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,2,3,1] => 0100111
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,2,3,1] => 0101111
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [8,4,5,6,7,2,3,1] => 0100011
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,2,3,1] => 0100111
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,2,3,1] => 0100111
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [8,6,5,4,7,2,3,1] => 0101111
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => 0100101
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,2,3,1] => 0100111
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,2,3,1] => 0101111
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,2,3,1] => 0101001
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [7,6,8,4,5,2,3,1] => 0101011
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => 0101011
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => 0101111
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => 0110001
[[[[.,[[.,.],[.,.]]],.],[.,.]],.] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,2,3,1] => 0110011
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,2,3,1] => 0110011
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,2,3,1] => 0110111
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,2,3,1] => 0110011
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,2,3,1] => 0110111
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => 0110111
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,2,3,1] => 0111011
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => 0111011
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => 0111101
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => 0111111
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => 1000001
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => 1010001
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [5,3,4,6,7,8,2,1] => 1001001
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => 1011001
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [6,3,4,5,7,8,2,1] => 1000101
[[[.,[.,[[[.,.],.],[.,.]]]],.],.] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [6,5,3,4,7,8,2,1] => 1001101
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => 1000101
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => 1011101
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [7,3,4,5,6,8,2,1] => 1000011
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [7,5,3,4,6,8,2,1] => 1001011
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [7,5,4,3,6,8,2,1] => 1011011
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => 1000111
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => 1010111
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => 1001111
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => 1000011
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => 1001011
[[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [6,4,5,7,3,8,2,1] => 1000111
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => 1001111
[[[.,[[[.,.],[.,[.,.]]],.]],.],.] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [7,4,5,6,3,8,2,1] => 1000111
[[[.,[[[.,.],[[.,.],.]],.]],.],.] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [7,5,4,6,3,8,2,1] => 1001111
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [6,7,4,5,3,8,2,1] => 1001011
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => 1010011
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [6,5,7,4,3,8,2,1] => 1010111
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [7,5,6,4,3,8,2,1] => 1010111
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => 1011011
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => 1011111
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [8,3,4,5,6,7,2,1] => 1000011
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [8,4,3,5,6,7,2,1] => 1010011
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [8,5,3,4,6,7,2,1] => 1001011
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [8,5,4,3,6,7,2,1] => 1011011
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [8,6,4,3,5,7,2,1] => 1010111
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [8,6,4,5,3,7,2,1] => 1001111
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [8,6,5,4,3,7,2,1] => 1011111
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [7,8,3,4,5,6,2,1] => 1000101
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [7,8,5,3,4,6,2,1] => 1001101
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [7,8,5,4,3,6,2,1] => 1011101
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [8,7,3,4,5,6,2,1] => 1000111
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [8,7,4,3,5,6,2,1] => 1010111
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [8,7,5,3,4,6,2,1] => 1001111
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [8,7,4,5,3,6,2,1] => 1001111
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => 1011111
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => 1001001
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [6,7,8,4,3,5,2,1] => 1011001
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [7,6,8,3,4,5,2,1] => 1001011
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [7,6,8,4,3,5,2,1] => 1011011
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [8,6,7,3,4,5,2,1] => 1001011
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [8,6,7,4,3,5,2,1] => 1011011
[[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [7,8,6,3,4,5,2,1] => 1001101
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [7,8,6,4,3,5,2,1] => 1011101
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1] => 1001111
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [8,7,6,4,3,5,2,1] => 1011111
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => 1010001
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [6,5,7,8,3,4,2,1] => 1010101
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [6,7,5,8,3,4,2,1] => 1010011
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [7,6,5,8,3,4,2,1] => 1010111
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [8,5,6,7,3,4,2,1] => 1010011
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [7,8,5,6,3,4,2,1] => 1010101
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => 1010111
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [7,6,8,5,3,4,2,1] => 1011011
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => 1011011
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => 1011101
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => 1011111
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => 1100001
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => 1101001
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [6,4,5,7,8,3,2,1] => 1100101
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => 1100101
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => 1101101
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => 1100011
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => 1101011
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [6,7,4,5,8,3,2,1] => 1100011
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => 1100111
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => 1100011
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 1100111
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [7,5,6,4,8,3,2,1] => 1100111
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => 1101011
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 1101111
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [8,4,5,6,7,3,2,1] => 1100011
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [8,5,4,6,7,3,2,1] => 1101011
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [8,6,4,5,7,3,2,1] => 1100111
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [8,5,6,4,7,3,2,1] => 1100111
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [8,6,5,4,7,3,2,1] => 1101111
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [8,7,4,5,6,3,2,1] => 1100111
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [8,7,5,4,6,3,2,1] => 1101111
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [6,7,8,4,5,3,2,1] => 1101001
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [7,6,8,4,5,3,2,1] => 1101011
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => 1101011
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => 1101101
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => 1101111
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => 1110001
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => 1110101
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => 1110011
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => 1110011
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => 1110111
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [8,5,6,7,4,3,2,1] => 1110011
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [8,6,5,7,4,3,2,1] => 1110111
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => 1110101
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [8,7,5,6,4,3,2,1] => 1110111
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => 1111001
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 1111011
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [8,6,7,5,4,3,2,1] => 1111011
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => 1111101
[[[[[[[[.,.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 00000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 10000000
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 11000000
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 11100000
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 11110000
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 11111000
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 11111100
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 11111110
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 000000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 100000000
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9] => 01000000
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 110000000
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 111000000
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 111100000
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 111110000
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 111111000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [8,6,5,4,3,2,1,7,9] => 11111010
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 111111100
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [9,7,6,5,4,3,2,1,8] => 11111101
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 111111110
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 111111111
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [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
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 00000010
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 00000001
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [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
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [9,2,3,4,5,6,7,8,1] => 00000011
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 000000010
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 000000001
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [10,8,6,4,2,1,3,5,7,9] => 101010101
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => 000011111
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [12,10,8,6,4,2,1,3,5,7,9,11] => 10101010101
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [7,6,8,5,9,4,10,3,11,2,12,1] => 00000111111
[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => [[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.] => [6,4,5,7,3,8,2,9,1,10] => 000011110
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]] => [8,9,6,7,4,5,2,3,10,1] => 000101011
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => 001010101
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => 00101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => 01111111
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => 011111111
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2] => 01111101
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 11111010
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2] => 0111111111
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [9,10,8,7,6,5,4,3,1,2] => 011111101
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => 01111011
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,3,1,2] => 01111011
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => [8,6,7,5,4,3,2,1,9] => 11110110
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 11110110
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 111111010
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [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
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => 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
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => 00000001
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 01000001
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => 10000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => 000000001
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000001
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 010000001
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 00100001
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => 00100001
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [9,2,3,1,4,5,6,7,8] => 01000001
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => 01000001
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => 100000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => 0000000001
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => 000011110
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => [9,10,6,7,4,5,2,3,1,8] => 010101001
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [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
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => 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
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => 10000001
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => 11000001
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => 11100001
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => 11110001
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => 11111001
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => 11111101
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => 100000001
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => 110000001
[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.] => [.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]] => [9,3,4,5,6,7,8,2,1] => 10000011
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => 111000001
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => 111100001
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => 111110001
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [9,6,7,8,5,4,3,2,1] => 11110011
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => 111111001
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [9,7,8,6,5,4,3,2,1] => 11111011
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => 111111101
[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [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
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9] => 01111110
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => 1111111101
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,2,3,1] => 01111101
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] => [8,9,7,6,5,4,2,1,3] => 10111101
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,2,3,1,9] => 01111110
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,2,1,3,9] => 10111110
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [9,8,7,6,5,4,3,1,2,10] => 011111110
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [8,9,6,7,5,4,3,2,1] => 11110101
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [7,8,9,5,6,4,3,2,1] => 11101001
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [6,7,8,9,4,5,3,2,1] => 11010001
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [5,6,7,8,9,3,4,2,1] => 10100001
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,2,3,1] => 01000001
[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]] => [[[[[[.,[[.,[.,.]],.]],.],.],.],.],.] => [3,2,4,1,5,6,7,8,9] => 01100000
[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]] => [[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.] => [4,3,2,5,1,6,7,8,9] => 01110000
[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]] => [[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.] => [5,4,3,2,6,1,7,8,9] => 01111000
[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]] => [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.] => [6,5,4,3,2,7,1,8,9] => 01111100
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => 01111110
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => 01111111
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [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
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [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
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => 011111111
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [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
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [9,7,6,5,4,3,1,2,8] => 01111101
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [3,4,5,6,7,8,1,2,9] => 00000010
[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => 11110010
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => [[.,[.,[[[[[[.,.],.],.],.],.],.]]],.] => [3,4,5,6,7,8,2,1,9] => 10000010
[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => 111110010
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [9,3,4,5,6,7,8,1,2] => 00000011
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,2,1,3] => 10000001
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => 000000011
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [8,9,2,3,4,5,6,7,1] => 00000101
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [10,2,3,4,5,6,7,8,9,1] => 000000011
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [8,9,6,5,4,3,2,1,7] => 11111001
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [9,7,6,5,4,3,2,8,1] => 01111111
[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [9,8,10,6,7,4,5,2,3,1] => 010101011
[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [10,8,9,6,7,4,5,2,3,1] => 010101011
[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],[[.,.],.]],.]] => [7,8,2,3,4,5,6,9,1] => 00000011
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [10,11,1,2,3,4,5,6,7,8,9] => 0000000001
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [8,9,2,1,3,4,5,6,7] => 10000001
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => 001111111
[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [10,8,9,6,7,4,5,2,1,3] => 100101011
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => 00011111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => 00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => 00000111
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => 000111111
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => 000011111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => 000001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => 000000111
[[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [9,8,10,7,6,5,4,3,1,2] => 011111011
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,3,1,2] => 01000001
[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [9,7,1,2,3,4,5,6,8] => 00000101
[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => [10,3,1,2,4,5,6,7,8,9] => 010000001
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [8,2,1,3,4,5,6,7,9] => 10000010
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => 01000010
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]] => [7,6,8,9,5,4,3,2,1] => 11110101
[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => 1111111011
[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]] => [8,7,9,10,6,5,4,3,2,1] => 111110101
[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => [11,9,10,8,7,6,5,4,3,2,1] => 1111111011
[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]] => [[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => 11010000
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => 00000011
[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]] => [[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => 00100000
[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]] => [[[.,[.,[[[[[.,.],.],.],.],.]]],.],.] => [3,4,5,6,7,2,1,8,9] => 10000100
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]] => [6,5,7,8,9,4,3,2,1] => 11101001
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => 01111011
[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [10,8,7,6,5,4,3,2,9,1] => 011111111
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => [4,5,6,7,8,9,10,2,3,1] => 010000001
[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [4,3,1,2,5,6,7,8,9] => 01100000
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [9,2,3,4,5,6,7,1,8] => 00000101
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => [8,2,3,4,5,6,7,9,1] => 00000011
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,3,9,1,2] => 00111111
[[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]],.] => [.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]] => [3,4,5,6,2,7,8,9,10,1] => 000010001
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => [.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,9,2,10,1] => 000000011
[[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]] => [10,9,8,7,6,5,4,3,2,11,1] => 0111111111
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => [9,8,2,3,4,5,6,7,1] => 00000111
[[[[[[.,[[.,.],.]],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,2,3,1] => 01111011
[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,1,2,3,9] => 00111110
[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => 11110100
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => [.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]] => [6,5,7,8,9,10,4,3,2,1] => 111010001
[[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.] => [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => 01111001
[[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]] => [9,8,2,3,4,5,6,1,7] => 00001011
[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,1,2,4] => 01011111
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]] => [[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [4,5,6,7,8,3,9,1,2] => 00000011
[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [[[[.,[[[[.,.],.],.],.]],.],.],[.,.]] => [9,2,3,4,5,1,6,7,8] => 00010001
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]] => [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => 10100000
[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [9,10,7,6,5,4,3,2,1,8] => 111111001
[[.,[.,[.,[.,[.,.]]]]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,4,3,2,1,5] => 111000001
[[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,1,2,3,5] => 00101111
[[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [9,8,7,5,1,2,3,4,6] => 00010111
[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [9,8,6,1,2,3,4,5,7] => 00001011
[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]] => [10,9,2,3,4,5,6,7,8,1] => 000000111
[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]] => [[[[.,[.,[[[[.,.],.],.],.]]],.],.],.] => [3,4,5,6,2,1,7,8,9] => 10001000
[[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [10,8,7,6,5,4,3,1,2,9] => 011111101
[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]] => [[[[[.,[.,[[[.,.],.],.]]],.],.],.],.] => [3,4,5,2,1,6,7,8,9] => 10010000
[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]] => [[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [3,4,5,1,2,6,7,8,9] => 00010000
[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]] => [6,2,3,4,5,7,8,9,10,1] => 000010001
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.
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.
searching the database
Sorry, this map was not found in the database.